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Chapter 10: Single-Subject Research

Single-Subject Research Designs

Learning Objectives

Describe the basic elements of a single-subject research design.
Design simple single-subject studies using reversal and multiple-baseline designs.
Explain how single-subject research designs address the issue of internal validity.
Interpret the results of simple single-subject studies based on the visual inspection of graphed data.

General Features of Single-Subject Designs

Before looking at any specific single-subject research designs, it will be helpful to consider some features that are common to most of them. Many of these features are illustrated in Figure 10.2, which shows the results of a generic single-subject study. First, the dependent variable (represented on the y -axis of the graph) is measured repeatedly over time (represented by the x -axis) at regular intervals. Second, the study is divided into distinct phases, and the participant is tested under one condition per phase. The conditions are often designated by capital letters: A, B, C, and so on. Thus Figure 10.2 represents a design in which the participant was tested first in one condition (A), then tested in another condition (B), and finally retested in the original condition (A). (This is called a reversal design and will be discussed in more detail shortly.)

A subject was tested under condition A, then condition B, then under condition A again.

Another important aspect of single-subject research is that the change from one condition to the next does not usually occur after a fixed amount of time or number of observations. Instead, it depends on the participant’s behaviour. Specifically, the researcher waits until the participant’s behaviour in one condition becomes fairly consistent from observation to observation before changing conditions. This is sometimes referred to as the steady state strategy (Sidman, 1960) [1] . The idea is that when the dependent variable has reached a steady state, then any change across conditions will be relatively easy to detect. Recall that we encountered this same principle when discussing experimental research more generally. The effect of an independent variable is easier to detect when the “noise” in the data is minimized.

Reversal Designs

The most basic single-subject research design is the reversal design , also called the ABA design . During the first phase, A, a baseline is established for the dependent variable. This is the level of responding before any treatment is introduced, and therefore the baseline phase is a kind of control condition. When steady state responding is reached, phase B begins as the researcher introduces the treatment. There may be a period of adjustment to the treatment during which the behaviour of interest becomes more variable and begins to increase or decrease. Again, the researcher waits until that dependent variable reaches a steady state so that it is clear whether and how much it has changed. Finally, the researcher removes the treatment and again waits until the dependent variable reaches a steady state. This basic reversal design can also be extended with the reintroduction of the treatment (ABAB), another return to baseline (ABABA), and so on.

The study by Hall and his colleagues was an ABAB reversal design. Figure 10.3 approximates the data for Robbie. The percentage of time he spent studying (the dependent variable) was low during the first baseline phase, increased during the first treatment phase until it leveled off, decreased during the second baseline phase, and again increased during the second treatment phase.

A graph showing the results of a study with an ABAB reversal design. Long description available.

Why is the reversal—the removal of the treatment—considered to be necessary in this type of design? Why use an ABA design, for example, rather than a simpler AB design? Notice that an AB design is essentially an interrupted time-series design applied to an individual participant. Recall that one problem with that design is that if the dependent variable changes after the treatment is introduced, it is not always clear that the treatment was responsible for the change. It is possible that something else changed at around the same time and that this extraneous variable is responsible for the change in the dependent variable. But if the dependent variable changes with the introduction of the treatment and then changes back with the removal of the treatment (assuming that the treatment does not create a permanent effect), it is much clearer that the treatment (and removal of the treatment) is the cause. In other words, the reversal greatly increases the internal validity of the study.

There are close relatives of the basic reversal design that allow for the evaluation of more than one treatment. In a multiple-treatment reversal design , a baseline phase is followed by separate phases in which different treatments are introduced. For example, a researcher might establish a baseline of studying behaviour for a disruptive student (A), then introduce a treatment involving positive attention from the teacher (B), and then switch to a treatment involving mild punishment for not studying (C). The participant could then be returned to a baseline phase before reintroducing each treatment—perhaps in the reverse order as a way of controlling for carryover effects. This particular multiple-treatment reversal design could also be referred to as an ABCACB design.

In an alternating treatments design , two or more treatments are alternated relatively quickly on a regular schedule. For example, positive attention for studying could be used one day and mild punishment for not studying the next, and so on. Or one treatment could be implemented in the morning and another in the afternoon. The alternating treatments design can be a quick and effective way of comparing treatments, but only when the treatments are fast acting.

Multiple-Baseline Designs

There are two potential problems with the reversal design—both of which have to do with the removal of the treatment. One is that if a treatment is working, it may be unethical to remove it. For example, if a treatment seemed to reduce the incidence of self-injury in a developmentally disabled child, it would be unethical to remove that treatment just to show that the incidence of self-injury increases. The second problem is that the dependent variable may not return to baseline when the treatment is removed. For example, when positive attention for studying is removed, a student might continue to study at an increased rate. This could mean that the positive attention had a lasting effect on the student’s studying, which of course would be good. But it could also mean that the positive attention was not really the cause of the increased studying in the first place. Perhaps something else happened at about the same time as the treatment—for example, the student’s parents might have started rewarding him for good grades.

One solution to these problems is to use a multiple-baseline design , which is represented in Figure 10.4. In one version of the design, a baseline is established for each of several participants, and the treatment is then introduced for each one. In essence, each participant is tested in an AB design. The key to this design is that the treatment is introduced at a different time for each participant. The idea is that if the dependent variable changes when the treatment is introduced for one participant, it might be a coincidence. But if the dependent variable changes when the treatment is introduced for multiple participants—especially when the treatment is introduced at different times for the different participants—then it is extremely unlikely to be a coincidence.

Three graphs depicting the results of a multiple-baseline study. Long description available.

As an example, consider a study by Scott Ross and Robert Horner (Ross & Horner, 2009) [2] . They were interested in how a school-wide bullying prevention program affected the bullying behaviour of particular problem students. At each of three different schools, the researchers studied two students who had regularly engaged in bullying. During the baseline phase, they observed the students for 10-minute periods each day during lunch recess and counted the number of aggressive behaviours they exhibited toward their peers. (The researchers used handheld computers to help record the data.) After 2 weeks, they implemented the program at one school. After 2 more weeks, they implemented it at the second school. And after 2 more weeks, they implemented it at the third school. They found that the number of aggressive behaviours exhibited by each student dropped shortly after the program was implemented at his or her school. Notice that if the researchers had only studied one school or if they had introduced the treatment at the same time at all three schools, then it would be unclear whether the reduction in aggressive behaviours was due to the bullying program or something else that happened at about the same time it was introduced (e.g., a holiday, a television program, a change in the weather). But with their multiple-baseline design, this kind of coincidence would have to happen three separate times—a very unlikely occurrence—to explain their results.

In another version of the multiple-baseline design, multiple baselines are established for the same participant but for different dependent variables, and the treatment is introduced at a different time for each dependent variable. Imagine, for example, a study on the effect of setting clear goals on the productivity of an office worker who has two primary tasks: making sales calls and writing reports. Baselines for both tasks could be established. For example, the researcher could measure the number of sales calls made and reports written by the worker each week for several weeks. Then the goal-setting treatment could be introduced for one of these tasks, and at a later time the same treatment could be introduced for the other task. The logic is the same as before. If productivity increases on one task after the treatment is introduced, it is unclear whether the treatment caused the increase. But if productivity increases on both tasks after the treatment is introduced—especially when the treatment is introduced at two different times—then it seems much clearer that the treatment was responsible.

In yet a third version of the multiple-baseline design, multiple baselines are established for the same participant but in different settings. For example, a baseline might be established for the amount of time a child spends reading during his free time at school and during his free time at home. Then a treatment such as positive attention might be introduced first at school and later at home. Again, if the dependent variable changes after the treatment is introduced in each setting, then this gives the researcher confidence that the treatment is, in fact, responsible for the change.

Data Analysis in Single-Subject Research

In addition to its focus on individual participants, single-subject research differs from group research in the way the data are typically analyzed. As we have seen throughout the book, group research involves combining data across participants. Group data are described using statistics such as means, standard deviations, Pearson’s r , and so on to detect general patterns. Finally, inferential statistics are used to help decide whether the result for the sample is likely to generalize to the population. Single-subject research, by contrast, relies heavily on a very different approach called visual inspection . This means plotting individual participants’ data as shown throughout this chapter, looking carefully at those data, and making judgments about whether and to what extent the independent variable had an effect on the dependent variable. Inferential statistics are typically not used.

In visually inspecting their data, single-subject researchers take several factors into account. One of them is changes in the level of the dependent variable from condition to condition. If the dependent variable is much higher or much lower in one condition than another, this suggests that the treatment had an effect. A second factor is trend , which refers to gradual increases or decreases in the dependent variable across observations. If the dependent variable begins increasing or decreasing with a change in conditions, then again this suggests that the treatment had an effect. It can be especially telling when a trend changes directions—for example, when an unwanted behaviour is increasing during baseline but then begins to decrease with the introduction of the treatment. A third factor is latency , which is the time it takes for the dependent variable to begin changing after a change in conditions. In general, if a change in the dependent variable begins shortly after a change in conditions, this suggests that the treatment was responsible.

In the top panel of Figure 10.5, there are fairly obvious changes in the level and trend of the dependent variable from condition to condition. Furthermore, the latencies of these changes are short; the change happens immediately. This pattern of results strongly suggests that the treatment was responsible for the changes in the dependent variable. In the bottom panel of Figure 10.5, however, the changes in level are fairly small. And although there appears to be an increasing trend in the treatment condition, it looks as though it might be a continuation of a trend that had already begun during baseline. This pattern of results strongly suggests that the treatment was not responsible for any changes in the dependent variable—at least not to the extent that single-subject researchers typically hope to see.

Results of a single-subject study showing level, trend and latency. Long description available.

The results of single-subject research can also be analyzed using statistical procedures—and this is becoming more common. There are many different approaches, and single-subject researchers continue to debate which are the most useful. One approach parallels what is typically done in group research. The mean and standard deviation of each participant’s responses under each condition are computed and compared, and inferential statistical tests such as the t test or analysis of variance are applied (Fisch, 2001) [3] . (Note that averaging across participants is less common.) Another approach is to compute the percentage of nonoverlapping data (PND) for each participant (Scruggs & Mastropieri, 2001) [4] . This is the percentage of responses in the treatment condition that are more extreme than the most extreme response in a relevant control condition. In the study of Hall and his colleagues, for example, all measures of Robbie’s study time in the first treatment condition were greater than the highest measure in the first baseline, for a PND of 100%. The greater the percentage of nonoverlapping data, the stronger the treatment effect. Still, formal statistical approaches to data analysis in single-subject research are generally considered a supplement to visual inspection, not a replacement for it.

Key Takeaways

Single-subject research designs typically involve measuring the dependent variable repeatedly over time and changing conditions (e.g., from baseline to treatment) when the dependent variable has reached a steady state. This approach allows the researcher to see whether changes in the independent variable are causing changes in the dependent variable.
In a reversal design, the participant is tested in a baseline condition, then tested in a treatment condition, and then returned to baseline. If the dependent variable changes with the introduction of the treatment and then changes back with the return to baseline, this provides strong evidence of a treatment effect.
In a multiple-baseline design, baselines are established for different participants, different dependent variables, or different settings—and the treatment is introduced at a different time on each baseline. If the introduction of the treatment is followed by a change in the dependent variable on each baseline, this provides strong evidence of a treatment effect.
Single-subject researchers typically analyze their data by graphing them and making judgments about whether the independent variable is affecting the dependent variable based on level, trend, and latency.
Does positive attention from a parent increase a child’s toothbrushing behaviour?
Does self-testing while studying improve a student’s performance on weekly spelling tests?
Does regular exercise help relieve depression?
Practice: Create a graph that displays the hypothetical results for the study you designed in Exercise 1. Write a paragraph in which you describe what the results show. Be sure to comment on level, trend, and latency.

Long Descriptions

Figure 10.3 long description: Line graph showing the results of a study with an ABAB reversal design. The dependent variable was low during first baseline phase; increased during the first treatment; decreased during the second baseline, but was still higher than during the first baseline; and was highest during the second treatment phase. [Return to Figure 10.3]

Figure 10.4 long description: Three line graphs showing the results of a generic multiple-baseline study, in which different baselines are established and treatment is introduced to participants at different times.

For Baseline 1, treatment is introduced one-quarter of the way into the study. The dependent variable ranges between 12 and 16 units during the baseline, but drops down to 10 units with treatment and mostly decreases until the end of the study, ranging between 4 and 10 units.

For Baseline 2, treatment is introduced halfway through the study. The dependent variable ranges between 10 and 15 units during the baseline, then has a sharp decrease to 7 units when treatment is introduced. However, the dependent variable increases to 12 units soon after the drop and ranges between 8 and 10 units until the end of the study.

For Baseline 3, treatment is introduced three-quarters of the way into the study. The dependent variable ranges between 12 and 16 units for the most part during the baseline, with one drop down to 10 units. When treatment is introduced, the dependent variable drops down to 10 units and then ranges between 8 and 9 units until the end of the study. [Return to Figure 10.4]

Figure 10.5 long description: Two graphs showing the results of a generic single-subject study with an ABA design. In the first graph, under condition A, level is high and the trend is increasing. Under condition B, level is much lower than under condition A and the trend is decreasing. Under condition A again, level is about as high as the first time and the trend is increasing. For each change, latency is short, suggesting that the treatment is the reason for the change.

In the second graph, under condition A, level is relatively low and the trend is increasing. Under condition B, level is a little higher than during condition A and the trend is increasing slightly. Under condition A again, level is a little lower than during condition B and the trend is decreasing slightly. It is difficult to determine the latency of these changes, since each change is rather minute, which suggests that the treatment is ineffective. [Return to Figure 10.5]

Sidman, M. (1960). Tactics of scientific research: Evaluating experimental data in psychology . Boston, MA: Authors Cooperative. ↵
Ross, S. W., & Horner, R. H. (2009). Bully prevention in positive behaviour support. Journal of Applied Behaviour Analysis, 42 , 747–759. ↵
Fisch, G. S. (2001). Evaluating data from behavioural analysis: Visual inspection or statistical models. Behavioural Processes, 54 , 137–154. ↵
Scruggs, T. E., & Mastropieri, M. A. (2001). How to summarize single-participant research: Ideas and applications. Exceptionality, 9 , 227–244. ↵

The researcher waits until the participant’s behaviour in one condition becomes fairly consistent from observation to observation before changing conditions. This way, any change across conditions will be easy to detect.

A study method in which the researcher gathers data on a baseline state, introduces the treatment and continues observation until a steady state is reached, and finally removes the treatment and observes the participant until they return to a steady state.

The level of responding before any treatment is introduced and therefore acts as a kind of control condition.

A baseline phase is followed by separate phases in which different treatments are introduced.

Two or more treatments are alternated relatively quickly on a regular schedule.

A baseline is established for several participants and the treatment is then introduced to each participant at a different time.

The plotting of individual participants’ data, examining the data, and making judgements about whether and to what extent the independent variable had an effect on the dependent variable.

Whether the data is higher or lower based on a visual inspection of the data; a change in the level implies the treatment introduced had an effect.

The gradual increases or decreases in the dependent variable across observations.

The time it takes for the dependent variable to begin changing after a change in conditions.

The percentage of responses in the treatment condition that are more extreme than the most extreme response in a relevant control condition.

Research Methods in Psychology - 2nd Canadian Edition Copyright © 2015 by Paul C. Price, Rajiv Jhangiani, & I-Chant A. Chiang is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Using Single Subject Experimental Designs

single subject experimental designs applied behavior analysis

What are the Characteristics of Single Subject Experimental Designs?

Single-subject designs are the staple of applied behavior analysis research. Those preparing for the BCBA exam or the BCaBA exam must know single subject terms and definitions. When choosing a single-subject experimental design, ABA researchers are looking for certain characteristics that fit their study. First, individuals serve as their own control in single subject research. In other words, the results of each condition are compared to the participant’s own data. If 3 people participate in the study, each will act as their own control. Second, researchers are trying to predict, verify, and replicate the outcomes of their intervention. Prediction, replication, and verification are essential to single-subject design research and help prove experimental control. Prediction: the hypothesis related to what the outcome will be when measured Verification : showing that baseline data would remain consistent if the independent variable was not manipulated Replication: repeating the independent variable manipulation to show similar results across multiple phases Some experimental designs like withdrawal designs are better suited for demonstrating experimental control than others, but each design has its place. We will now look at the different types of single subject experimental designs and the core features of each.

Reversal Design/Withdrawal Design/A-B-A

Arguably the simplest single subject design, the reversal/withdrawal design is excellent at identifying experimental control. First, baseline data is recorded. Then, an intervention is introduced and the effects are recorded. Finally, the intervention is withdrawn and the experiment returns to baseline. The researcher or researchers then visually analyze the changes from baseline to intervention and determine whether or not experimental control was established. Prediction, verification, and replication are also clearly demonstrated in the withdrawal design. Below is a simple example of this A-B-A design.

Advantages: Demonstrate experimental control Disadvantages: Ethical concerns, some behaviors cannot be reversed, not great for high-risk or dangerous behaviors

Multiple Baseline Design/Multiple Probe Design

Multiple baseline designs are used when researchers need to measure across participants, behaviors, or settings. For instance, if you wanted to examine the effects of an independent variable in a classroom, in a home setting, and in a clinical setting, you might use a multiple baseline across settings design. Multiple baseline designs typically involve 3-5 subjects, settings, or behaviors. An intervention is introduced into each segment one at a time while baseline continues in the other conditions. Below is a rough example of what a multiple baseline design typically looks like:

multiple baseline design single subject design

Multiple probe designs are identical to multiple baseline designs except baseline is not continuous. Instead, data is taken only sporadically during the baseline condition. You may use this if time and resources are limited, or you do not anticipate baseline changing. Advantages: No withdrawal needed, examine multiple dependent variables at a time Disadvantages : Sometimes difficult to demonstrate experimental control

Alternating Treatment Design

The alternating treatment design involves rapid/semirandom alternating conditions taking place all in the same phase. There are equal opportunities for conditions to be present during measurement. Conditions are alternated rapidly and randomly to test multiple conditions at once.

Advantages: No withdrawal, multiple independent variables can be tried rapidly Disadvantages : The multiple treatment effect can impact measurement

Changing Criterion Design

The changing criterion design is great for reducing or increasing behaviors. The behavior should already be in the subject’s repertoire when using changing criterion designs. Reducing smoking or increasing exercise are two common examples of the changing criterion design. With the changing criterion design, treatment is delivered in a series of ascending or descending phases. The criterion that the subject is expected to meet is changed for each phase. You can reverse a phase of a changing criterion design in an attempt to demonstrate experimental control.

Summary of Single Subject Experimental Designs

Single subject designs are popular in both social sciences and in applied behavior analysis. As always, your research question and purpose should dictate your design choice. You will need to know experimental design and the details behind single subject design for the BCBA exam and the BCaBA exam. For BCBA exam study materials check out our BCBA exam prep. For a full breakdown of the BCBA fifth edition task list, check out our YouTube :

10.2 Single-Subject Research Designs

Learning objectives.

Describe the basic elements of a single-subject research design.
Design simple single-subject studies using reversal and multiple-baseline designs.
Explain how single-subject research designs address the issue of internal validity.
Interpret the results of simple single-subject studies based on the visual inspection of graphed data.

General Features of Single-Subject Designs

Before looking at any specific single-subject research designs, it will be helpful to consider some features that are common to most of them. Many of these features are illustrated in Figure 10.1, which shows the results of a generic single-subject study. First, the dependent variable (represented on the y -axis of the graph) is measured repeatedly over time (represented by the x -axis) at regular intervals. Second, the study is divided into distinct phases, and the participant is tested under one condition per phase. The conditions are often designated by capital letters: A, B, C, and so on. Thus Figure 10.1 represents a design in which the participant was tested first in one condition (A), then tested in another condition (B), and finally retested in the original condition (A). (This is called a reversal design and will be discussed in more detail shortly.)

Figure 10.2 Results of a Generic Single-Subject Study Illustrating Several Principles of Single-Subject Research

Figure 10.1 Results of a Generic Single-Subject Study Illustrating Several Principles of Single-Subject Research

Another important aspect of single-subject research is that the change from one condition to the next does not usually occur after a fixed amount of time or number of observations. Instead, it depends on the participant’s behavior. Specifically, the researcher waits until the participant’s behavior in one condition becomes fairly consistent from observation to observation before changing conditions. This is sometimes referred to as the steady state strategy (Sidman, 1960) [1] . The idea is that when the dependent variable has reached a steady state, then any change across conditions will be relatively easy to detect. Recall that we encountered this same principle when discussing experimental research more generally. The effect of an independent variable is easier to detect when the “noise” in the data is minimized.

Reversal Designs

The most basic single-subject research design is the reversal design , also called the ABA design . During the first phase, A, a baseline is established for the dependent variable. This is the level of responding before any treatment is introduced, and therefore the baseline phase is a kind of control condition. When steady state responding is reached, phase B begins as the researcher introduces the treatment. There may be a period of adjustment to the treatment during which the behavior of interest becomes more variable and begins to increase or decrease. Again, the researcher waits until that dependent variable reaches a steady state so that it is clear whether and how much it has changed. Finally, the researcher removes the treatment and again waits until the dependent variable reaches a steady state. This basic reversal design can also be extended with the reintroduction of the treatment (ABAB), another return to baseline (ABABA), and so on.

The study by Hall and his colleagues employed an ABAB reversal design. Figure 10.2 approximates the data for Robbie. The percentage of time he spent studying (the dependent variable) was low during the first baseline phase, increased during the first treatment phase until it leveled off, decreased during the second baseline phase, and again increased during the second treatment phase.

Figure 10.3 An Approximation of the Results for Hall and Colleagues’ Participant Robbie in Their ABAB Reversal Design

Figure 10.2 An Approximation of the Results for Hall and Colleagues’ Participant Robbie in Their ABAB Reversal Design

There are close relatives of the basic reversal design that allow for the evaluation of more than one treatment. In a multiple-treatment reversal design , a baseline phase is followed by separate phases in which different treatments are introduced. For example, a researcher might establish a baseline of studying behavior for a disruptive student (A), then introduce a treatment involving positive attention from the teacher (B), and then switch to a treatment involving mild punishment for not studying (C). The participant could then be returned to a baseline phase before reintroducing each treatment—perhaps in the reverse order as a way of controlling for carryover effects. This particular multiple-treatment reversal design could also be referred to as an ABCACB design.

Multiple-Baseline Designs

There are two potential problems with the reversal design—both of which have to do with the removal of the treatment. One is that if a treatment is working, it may be unethical to remove it. For example, if a treatment seemed to reduce the incidence of self-injury in a child with an intellectual delay, it would be unethical to remove that treatment just to show that the incidence of self-injury increases. The second problem is that the dependent variable may not return to baseline when the treatment is removed. For example, when positive attention for studying is removed, a student might continue to study at an increased rate. This could mean that the positive attention had a lasting effect on the student’s studying, which of course would be good. But it could also mean that the positive attention was not really the cause of the increased studying in the first place. Perhaps something else happened at about the same time as the treatment—for example, the student’s parents might have started rewarding him for good grades. One solution to these problems is to use a multiple-baseline design , which is represented in Figure 10.3. There are three different types of multiple-baseline designs which we will now consider.

Multiple-Baseline Design Across Participants

In one version of the design, a baseline is established for each of several participants, and the treatment is then introduced for each one. In essence, each participant is tested in an AB design. The key to this design is that the treatment is introduced at a different time for each participant. The idea is that if the dependent variable changes when the treatment is introduced for one participant, it might be a coincidence. But if the dependent variable changes when the treatment is introduced for multiple participants—especially when the treatment is introduced at different times for the different participants—then it is unlikely to be a coincidence.

Figure 10.4 Results of a Generic Multiple-Baseline Study. The multiple baselines can be for different participants, dependent variables, or settings. The treatment is introduced at a different time on each baseline.

Figure 10.3 Results of a Generic Multiple-Baseline Study. The multiple baselines can be for different participants, dependent variables, or settings. The treatment is introduced at a different time on each baseline.

As an example, consider a study by Scott Ross and Robert Horner (Ross & Horner, 2009) [2] . They were interested in how a school-wide bullying prevention program affected the bullying behavior of particular problem students. At each of three different schools, the researchers studied two students who had regularly engaged in bullying. During the baseline phase, they observed the students for 10-minute periods each day during lunch recess and counted the number of aggressive behaviors they exhibited toward their peers. After 2 weeks, they implemented the program at one school. After 2 more weeks, they implemented it at the second school. And after 2 more weeks, they implemented it at the third school. They found that the number of aggressive behaviors exhibited by each student dropped shortly after the program was implemented at his or her school. Notice that if the researchers had only studied one school or if they had introduced the treatment at the same time at all three schools, then it would be unclear whether the reduction in aggressive behaviors was due to the bullying program or something else that happened at about the same time it was introduced (e.g., a holiday, a television program, a change in the weather). But with their multiple-baseline design, this kind of coincidence would have to happen three separate times—a very unlikely occurrence—to explain their results.

Multiple-Baseline Design Across Behaviors

Multiple-Baseline Design Across Settings

Data Analysis in Single-Subject Research

In addition to its focus on individual participants, single-subject research differs from group research in the way the data are typically analyzed. As we have seen throughout the book, group research involves combining data across participants. Group data are described using statistics such as means, standard deviations, correlation coefficients, and so on to detect general patterns. Finally, inferential statistics are used to help decide whether the result for the sample is likely to generalize to the population. Single-subject research, by contrast, relies heavily on a very different approach called visual inspection . This means plotting individual participants’ data as shown throughout this chapter, looking carefully at those data, and making judgments about whether and to what extent the independent variable had an effect on the dependent variable. Inferential statistics are typically not used.

In visually inspecting their data, single-subject researchers take several factors into account. One of them is changes in the level of the dependent variable from condition to condition. If the dependent variable is much higher or much lower in one condition than another, this suggests that the treatment had an effect. A second factor is trend , which refers to gradual increases or decreases in the dependent variable across observations. If the dependent variable begins increasing or decreasing with a change in conditions, then again this suggests that the treatment had an effect. It can be especially telling when a trend changes directions—for example, when an unwanted behavior is increasing during baseline but then begins to decrease with the introduction of the treatment. A third factor is latency , which is the time it takes for the dependent variable to begin changing after a change in conditions. In general, if a change in the dependent variable begins shortly after a change in conditions, this suggests that the treatment was responsible.

In the top panel of Figure 10.4, there are fairly obvious changes in the level and trend of the dependent variable from condition to condition. Furthermore, the latencies of these changes are short; the change happens immediately. This pattern of results strongly suggests that the treatment was responsible for the changes in the dependent variable. In the bottom panel of Figure 10.4, however, the changes in level are fairly small. And although there appears to be an increasing trend in the treatment condition, it looks as though it might be a continuation of a trend that had already begun during baseline. This pattern of results strongly suggests that the treatment was not responsible for any changes in the dependent variable—at least not to the extent that single-subject researchers typically hope to see.

Figure 10.5 Results of a Generic Single-Subject Study Illustrating Level, Trend, and Latency. Visual inspection of the data suggests an effective treatment in the top panel but an ineffective treatment in the bottom panel.

Figure 10.4 Results of a Generic Single-Subject Study Illustrating Level, Trend, and Latency. Visual inspection of the data suggests an effective treatment in the top panel but an ineffective treatment in the bottom panel.

The results of single-subject research can also be analyzed using statistical procedures—and this is becoming more common. There are many different approaches, and single-subject researchers continue to debate which are the most useful. One approach parallels what is typically done in group research. The mean and standard deviation of each participant’s responses under each condition are computed and compared, and inferential statistical tests such as the t test or analysis of variance are applied (Fisch, 2001) [3] . (Note that averaging across participants is less common.) Another approach is to compute the percentage of non-overlapping data (PND) for each participant (Scruggs & Mastropieri, 2001) [4] . This is the percentage of responses in the treatment condition that are more extreme than the most extreme response in a relevant control condition. In the study of Hall and his colleagues, for example, all measures of Robbie’s study time in the first treatment condition were greater than the highest measure in the first baseline, for a PND of 100%. The greater the percentage of non-overlapping data, the stronger the treatment effect. Still, formal statistical approaches to data analysis in single-subject research are generally considered a supplement to visual inspection, not a replacement for it.

Key Takeaways

Single-subject research designs typically involve measuring the dependent variable repeatedly over time and changing conditions (e.g., from baseline to treatment) when the dependent variable has reached a steady state. This approach allows the researcher to see whether changes in the independent variable are causing changes in the dependent variable.
In a reversal design, the participant is tested in a baseline condition, then tested in a treatment condition, and then returned to baseline. If the dependent variable changes with the introduction of the treatment and then changes back with the return to baseline, this provides strong evidence of a treatment effect.
In a multiple-baseline design, baselines are established for different participants, different dependent variables, or different settings—and the treatment is introduced at a different time on each baseline. If the introduction of the treatment is followed by a change in the dependent variable on each baseline, this provides strong evidence of a treatment effect.
Single-subject researchers typically analyze their data by graphing them and making judgments about whether the independent variable is affecting the dependent variable based on level, trend, and latency.
Does positive attention from a parent increase a child’s tooth-brushing behavior?
Does self-testing while studying improve a student’s performance on weekly spelling tests?
Does regular exercise help relieve depression?
Practice: Create a graph that displays the hypothetical results for the study you designed in Exercise 1. Write a paragraph in which you describe what the results show. Be sure to comment on level, trend, and latency.
Sidman, M. (1960). Tactics of scientific research: Evaluating experimental data in psychology . Boston, MA: Authors Cooperative. ↵
Ross, S. W., & Horner, R. H. (2009). Bully prevention in positive behavior support. Journal of Applied Behavior Analysis, 42 , 747–759. ↵
Fisch, G. S. (2001). Evaluating data from behavioral analysis: Visual inspection or statistical models. Behavioral Processes, 54 , 137–154. ↵
Scruggs, T. E., & Mastropieri, M. A. (2001). How to summarize single-participant research: Ideas and applications. Exceptionality, 9 , 227–244. ↵

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Single-Subject Research

45 Single-Subject Research Designs

Learning objectives.

Describe the basic elements of a single-subject research design.
Design simple single-subject studies using reversal and multiple-baseline designs.
Explain how single-subject research designs address the issue of internal validity.
Interpret the results of simple single-subject studies based on the visual inspection of graphed data.

General Features of Single-Subject Designs

Before looking at any specific single-subject research designs, it will be helpful to consider some features that are common to most of them. Many of these features are illustrated in Figure 10.1, which shows the results of a generic single-subject study. First, the dependent variable (represented on the y -axis of the graph) is measured repeatedly over time (represented by the x -axis) at regular intervals. Second, the study is divided into distinct phases, and the participant is tested under one condition per phase. The conditions are often designated by capital letters: A, B, C, and so on. Thus Figure 10.1 represents a design in which the participant was tested first in one condition (A), then tested in another condition (B), and finally retested in the original condition (A). (This is called a reversal design and will be discussed in more detail shortly.)

Another important aspect of single-subject research is that the change from one condition to the next does not usually occur after a fixed amount of time or number of observations. Instead, it depends on the participant’s behavior. Specifically, the researcher waits until the participant’s behavior in one condition becomes fairly consistent from observation to observation before changing conditions. This is sometimes referred to as the steady state strategy (Sidman, 1960) [1] . The idea is that when the dependent variable has reached a steady state, then any change across conditions will be relatively easy to detect. Recall that we encountered this same principle when discussing experimental research more generally. The effect of an independent variable is easier to detect when the “noise” in the data is minimized.

Reversal Designs

The most basic single-subject research design is the reversal design , also called the ABA design . During the first phase, A, a baseline is established for the dependent variable. This is the level of responding before any treatment is introduced, and therefore the baseline phase is a kind of control condition. When steady state responding is reached, phase B begins as the researcher introduces the treatment. There may be a period of adjustment to the treatment during which the behavior of interest becomes more variable and begins to increase or decrease. Again, the researcher waits until that dependent variable reaches a steady state so that it is clear whether and how much it has changed. Finally, the researcher removes the treatment and again waits until the dependent variable reaches a steady state. This basic reversal design can also be extended with the reintroduction of the treatment (ABAB), another return to baseline (ABABA), and so on.

ABAB Reversal Design. Image description available.

There are close relatives of the basic reversal design that allow for the evaluation of more than one treatment. In a multiple-treatment reversal design , a baseline phase is followed by separate phases in which different treatments are introduced. For example, a researcher might establish a baseline of studying behavior for a disruptive student (A), then introduce a treatment involving positive attention from the teacher (B), and then switch to a treatment involving mild punishment for not studying (C). The participant could then be returned to a baseline phase before reintroducing each treatment—perhaps in the reverse order as a way of controlling for carryover effects. This particular multiple-treatment reversal design could also be referred to as an ABCACB design.

Multiple-Baseline Designs

There are two potential problems with the reversal design—both of which have to do with the removal of the treatment. One is that if a treatment is working, it may be unethical to remove it. For example, if a treatment seemed to reduce the incidence of self-injury in a child with an intellectual delay, it would be unethical to remove that treatment just to show that the incidence of self-injury increases. The second problem is that the dependent variable may not return to baseline when the treatment is removed. For example, when positive attention for studying is removed, a student might continue to study at an increased rate. This could mean that the positive attention had a lasting effect on the student’s studying, which of course would be good. But it could also mean that the positive attention was not really the cause of the increased studying in the first place. Perhaps something else happened at about the same time as the treatment—for example, the student’s parents might have started rewarding him for good grades. One solution to these problems is to use a multiple-baseline design , which is represented in Figure 10.3. There are three different types of multiple-baseline designs which we will now consider.

Multiple-Baseline Design Across Participants

Results of a Generic Multiple-Baseline Study. Image description available.

As an example, consider a study by Scott Ross and Robert Horner (Ross & Horner, 2009) [2] . They were interested in how a school-wide bullying prevention program affected the bullying behavior of particular problem students. At each of three different schools, the researchers studied two students who had regularly engaged in bullying. During the baseline phase, they observed the students for 10-minute periods each day during lunch recess and counted the number of aggressive behaviors they exhibited toward their peers. After 2 weeks, they implemented the program at one school. After 2 more weeks, they implemented it at the second school. And after 2 more weeks, they implemented it at the third school. They found that the number of aggressive behaviors exhibited by each student dropped shortly after the program was implemented at the student’s school. Notice that if the researchers had only studied one school or if they had introduced the treatment at the same time at all three schools, then it would be unclear whether the reduction in aggressive behaviors was due to the bullying program or something else that happened at about the same time it was introduced (e.g., a holiday, a television program, a change in the weather). But with their multiple-baseline design, this kind of coincidence would have to happen three separate times—a very unlikely occurrence—to explain their results.

Multiple-Baseline Design Across Behaviors

Multiple-Baseline Design Across Settings

Data Analysis in Single-Subject Research

In addition to its focus on individual participants, single-subject research differs from group research in the way the data are typically analyzed. As we have seen throughout the book, group research involves combining data across participants. Group data are described using statistics such as means, standard deviations, correlation coefficients, and so on to detect general patterns. Finally, inferential statistics are used to help decide whether the result for the sample is likely to generalize to the population. Single-subject research, by contrast, relies heavily on a very different approach called visual inspection . This means plotting individual participants’ data as shown throughout this chapter, looking carefully at those data, and making judgments about whether and to what extent the independent variable had an effect on the dependent variable. Inferential statistics are typically not used.

In visually inspecting their data, single-subject researchers take several factors into account. One of them is changes in the level of the dependent variable from condition to condition. If the dependent variable is much higher or much lower in one condition than another, this suggests that the treatment had an effect. A second factor is trend , which refers to gradual increases or decreases in the dependent variable across observations. If the dependent variable begins increasing or decreasing with a change in conditions, then again this suggests that the treatment had an effect. It can be especially telling when a trend changes directions—for example, when an unwanted behavior is increasing during baseline but then begins to decrease with the introduction of the treatment. A third factor is latency , which is the time it takes for the dependent variable to begin changing after a change in conditions. In general, if a change in the dependent variable begins shortly after a change in conditions, this suggests that the treatment was responsible.

The results of single-subject research can also be analyzed using statistical procedures—and this is becoming more common. There are many different approaches, and single-subject researchers continue to debate which are the most useful. One approach parallels what is typically done in group research. The mean and standard deviation of each participant’s responses under each condition are computed and compared, and inferential statistical tests such as the t test or analysis of variance are applied (Fisch, 2001) [3] . (Note that averaging across participants is less common.) Another approach is to compute the percentage of non-overlapping data (PND) for each participant (Scruggs & Mastropieri, 2001) [4] . This is the percentage of responses in the treatment condition that are more extreme than the most extreme response in a relevant control condition. In the study of Hall and his colleagues, for example, all measures of Robbie’s study time in the first treatment condition were greater than the highest measure in the first baseline, for a PND of 100%. The greater the percentage of non-overlapping data, the stronger the treatment effect. Still, formal statistical approaches to data analysis in single-subject research are generally considered a supplement to visual inspection, not a replacement for it.

Image Description

Figure 10.2 long description: Line graph showing the results of a study with an ABAB reversal design. The dependent variable was low during first baseline phase; increased during the first treatment; decreased during the second baseline, but was still higher than during the first baseline; and was highest during the second treatment phase. [Return to Figure 10.2]

Figure 10.3 long description: Three line graphs showing the results of a generic multiple-baseline study, in which different baselines are established and treatment is introduced to participants at different times.

Figure 10.4 long description: Two graphs showing the results of a generic single-subject study with an ABA design. In the first graph, under condition A, level is high and the trend is increasing. Under condition B, level is much lower than under condition A and the trend is decreasing. Under condition A again, level is about as high as the first time and the trend is increasing. For each change, latency is short, suggesting that the treatment is the reason for the change.

Sidman, M. (1960). Tactics of scientific research: Evaluating experimental data in psychology . Boston, MA: Authors Cooperative. ↵
Ross, S. W., & Horner, R. H. (2009). Bully prevention in positive behavior support. Journal of Applied Behavior Analysis, 42 , 747–759. ↵
Fisch, G. S. (2001). Evaluating data from behavioral analysis: Visual inspection or statistical models. Behavioral Processes, 54 , 137–154. ↵
Scruggs, T. E., & Mastropieri, M. A. (2001). How to summarize single-participant research: Ideas and applications. Exceptionality, 9 , 227–244. ↵

When the researcher waits until the participant’s behavior in one condition becomes fairly consistent from observation to observation before changing conditions.

The most basic single-subject research design in which the researcher measures the dependent variable in three phases: Baseline, before a treatment is introduced (A); after the treatment is introduced (B); and then a return to baseline after removing the treatment (A). It is often called an ABA design.

Another term for reversal design.

The beginning phase of an ABA design which acts as a kind of control condition in which the level of responding before any treatment is introduced.

In this design the baseline phase is followed by separate phases in which different treatments are introduced.

In this design two or more treatments are alternated relatively quickly on a regular schedule.

In this design, multiple baselines are either established for one participant or one baseline is established for many participants.

This means plotting individual participants’ data, looking carefully at those plots, and making judgments about whether and to what extent the independent variable had an effect on the dependent variable.

This is the percentage of responses in the treatment condition that are more extreme than the most extreme response in a relevant control condition.

Research Methods in Psychology Copyright © 2019 by Rajiv S. Jhangiani, I-Chant A. Chiang, Carrie Cuttler, & Dana C. Leighton is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Terms to Use for Articles

"reversal design" OR "withdrawal design" OR "ABAB design" OR "A-B-A-B design" OR "ABC design" OR "A-B-C design" OR "ABA design" OR "A-B-A design" OR "multiple baseline" OR "alternating treatments design" OR "multi-element design" OR "multielement design" OR "changing criterion design" OR "single case design" OR "single subject design" OR “single case series" or "single subject" or "single case"

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Research Hints

Stimming – or self-stimulatory behaviour – is repetitive or unusual body movement or noises . Stimming might include:

hand and finger mannerisms – for example, finger-flicking and hand-flapping
unusual body movements – for example, rocking back and forth while sitting or standing
posturing – for example, holding hands or fingers out at an angle or arching the back while sitting
visual stimulation – for example, looking at something sideways, watching an object spin or fluttering fingers near the eyes
repetitive behaviour – for example, opening and closing doors or flicking switches
chewing or mouthing objects
listening to the same song or noise over and over.

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Single Case Design (Research Articles)

Single Case Design (APA Dictionary of Psychology) an approach to the empirical study of a process that tracks a single unit (e.g., person, family, class, school, company) in depth over time. Specific types include the alternating treatments design, the multiple baseline design, the reversal design, and the withdrawal design. In other words, it is a within-subjects design with just one unit of analysis. For example, a researcher may use a single-case design for a small group of patients with a tic. After observing the patients and establishing the number of tics per hour, the researcher would then conduct an intervention and watch what happens over time, thus revealing the richness of any change. Such studies are useful for generating ideas for broader studies and for focusing on the microlevel concerns associated with a particular unit. However, data from these studies need to be evaluated carefully given the many potential threats to internal validity; there are also issues relating to the sampling of both the one unit and the process it undergoes. Also called N-of-1 design; N=1 design; single-participant design; single-subject (case) design.
Anatomy of a Primary Research Article Document that goes through a research artile highlighting evaluative criteria for every section. Document from Mohawk Valley Community College. Permission to use sought and given
Single Case Design (Explanation) Single case design (SCD), often referred to as single subject design, is an evaluation method that can be used to rigorously test the success of an intervention or treatment on a particular case (i.e., a person, school, community) and to also provide evidence about the general effectiveness of an intervention using a relatively small sample size. The material presented in this document is intended to provide introductory information about SCD in relation to home visiting programs and is not a comprehensive review of the application of SCD to other types of interventions.
Single-Case Design, Analysis, and Quality Assessment for Intervention Research The purpose of this article is to describe single-case studies, and contrast them with case studies and randomized clinical trials Lobo, M. A., Moeyaert, M., Baraldi Cunha, A., & Babik, I. (2017). Single-case design, analysis, and quality assessment for intervention research. Journal of neurologic physical therapy : JNPT, 41(3), 187–197. https://doi.org/10.1097/NPT.0000000000000187
The difference between a case study and single case designs There is a big difference between case studies and single case designs, despite them superficially sounding similar. (This is from a Blog posting)
Single Case Design (Amanda N. Kelly, PhD, BCBA-D, LBA-aka Behaviorbabe) Despite the aka Behaviorbabe, Dr. Amanda N. Kelly, PhD, BCBA-D, LBA] provides a tutorial and explanation of single case design in simple terms.
Lobo (2018). Single-Case Design, Analysis, and Quality Assessment for Intervention Research Lobo, M. A., Moeyaert, M., Cunha, A. B., & Babik, I. (2017). Single-case design, analysis, and quality assessment for intervention research. Journal of neurologic physical therapy: JNPT, 41(3), 187.. https://doi.org/10.1097/NPT.0000000000000187
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15.2 Types of Single-Systems Research Designs

Learning objectives.

Learners will be able to…

intro & more content is needed, but here is a start…

https://kpu.pressbooks.pub/psychmethods4e/chapter/single-subject-research-designs/ (Section: Reversal Designs) NOTE: THIS HAS FIGURES WE MIGHT WANT TO USE
Mauldin, 11.2

Withdrawal, or Reversal, Design

Another option would be to withdraw treatment for a specified time and continue to measure the client, establishing a new baseline. If the client continues to improve after the treatment is withdrawn, then it is likely to have lasting effects. This is called a withdrawal design and is represented as A-B-A or A-B-A-B.

Reversal Designs : It is the most single-subject research design, also known as ABA design. During the first phase, A, a baseline is established for the dependent variable. This is the level of responding before any treatment is introduced, and therefore the baseline phase is a kind of control condition. When steady state responding is reached, phase B begins as the researcher introduces the treatment. There may be a period of adjustment to the treatment during which the behavior of interest becomes more variable and begins to increase or decrease. Again, the researcher waits until that dependent variable reaches a steady state so that it is clear whether and how much it has changed. Finally, the researcher removes the treatment and again waits until the dependent variable reaches a steady state. This basic reversal design can also be extended with the reintroduction of the treatment (ABAB), another return to baseline (ABABA), and so on.

There are close relatives of the basic reversal design that allow for the evaluation of more than one treatment. In, m ultiple-treatment reversal design, you start with a baseline phase and then try different treatments one by one. For example, one might begin by observing a disruptive student’s behavior (A), then give them positive attention from the teacher (B), and later try mild punishment for not studying (C) we can go back to the baseline before reintroducing each treatment, maybe in the reverse order to account for any effect from previous treatments. This type of design is also called as ABCACB design. a baseline phase is followed by separate phases in which different treatments are introduced.

Alternating-treatment designs : In an alternating treatment design, two or more treatments are altered relatively quickly on a regular schedule. For example, positive attention for studying could be used one day and mild punishment for not stuyding the next, and so on. Or one treatment could be implemented in the morning and another in the afternoon. Alternating treatment designs are often a quick and effective way of comparing treatments, but only when the treatments are fast acting.

Mutiple-baseline design

There are two potential problems with the reversal design—both of which have to do with the removal of the treatment. One is that if a treatment is working, it may be unethical to remove it. For example, if a treatment seemed to reduce the incidence of self-injury in a child with an intellectual delay, it would be unethical to remove that treatment just to show that the incidence of self-injury increases. The second problem is that the dependent variable may not return to baseline when the treatment is removed. For example, when positive attention for studying is removed, a student might continue to study at an increased rate. This could mean that the positive attention had a lasting effect on the student’s studying, which of course would be good. But it could also mean that the positive attention was not really the cause of the increased studying in the first place. Perhaps something else happened at about the same time as the treatment—for example, the student’s parents might have started rewarding him for good grades. One solution to these problems is to use a , which is represented in Figure 10.3. There are three different types of multiple-baseline designs which we will now consider.

Multiple-Baseline Design Across Participants

Multiple-Baseline Design Across Behaviors

Multiple-Baseline Design Across Settings

Multiple Treatment Design

In single-subjects design, it is possible to begin a new course of treatment or add a new dimension to an existing treatment. This is called a multiple treatment design . The graphing would continue as before, but with another vertical line representing the second intervention, indicating a new treatment began.

Key Takeaways

According to the APA Dictionary of Psychology : an experimental design in which the treatment or other intervention is removed during one or more periods. A typical withdrawal design consists of three phases: an initial condition for obtaining a baseline, a condition in which the treatment is applied, and another baseline condition in which the treatment has been withdrawn. Often, the baseline condition is represented by the letter A and the treatment condition by the letter B, such that this type of withdrawal design is known as an A-B-A design. A fourth phase of reapplying the intervention may be added, as well as a fifth phase of removing the intervention, to determine whether the effect of the intervention can be reproduced.

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Single-Subject Experimental Design for Evidence-Based Practice

Breanne j. byiers.

a University of Minnesota, Minneapolis

Joe Reichle

Frank j. symons.

Single-subject experimental designs (SSEDs) represent an important tool in the development and implementation of evidence-based practice in communication sciences and disorders. The purpose of this article is to review the strategies and tactics of SSEDs and their application in speech-language pathology research.

The authors discuss the requirements of each design, followed by advantages and disadvantages. The logic and methods for evaluating effects in SSED are reviewed as well as contemporary issues regarding data analysis with SSED data sets. Examples of challenges in executing SSEDs are included. Specific exemplars of how SSEDs have been used in speech-language pathology research are provided throughout.

SSED studies provide a flexible alternative to traditional group designs in the development and identification of evidence-based practice in the field of communication sciences and disorders.

The use of single-subject experimental designs (SSEDs) has a rich history in communication sciences and disorders (CSD) research. A number of important studies dating back to the 1960s and 1970s investigated fluency treatments using SSED approaches (e.g., Hanson, 1978 ; Haroldson, Martin, & Starr, 1968 ; Martin & Siegel, 1966 ; Reed & Godden, 1977 ). Several reviews, tutorials, and textbooks describing and promoting the use of SSEDs in CSD were published subsequently in the 1980s and 1990s (e.g., Connell, & Thompson, 1986 ; Fukkink, 1996 ; Kearns, 1986 ; McReynolds & Kearns, 1983 ; McReynolds & Thompson, 1986 ; Robey, Schultz, Crawford, & Sinner, 1999 ). Despite their history of use within CSD, SSEDs are sometimes overlooked in contemporary discussions of evidence-based practice. This article provides a comprehensive overview of SSEDs specific to evidence-based practice issues in CSD that, in turn, could be used to inform disciplinary research as well as clinical practice.

In the current climate of evidence-based practice, the tools provided by SSEDs are relevant for researchers and practitioners alike. The American Speech-Language-Hearing Association ( ASHA; 2005 ) promotes the incorporation of evidence-based practice into clinical practice, defining evidence-based practice as “an approach in which current, high-quality research evidence is integrated with practitioner experience and client preferences and values into the process of making clinical decisions.” The focus on the individual client afforded by SSEDs makes them ideal for clinical applications. The potential strength of the internal validity of SSEDs allows researchers, clinicians, and educators to ask questions that might not be feasible or possible to answer with traditional group designs. Because of these strengths, both clinicians and researchers should be familiar with the application, interpretation, and relationship between SSEDs and evidence-based practice.

The goal of this tutorial is to familiarize readers with the logic of SSEDs and how they can be used to establish evidence-based practice. The basics of SSED methodology are described, followed by descriptions of several commonly implemented SSEDs, including their benefits and limitations, and a discussion of SSED analysis and evaluation issues. A set of standards for the assessment of evidence quality in SSEDs is then reviewed. Examples of how SSEDs have been used in CSD research are provided throughout. Finally, a number of current issues in SSEDs, including effect size calculations and the use of statistical techniques in the analysis of SSED data, are considered.

The Role of SSEDs in Evidence-Based Practice

Numerous criteria have been developed to identify best educational and clinical practices that are supported by research in psychology, education, speech-language science, and related rehabilitation disciplines. Some of the guidelines include SSEDs as one experimental design that can help identify the effectiveness of specific treatments (e.g., Chambless et al., 1998 ; Horner et al., 2005 ; Yorkston et al., 2001 ). Many research communities, however, hold the position that randomized control trials (RCTs) represent the “gold standard” for research methodology aimed at validating best intervention practices; therefore, RCTs de facto become the only valid research methodology that is necessary for establishing evidence-based practice.

RCTs do have many specific advantages related to understanding causal relations by addressing methodological issues that may compromise the internal validity of research studies. Kazdin (2010) , however, compellingly argued that certain characteristics of SSEDs make them an important addition and alternative to large-group designs. He argued that RCTs may not be feasible with many types of interventions, as resources for such large-scale studies may not be available to test the thousands of treatments likely in use in any given field. In addition, the carefully controlled conditions in which RCTs must be conducted to ensure that the results are interpretable may not be comparable and/or possible to implement in real-life (i.e., uncontrolled) conditions. SSEDs are an ideal tool for establishing the viability of treatments in real-life settings before attempts are made to implement them at the large scale needed for RCTs (i.e., scaling up). Ideally, several studies using a variety of methodologies will be conducted to establish an intervention as evidence-based practice. When a treatment is established as evidence based using RCTs, it is often interpreted as meaning that the intervention is effective with most or all individuals who participated. Unfortunately, this may not be the case (i.e., there are responders and nonresponders). Thus, systematic evaluation of the effects of a treatment at an individual level may be needed, especially within the context of educational or clinical practice. SSEDs can be helpful in identifying the optimal treatment for a specific client and in describing individual-level effects.

Analysis of Effects in SSEDs

Desirable qualities of baseline data.

The analysis of experimental control in all SSEDs is based on visual comparison between two or more conditions. The conditions tested typically include a baseline condition, during which no intervention is in place, as well as one or more intervention conditions. The baseline phase establishes a benchmark against which the individual's behavior in subsequent conditions can be compared. The data from this phase must have certain qualities to provide an appropriate basis for comparison. The first quality of ideal baseline data is stability, meaning that they display limited variability. With stable data, the range within which future data points will fall is predictable. The second quality of ideal baseline data is a lack of a clear trend of improvement. The difficulty posed by trends in baseline data is dictated by the direction of behavior change expected during the intervention phase: If the behavior reflected in the dependent measure is expected to increase as a result of the intervention, a decreasing trend during baseline does not pose a significant problem. If, on the other hand, the trend for the dependent measure is increasing during baseline, determining whether or not a continued increase during the intervention phase constitutes a treatment effect is likely to be compromised. By convention, a minimum of three baseline data points are required to establish dependent measure stability ( Kazdin, 2010 ), with more being preferable. If stability is not established in the initial sessions, additional measurements should be obtained until stability is achieved. Alternatively, steps can be taken to introduce additional controls (strengthening internal validity) into the baseline sessions that may contribute to variability.

Visual Data Inspection as a Data Reduction Strategy: Changes in Level, Trend, and Variability

Once the data in all conditions have been obtained, they are examined for changes in one or more of three parameters: level, trend (slope), and variability. Level refers to the average rate of performance during a phase. Panel A of Figure 1 shows hypothetical data demonstrating a change in level. In this case, the average rate of performance during the baseline phase is lower than the average rate of performance during the intervention phase. Figure 1 also illustrates that the change in level occurred immediately following the change in phase. The change in level is evident, in part, because there is no overlap between the phases, meaning that the lowest data point from the intervention phase is still higher than the highest data point from the baseline phase.

An external file that holds a picture, illustration, etc.
Object name is nihms-570833-f0001.jpg

Hypothetical data demonstrating unambiguous changes in level (Panel A), trend (Panel B), and variability (Panel C).

On the other hand, there is overlap between the baseline and intervention phases in Panel B of Figure 1 , and the overall level of the dependent variable does not differ much between the phases. There is, however, a change in trend, as there is a consistent decreasing trend during the baseline phase, which is reversed in the intervention phase.

Finally, in Panel C, there is no evidence for changes in level or trend. There is, however, a change in variability. During the baseline phase, performance in the dependent measure is highly variable, with a minimum of 0% and a maximum of 100%. In contrast, during the intervention phase, performance is stable, with a range of only 6%. All three of these types of changes may be used as evidence for the effects of an independent variable in an appropriate experimental design.

When such changes are large and immediate, visual inspection is relatively straightforward, as in all three graphs in Figure 1 . In many real-life data sets, however, effects are more ambiguous. Take, for example, the graphs in Figure 2 . If only the average performance during each phase is considered, each of these graphs includes a between-phase change in level. On closer inspection, however, each presents a problem that threatens the internal validity of the experiment and the ability of the clinical researcher to make a warranted causal inference about the relation between treatment (the independent variable) and effect (the dependent variable).

An external file that holds a picture, illustration, etc.
Object name is nihms-570833-f0002.jpg

Hypothetical data demonstrating demonstrations of non-effect: delayed latency to change (Panel A), trend in desired direction during baseline phase (Panel B), highly variable data with overlap between baseline and intervention phases (Panel C).

In Panel A of Figure 2 , no change is observed until the third session of the intervention phase. This latency brings into question the assumption that the manipulation of the independent variable is responsible for the observed changes in the dependent variable. It is possible that the observed change may be more appropriately attributed to some factor outside the control of the experimenter. To rule out the plausibility of an extraneous variable, the experimental effect must be replicated, thereby showing that although there may be a delay, changes in the dependent variable reliably occur following changes to the independent variable. This type of replication (within study) is a primary characteristic of SSEDs and is the primary basis for internally valid inferences.

By contrast, Panel B of Figure 2 shows a data set in which an increasing trend is present during the baseline phase. As a result, any increases observed during the intervention phase may simply be a continuation of that trend rather than the result of the manipulation of the independent variable. This underscores the importance of “good” baseline data, and, in particular, of the need to continue collecting baseline data to eliminate the possibility that any trends observed are likely to continue in the absence of an intervention.

Panel C also underscores the importance of “good” baseline data. Although no consistent trend is present in the baseline phase, the data are highly variable. As a result, there is an overlap between many of the sessions in the baseline and intervention phases, even though the average level of performance is higher in the intervention phase ( M = 37%) than in the baseline phase ( M = 57%). Because the determination of experimental effects in SSEDs is based on visual inspection of the results rather than statistical analyses, such an overlap obscures any potential effects. As a result, when baseline data such as these are collected, the researcher should attempt to eliminate possible sources of variability to help establish a clear pattern of responding.

Threats to the internal validity of SSEDs, such as those demonstrated in Figure 2 , are described as “demonstrations of noneffect” in the language of a panel assembled by the What Works Clearinghouse (WWCH), an initiative of the Institute for Education Sciences (IES) that was appointed to develop a set of criteria for determining whether the results of SSEDs provide evidence of sufficient quality to identify an intervention as evidence based ( Kratochwill et al., 2010 ). A description of the criteria developed by the panel as well as their application to evidence-based practice in CSD follows.

Criteria for Evidence Quality in SSEDs

A number of groups from different fields have developed criteria to assess the quality of evidence used to support the effectiveness of interventions and to facilitate the incorporation of research findings into practice. Among the most recent of these criteria focusing specifically on SSEDs are those developed by the WWCH panel. Considering the WWCH criteria, determining whether an intervention qualifies as evidence based involves a three-step sequence. The first step involves assessing the adequacy of the experimental design (see Table 1 ) to determine whether it meets the standards, with or without reservations. If the design is not found to be adequate, no further steps are needed. If the design meets the standards, the second step is to conduct a visual analysis of the results to determine whether the data suggest an experimental effect. If the visual analysis supports the presence of an effect, the data should be examined for demonstrations of noneffect, such as those depicted in Figure 2 . If no evidence of an experimental effect is found, the process is terminated. If the visual analysis suggests that the results support the effectiveness of the intervention, the reviewer can move on to the third step: assessing the overall state of the evidence in favor of an intervention by examining the number of times its effectiveness has been demonstrated, both within and across participants. The importance of replication in SSEDs is discussed in more detail in the next section. If the design meets the standards and the visual analysis indicates that there is an effect, with no demonstrations of noneffect, the study would be considered one that provides strong evidence. If it meets the standards and there is evidence of an effect, but the results include at least one demonstration of noneffect, then the study would be considered one that provides moderate evidence. The results of all studies that reported the effects of a particular intervention can then be examined for overall level of evidence in favor of the treatment.

Summary of What Works Clearinghouse criteria for experimental designs.

Replication for Internal and External Validity

Replication is one of the hallmarks of SSEDs. Experimental control is demonstrated when the effects of the intervention are repeatedly and reliably demonstrated within a single participant or across a small number of participants. The way in which the effects are replicated depends on the specific experimental design implemented. For many designs, each time the intervention is implemented (or withdrawn following an initial intervention phase), an opportunity to provide an instance of effect replication is created. This within-study replication is the basis of internal validity for SSEDs.

By replicating an investigation across different participants, or different types of participants, researchers and clinicians can examine the generality of the treatment effects and thus potentially enhance external validity. Kazdin (2010) distinguished between two types of replication. Direct replication refers to the application of an intervention to new participants under exactly, or nearly exactly, the same conditions as those included in the original study. This type of replication allows the researcher or clinician to determine whether the findings of the initial study were specific to the participant(s) who were involved. Systematic replication involves the repetition of the investigation while systematically varying one or more aspects of the original study. This might include applying the intervention to participants with more heterogeneous characteristics, conducting the intervention in a different setting with different dependent variables, and so forth. The variation inherent to systematic replication allows the researcher, educator, or clinician to determine the extent to which the findings will generalize across different types of participants, settings, or target behaviors. As noted by Johnston and Pennypacker (2009) , conducting direct replications of an effect tells us about the certainty of our knowledge, whereas conducting systematic replications can expand the extent of our knowledge.

An intervention or treatment cannot be considered evidence based following the results of a single study. The WWCH panel recommended that an intervention have a minimum of five supporting SSED studies meeting the evidence standards if the studies are to be combined into a single summary rating of the intervention's effectiveness. Further, these studies must have been conducted by at least three different research teams at three different geographical locations and must have included a combined number of at least 20 participants or cases (see O'Neill, McDonnell, Billingsley, & Jenson, 2011 , for a summary of different evidence-based practice guidelines on replication). The panel also suggested the use of some type of effect size to quantify intervention effects within each study, thereby facilitating the computation of a single summary rating of the evidence in favor of the invention (a discussion of the advantages and disadvantages of SSEDs and effects sizes follows later). In the next section, the specific types of SSEDs are described and reviewed.

Types of SSEDs

Six primary design types are discussed: the pre-experimental (or AB) design, the withdrawal (or ABA/ABAB) design, the multiple-baseline/multiple-probe design, the changing-criterion design, the multiple-treatment design, and the alternating treatments and adapted alternating treatments designs (see Table 2 ).

Summary of single-subject experimental designs (SSEDs).

Pre-Experimental (AB) Design

Although the AB design is often described as a SSED, it is more accurately considered a pre-experimental design because it does not sufficiently control for many threats to internal validity and, therefore, does not demonstrate experimental control. As a result, the AB design is best thought of as one that demonstrates correlation between the independent and dependent variables but not necessarily causation. Nevertheless, the AB design is an important building block for true experimental designs. It is made up of two phases: the A (baseline) phase and the B (intervention) phase. Several baseline sessions establish the pre-intervention level of performance. As previously noted, the purpose of the baseline phase is to establish the existing levels/patterns of the behavior(s) of interest, thus allowing for future performance predictions under the continued absence of intervention. Due to the lack of replication of the experimental effect in an AB design, however, it is impossible to say with certainty whether any observed changes in the dependent variable are a reliable, replicable result of the manipulation of the independent variable. As a result, it is possible that any number of external factors may be responsible for the observed changes. Nevertheless, these designs can provide preliminary objective data regarding the effects of an intervention when time and resources are limited (see Kazdin, 2010 ).

Withdrawal (ABA and ABAB) Designs

The withdrawal design is one option for answering research questions regarding the effects of a single intervention or independent variable. Like the AB design, the ABA design begins with a baseline phase (A), followed by an intervention phase (B). However, the ABA design provides an additional opportunity to demonstrate the effects of the manipulation of the independent variable by withdrawing the intervention during a second “A” phase. A further extension of this design is the ABAB design, in which the intervention is re-implemented in a second “B” phase. ABAB designs have the benefit of an additional demonstration of experimental control with the reimplementation of the intervention. Additionally, many clinicians/educators prefer the ABAB design because the investigation ends with a treatment phase rather than the absence of an intervention.

It is worth noting that although they are often used interchangeably in the literature, the terms withdrawal design and reversal design refer to two related but distinctly different research designs. In the withdrawal design, the third phase represents a change back to pre-intervention conditions or the withdrawal of the intervention. In contrast, the reversal design requires the active reversal of the intervention conditions. For example, reinforcement is provided contingent on the occurrence of a response incompatible with the response reinforced during the intervention (B) phases (see Barlow, Nock, & Hersen, 2009 , for a complete discussion of the mechanics and relative advantages of reversal designs).

A recent example of the withdrawal design was executed by Tincani, Crozier, and Alazetta (2006) . They implemented an ABAB design to demonstrate the effects of positive reinforcement for vocalizations within a Picture Exchange Communication System (PECS) intervention with school-age children with autism (see Figure 3 ). A visual analysis of the results reveals large, immediate changes in percentage of vocal approximations emitted by the student each time the independent variable is manipulated, and there are no overlapping data between the baseline and intervention phases. Finally, there are no demonstrations of a noneffect. As a result, this case would be considered strong evidence supporting the effectiveness of the intervention based on the WWCH evidence-based practice criteria. The study meets the standards (with reservations) because (a) the researchers actively manipulated the independent variable (presence/absence of vocal reinforcement), (b) data on the dependent variable were collected systematically over time, (c) a minimum of four data points were collected in each phase (at least five are needed to meet the standards without reservations), and (d) the effect was replicated three times (the intervention was implemented, withdrawn, and implemented again).

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Percentage of trials containing vocal approximations during no positive reinforcement of vocalization (baseline; see Panel A) and positive reinforcement of vocalization (see Panel B), using an ABAB design. Voc. = vocal; PR = positive reinforcement. From “The Picture Exchange Communication System: Effects on manding and speech development for school-aged children with autism,” by Tincani, Crozier, and Alazetta, 2006 , Education and Training in Developmental Disabilities, 41, p. 183. Copyright 2006 by Council for Exceptional Children, Division on Developmental Disabilities. Reprinted with permission.

Advantages and disadvantages of withdrawal designs

Withdrawal designs (e.g., ABA and ABAB) provide a high degree of experimental control while being relatively straightforward to plan and implement. However, a major assumption of ABAB designs is that the dependent variable being targeted is reversible (e.g., will return to pre-intervention levels when the intervention is withdrawn). If the individual continues to perform the behavior at the same level even though the intervention is withdrawn, a functional relationship between the independent and dependent variables cannot be demonstrated. When this happens, the study becomes susceptible to the same threats to internal validity that are inherent in the AB design.

Although many behaviors would be expected to return to pre-intervention levels when the conditions change, others would not. For example, if one's objective were to teach or establish a new behavior that an individual could not previously perform, returning to baseline conditions would not likely cause the individual to “unlearn” the behavior. Similarly, studies aiming to improve proficiency in a skill through practice may not experience returns to baseline levels when the intervention is withdrawn. In other cases, the behavior of the parents, teachers, or staff implementing the intervention may not revert to baseline levels with adequate fidelity. In other cases still, the behavior may come to be maintained by other contingencies not under the control of the experimenter.

Another potential disadvantage of these designs is the ethical issue associated with withdrawing an apparently effective intervention. Additionally, stakeholders may be unwilling (or unable) to return to baseline conditions, especially given the expectation that the behavior will return to baseline levels (or worse) when the intervention is withdrawn.

Overall, ABAB designs are one of the most straightforward and strongest SSED “treatment effect demonstration” strategies. Ethical considerations regarding the withdrawal of the intervention and the reversibility of the behavior need to be taken into account before the study begins. Further extensions of the ABAB design logic to comparisons between two or more interventions are discussed later in this article.

Multiple-Baseline and Multiple-Probe Designs

Multiple-baseline and multiple-probe designs are appropriate for answering research questions regarding the effects of a single intervention or independent variable across three or more individuals, behaviors, stimuli, or settings. On the surface, multiple-baseline designs appear to be a series of AB designs stacked on top of one another. However, by introducing the intervention phases in a staggered fashion, the effects can be replicated in a way that demonstrates experimental control. In a multiple-baseline study, the researcher selects multiple (typically three to four) conditions in which the intervention can be implemented. These conditions may be different behaviors, people, stimuli, or settings. Each condition is plotted in its own panel, or leg , that resembles an AB graph. Baseline data collection begins simultaneously across all the legs. The intervention is introduced systematically in one condition while baseline data collection continues in the others. Once responding is stable in the intervention phase in the first leg, the intervention is introduced in the next leg, and this continues until the AB sequence is complete in all the legs.

Figure 4 shows the results from a study using a multiple-baseline, across-participants design examining the collateral language effects of a question-asking training procedure for children with autism ( Koegel, Koegel, Green-Hopkins, & Barnes, 2010 ). The design meets the WWCH standards. The independent variable (the question-asking procedure) was actively manipulated, and the dependent variable (percentage of unprompted questions asked by each child) was measured systematically across time, with appropriate levels of interobserver agreement reported. Except for the generalization phase, at least five data points were collected in each phase. Because the generalization phase is not integral to the demonstration of the experimental control, this does not affect the sufficiency of the design: The effects were replicated across three activities.

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Percentage of unprompted questions asked by three participants in baseline, intervention, and generalization sessions using a multiple-baseline, across-participants design. From “Question-asking and collateral language acquisition in children with autism,” by Koegel, Koegel, Green-Hopkins, and Barnes (2010) , Journal of Autism and Developmental Disorders, 40, p. 512. Copyright 2009 by the authors. Reprinted with permission.

Visual analysis of the results supports the effectiveness of the intervention in that there was an immediate change in unprompted question-asking with the implementation of the intervention for all three children, with no overlap between the baseline and intervention phases. No indications of noneffect are present in the data. As a result, this study provides strong evidence that the question-asking intervention results in increases in collateral question-asking.

The data from the final phase of the study depicted in Figure 4 are worth noting because they show the continued performance of the dependent variable in the absence of the treatment. In some ways, this is akin to a return to baseline conditions, as in the second “A” condition of a withdrawal design. In this case, however, the behavior does not return to pre-intervention levels, suggesting that the behavior is nonreversible and that using a reversal design to demonstrate the effects of the intervention would have been inappropriate. For this study, the maintenance of the behavior after the intervention was withdrawn supports its long-term effectiveness without undermining the experimental control.

In some cases, the simultaneous and continuous data collection in all legs of multiple-baseline designs is not feasible or necessary. Multiple-probe designs are a common variation on multiple baselines in which continuous baseline assessment is replaced by intermittent probes to document performance in each of the conditions during baseline. Probes reduce the burden of data collection because they remove the need for continuous collection in all phases simultaneously (see Horner & Baer, 1978 , for a full description of multiple-probe designs). Pre-intervention probes in Condition 1 are obtained continuously until a stable pattern of performance is established. Meanwhile, single data collection sessions would be conducted in each of the other conditions to assess pre-intervention levels. Once responding has reached the criterion threshold in the intervention phase of the first leg, continuous measurement of pre-intervention levels is introduced in the second. When stable responding during the intervention phase is observed, intermittent probes can be implemented to demonstrate continued performance, and intervention is introduced in the second leg. This pattern is repeated until the effects of the intervention have been demonstrated across all the conditions.

Multiple-probe designs may not be appropriate for behaviors with significant variability because the intermittent probes may not provide sufficient data to demonstrate a functional relationship. If a stable pattern of responding is not clear during the baseline phase with probes, the continuous assessment of a multiple-baseline format may be necessary.

When selecting conditions for a multiple-baseline (or multiple-probe) design, it is important to consider both the independence and equivalence of the conditions. Independence means that changing behavior in one condition will not affect performance in the others. If the conditions are not independent, implementing the intervention in one condition may lead to changes in behavior in another condition while it remains in the baseline phase ( McReynolds & Kearns, 1983 ). This makes it challenging (if not impossible) to demonstrate convincingly that the intervention is responsible for changes in the behavior across all the conditions. When implementing the intervention across individuals, it may be necessary—to avoid diffusion of the treatment—to ensure that the participants do not interact with one another. When the intervention is implemented across behaviors, the behaviors must be carefully selected to ensure that any learning that takes place in one will not transfer to the next. Similarly, contexts or stimuli must be sufficiently dissimilar so as to minimize the likelihood of effect generalization.

Although an assumption of independence suggests that researchers should select conditions that are clearly dissimilar from one another, the conditions must be similar enough that the effects of the independent variable can be replicated across each of them. If the multiple baselines are conducted across participants, this means that all the participants must be comparable in their behaviors and other characteristics. If the multiple baselines are being conducted across behaviors, those behaviors must be similar in function, topography, and the effort required to produce them while remaining independent of one another.

Advantages and disadvantages of multiple-baseline/multiple-probe designs

Because replication of the experimental effect is across conditions in multiple-baseline/multiple-probe designs, they do not require the withdrawal of the intervention. This can make them more practical with behaviors for which a return to baseline levels cannot occur. Depending on the speed of the changes in the previous conditions, however, one or more conditions may remain in the baseline phase for a relatively long time. Thus, when multiple baselines are conducted across participants, one or more individuals may wait some time before receiving a potentially beneficial intervention.

The need for multiple conditions can make multiple-baseline/multiple-probe designs inappropriate when the intervention can be applied to only one individual, behavior, and setting. Also, potential generalization effects such as these must be considered and carefully controlled to minimize threats to internal validity when these designs are used. Nevertheless, multiple-baseline designs often are appealing to researchers and interventionists because they do not require the behavior to be reversible and do not require the withdrawal of an effective intervention.

Changing-Criterion Designs

Similar to withdrawal and multiple-baseline/multiple-probe designs, changing-criterion designs are appropriate for answering questions regarding the effects of a single intervention or independent variable on one or more dependent variables. In the previous designs, however, the assumption is that manipulating the independent variable will result in large, immediate changes to the dependent variable(s). In contrast, a major assumption of the changing-criterion is that the dependent variable can be increased or decreased incrementally with stepwise changes to the dependent variable. Typically, this is achieved by arranging a consequence (e.g., reinforcement) contingent on the participant meeting the predefined criterion. The changing-criterion design can be considered a special variation of multiple-baseline designs in that each phase serves as a baseline for the subsequent one ( Hartmann & Hall, 1976 ). However, rather than having multiple baselines across participants, settings, or behaviors, the changing-criterion design uses multiple levels of the independent variable. Experimental control is demonstrated when the behavior changes repeatedly to meet the new criterion (i.e., level of the independent variable).

Figure 5 shows the results of a study by Facon, Sahiri, and Riviere (2008) . In this study, a token reinforcement procedure was used to increase the speech volume of a child with selective mutism and mental retardation. During the baseline phase, the child's speech was barely audible, averaging 43 dB. For each new phase in the treatment condition, a criterion level for speech volume was set, which dictated what level of performance the child had to demonstrate to earn the reinforcement tokens. The horizontal lines on the graph represent the criterion set for each phase. To ensure the student's success during the intervention, the initial criterion was set at 43 dB. Researchers established a priori decision rules for changes to the criterion: The criterion would be increased when 80% of the child's utterances during three consecutive sessions were equal to or above the current criterion. Each new criterion value was equal to the mean loudness of the five best verbal responses during the last session of the previous phase.

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Speech volume during a token reinforcement intervention and follow-up using a changing-criterion design. From “A controlled single-case treatment of severe long-term selective mutism in a child with mental retardation,” by Facon, Sahiri, and Riviere, (2008) , Behavior Therapy, 39, p. 313. Copyright 2008 by Elsevier. Reprinted with permission.

The design of this study meets the WWCH standards, but with reservations. The independent variable (in this case, the token reinforcement system with the increasing dB criterion) was actively manipulated by the researchers, and the dependent variable was measured systematically over time. Each phase included a minimum of three data points (but not the five points required to meet the standards fully), and the number of phases with different criteria far exceeded the minimum three required.

Upon visual inspection, the results support the effectiveness of the intervention. There were few overlapping data points between the different criterion phases, and changes to the criterion usually resulted in immediate increases in the target behavior. These results would have been further strengthened by the inclusion of bidirectional changes, or mini-reversals, to the criterion ( Kazdin, 2010 ). Such temporary changes in the level of the dependent measure(s) in the direction opposite from that of the treatment effect enhance experimental control because they demonstrate that the dependent variable covaries with the independent variable. As such, bidirectional changes are much less likely to be the result of extraneous factors. Nevertheless, the results did not show any evidence of noneffect, and the results would be considered strong evidence in favor of the intervention.

Advantages and disadvantages of changing-criterion designs

Changing-criterion designs are ideal for behaviors for which it is unrealistic to expect large, immediate changes to coincide with manipulation of the independent variable. They do not require the withdrawal of treatment and, therefore, do not present any ethical concerns associated with removing potentially beneficial treatments. Unlike multiple-baseline/multiple-probe designs, changing-criterion studies require only one participant, behavior, and setting. Not all interventions, however, can be studied using a changing-criterion design; only interventions in which consequences for meeting or not meeting the established criterion levels of the behavior can be used. In addition, because the participant must be able to meet a certain criterion to contact the contingency, the participant must have some level of the target behavior in his or her repertoire before the study begins. Changing-criterion designs are not appropriate for behaviors that are severe or life threatening because they do not result in immediate, substantial changes. For teaching many complex tasks, however, shaping a behavior through a series of graduated steps is an appropriate strategy, and the changing-criterion design is a good option for a demonstrating the intervention's effectiveness.

Multiple-Treatment Designs

Thus far, the designs that we have described are only appropriate to answer questions regarding the effects of a single intervention or variable. In many cases, however, investigators—whether they are researchers, educators, or clinicians—are interested in not only whether an intervention works but also whether it works better than an alternative intervention. One strategy for comparing the effects of two interventions is to simply extend the logic of withdrawal designs to include more phases and more conditions. The most straightforward design of this type is the ABACAC design, which begins with an ABA design and is followed by a CAC design. The second “A” phase acts as both the withdrawal condition for the ABA portion of the experiment and the baseline phase for the ACAC portion. This design is ideal in situations where an ABA or ABAB study was planned but the effects of the intervention were not as sizable as had been hoped. Under these conditions, the intervention can be modified, or another intervention selected, and the effects of the new intervention can be demonstrated. The design has the same advantages and disadvantages of basic withdrawal designs but allows for a comparison of effects for two different treatments. A major drawback, however, is that the logic of SSEDs allows only for the comparison of adjacent conditions. This restriction helps to minimize threats to internal validity, such as maturation, that can lead to gradual changes in behavior over time, independent of study conditions. As a result, it is not appropriate to comment on the relative effects of the interventions (i.e., the “B” and “C” phases) in an ABACAC study because they never occur next to one another. Rather, one can only conclude that one, both, or neither intervention is effective relative to baseline. On the other hand, beginning with a full reversal or withdrawal design (ABAB), with it followed by a demonstration of the effects of the second intervention (CAC, resulting in ABABCAC), allows for the direct comparison of the two interventions. The BC comparison, however, is never repeated in this sequence, limiting the internal validity of the comparison.

Besides comparing the relative effects of two or more distinct interventions, multiple-treatment-phase designs can be used to assess the additive effects of treatment components. For example, if a treatment package consists of two separate components (components “B” and “C”), one can determine whether the intervention effects are due to one component alone or whether both are needed. Ward-Horner and Sturmey (2010) identified two methods for conducting component analyses: dropout , in which components were systematically removed from the treatment package to determine whether the treatment retained its effectiveness, and add-in , in which components were assessed individually before the implementation of the full treatment package. Each of these methods has its own advantages and disadvantages (see Ward-Horner & Sturmey, 2010 , for a full discussion), but taken together, component analyses can provide a great deal of information about the necessity and sufficiency of treatment components. In addition, they can inform strategies for fading out treatments while maintaining their effects.

Wacker and colleagues (1990) conducted dropout-type component analyses of functional communication training (FCT) procedures for three individuals with challenging behavior. The data presented in Figure 6 show the percentage of intervals with hand biting, prompts, and mands (signing) across functional analysis, treatment package, and component analysis phases. The functional analysis results indicated that the target behavior (hand biting) was maintained by access to tangibles as well as by escape from demands. In the second phase, a treatment package that included FCT and time-out was implemented. By the end of the phase, the target behavior was eliminated, prompting had decreased, and signing had increased. To identify the active components of the treatment package, a dropout component analysis was conducted. First, the time-out component of the intervention was removed, leaving the FCT component alone. A decreasing trend in signing and an increasing trend in hand biting were observed. This was reversed when the full treatment packaged was reimplemented. In the third phase of the component analysis, the FCTcomponent was removed, leaving time-out and differential reinforcement of other behavior (DRO). Again, a decreasing trend in signing and an increasing trend in hand biting were observed, which were again reversed when the full treatment package was applied.

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Percent of intervals with challenging behavior and mands during functional analysis, intervention demonstration, and component analysis. From “A component analysis of functional communication training across three topographies of severe behavior problems,” by Wacker et al., 1990 , Journal of Applied Behavior Analysis, 23, p. 424. Copyright 2008 by the Society for the Experimental Analysis of Behavior. Reprinted with permission.

Overall, visual inspection of these data provides a strong argument for the necessity of both the FCT and time-out components in the effectiveness of the treatment package, and no indications of noneffect are present in the data. The design, however, does not meet the standards set forth by the WWCH panel. This is because (a) the final two final treatment phases do not include the minimum of three data points and (b) the individual treatment component phases (FCT only and time-out/DRO) were implemented only once each. As a result, the data from this study could not be used to support the treatment package as an evidence-based practice by the IES standards. Additional data points within each phase, as well as replications of the phases, would strengthen the study results.

One disadvantage of all designs that involve two or more interventions or independent variables is the potential for multiple-treatment interference. This occurs when the same participant receives two or more treatments whose effects may not be independent. As a result, it is possible that the order in which the interventions are given will affect the results. For example, the effects of two interventions may be additive, so that the effects of Intervention 2 are enhanced beyond what they should be because Intervention 2 followed Intervention 1. In essence, this creates the potential for an order effect (or a carryover effect). Alternatively, Intervention 1 may have measurable but delayed effects on the dependent variable, making it appear that Intervention 2 is effective when the results should be attributed to Intervention 1. Such possibilities should be considered when multi-treatment studies are being planned (see Hains & Baer, 1989 , for a comprehensive discussion of multiple-treatment interference). A final, longer phase in which the final “winning” treatment is implemented for an extended time can help alleviate some of the concerns regarding multiple-treatment interference.

Advantages and disadvantages of multiple-treatment designs

Designs such as ABCABC and ABCBCA can be very useful when a researcher wants to examine the effects of two interventions. These designs provide strong internal validity evidence regarding the effectiveness of the interventions. External validity, however, may be compromised by the threat of multiple-treatment interference. Additionally, the same advantages and disadvantages of ABAB designs apply, including issues related to the reversibility of the target behavior. Despite their limitations, these designs can provide strong empirical data upon which to base decisions regarding the selection of treatments for an individual client. Although, in theory, these types of designs can be extended to compare any number of interventions or conditions, doing so beyond two becomes excessively cumbersome; therefore, the alternating treatments design should be considered.

Alternating Treatments and Adapted Alternating Treatments Designs

Alternating treatments design (atd).

The logic of the ATD is similar to that of multiple-treatment designs, and the types of research questions that it can address are also comparable. The major distinction is that the ATD involves the rapid alternation of two or more interventions or conditions ( Barlow & Hayes, 1979 ). Data collection typically begins with a baseline (A) phase, similar to that of a multiple-treatment study, but during the next phase, each session is randomly assigned to one of two or more intervention conditions. Because there are no longer distinct phases of each intervention, the interpretation of the results of ATD studies differs from that of the studies reviewed so far. Rather than comparing between phases, all the data points within a condition (e.g., all sessions of Intervention 1) are connected (even if they do not occur adjacently). Demonstration of experimental control is achieved by having differentiation between conditions, meaning that the data paths of the conditions do not overlap.

In ATDs, it is important that all potential “nuisance” variables be controlled or counterbalanced. For example, having different experimenters conduct sessions in different conditions, or running different session conditions at different times of day, may influence the results beyond the effect of the independent variables specified. Therefore, all experimental procedures must be analyzed to ensure that all conditions are identical except for the variable(s) of interest. Presenting conditions in random order can help eliminate issues regarding temporal cycles of behavior as well as ensure that there are equal numbers of sessions for each condition.

Lang and colleagues (2011) used an ATD to examine the effects of language of instruction on correct responding and inappropriate behavior (tongue clicks) with a student with autism from a Spanish-speaking family. To ensure that the conditions were equivalent, all aspects of the teaching sessions except for the independent variable (language of instruction) were held constant. Specifically, the same teacher, materials, task demands, reinforcers, and reinforcer schedules were used in both the English and Spanish sessions.

The results of this study (see Figure 7 ) demonstrated that the student produced a higher number of correct responses and engaged in fewer challenging behaviors when instruction was delivered in Spanish than in English. The superiority of the Spanish instruction was evident in this case because there was no overlap in correct responding or inappropriate behaviors between the English and Spanish conditions.

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Number of correct responses and tongue clicks during discrete trial training sessions in Spanish (Sp.) and English (Eng.) using an alternating treatments design. From “Effects of language instruction on response accuracy and challenging behavior in a child with autism,” by Lang et al., 2011 , Journal of Behavioral Education, 20, p. 256. Copyright 2001 by Springer Science+Business Media, LLC. Reprinted with permission.

Although visual analysis supported the inference that treatment effects were functionally related to the independent variable, the results of this study did not meet the design standards set out by the WWCH panel because the design consisted of only two treatments in comparison with each other. To meet the criterion of having at least three attempts to demonstrate an effect, studies using an ATD must include a direct comparison of three interventions, or two interventions compared with a baseline. To be considered as support for an evidence-based practice, this design would need to have incorporated a third intervention condition or to have begun with a baseline condition.

Adapted alternating treatments design (AATD)

One commonly used alternative to the ATD is called the adapted alternating treatments design (AATD; Sindelar, Rosenburg, & Wilson, 1985 ). Whereas the traditional ATD assesses the effects of different interventions or independent variables on a single outcome variable, in the AATD, a different set of responses is assigned to each intervention or independent variable. The resulting design is similar to a multiple-baseline, across-behaviors design with concurrent training for all behaviors. For example, Conaghan, Singh, Moe, Landrum, and Ellis (1992) assigned a different set of 10 phrases to each of three conditions (directed rehearsal, directed rehearsal plus positive reinforcement, and control). This strategy allowed the researchers to determine whether the acquisition of new signed phrases differed across the three conditions. Figure 8 shows one participant's correct responses during sessions across baseline phases, alternating treatments phases, and extended treatment phases.

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Number of phrases signed correctly during directed rehearsal, directed rehearsal with positive reinforcement, and control sessions using an adapted alternating treatments design. From “Acquisition and generalization of manual signs by hearing-impaired adults with mental retardation,” by Conaghan, Singh, Moe, Landrum, and Ellis, 1992 , Journal of Behavioral Education, 2, p. 192. Copyright 1992 by Human Sciences Press. Reprinted with permission.

Unlike the Lang et al. (2011) study, the design used in this study met the WWCH standards. This was because, in addition to meeting the minimum number of sessions per phase, it included a direct comparison between three conditions as well as a direct comparison with a baseline phase. The data from the baseline phase established that the participant did not respond correctly in the absence of the intervention. The data from the alternating treatments phase supported the effectiveness of the directed rehearsal and directed rehearsal plus positive reinforcement conditions compared with the control condition. They also supported the relative effectiveness of the directed rehearsal with reinforcement compared with directed rehearsal alone.

During the initial four sessions of the alternating treatments phase, responding remained at zero for all three word sets. Steadily increasing trends were observed in both of the directed rehearsal conditions beginning in the fifth session, whereas responding remained at zero in the control condition. The rate of acquisition in the directed rehearsal plus positive reinforcement condition was higher than in directed rehearsal alone throughout the alternating treatments phase. The latency in correct responding observed during the initial sessions of the alternating treatments was a demonstration of noneffect. The fact that no change in responding was observed in the control condition, however, is evidence that the changes were due to the intervention rather than a result of some factor outside of the study. As further demonstration of the experimental effect of directed rehearsal plus reinforcement, a final condition was implemented in which the treatment package was used to teach the phrases from the other two conditions. This condition further strengthened the evidence for the effectiveness of the intervention, as performance on all three words sets reached 100% by the end of the phase. In sum, the latency to change observed during the alternating treatments phase meant that this study merits a rating of moderate evidence in favor of the intervention.

Advantages and disadvantages of ATDs and AATDs

ATDs and AATDs can be useful in comparing the effects of two or more interventions or independent variables. Unlike multiple-treatment designs, these designs can allow multiple comparisons in relatively few sessions. The issues related to multiple-treatment interference are also relevant with the ATD because the dependent variable is exposed to each of the independent variables, thus making it impossible to disentangle their independent effects. To ensure that the selected treatment remains effective when implemented alone, a final phase demonstrating the effects of the best treatment is recommended ( Holcombe & Wolery, 1994 ), as was done in the study by Conaghan et al., 1992 . Many researchers pair an independent but salient stimulus with each treatment (i.e., room, color of clothing, etc.) to ensure that the participants are able to discriminate which intervention is in effect during each session ( McGonigle, Rojahn, Dixon, & Strain, 1987 ). Nevertheless, outcome behaviors must be readily reversible if differentiation between conditions is to be demonstrated.

The AATD eliminates some of the concerns regarding multiple-treatment interference because different behaviors are exposed to different conditions. As in the multiple-baseline/multiple-probe designs, the possibility of generalization across behaviors must be considered, and steps should be taken to ensure the independence of the behaviors selected. In addition, care must be taken to ensure equal difficulty of the responses assigned to different conditions.

Having reviewed the logic underlying SSED, the basic approach to analysis (visual inspection relying on observed changes in level, trend, and variability), and the core strategies for arranging conditions (i.e., design types), in the following section we briefly discuss a number of quantitative evaluation issues concerning SSED. The issues are germane because of the WWCH and related efforts to establish standard approaches for evaluating SSED data sets as well as the problem of whether and how to derive standardized effect sizes from SSED data sets for inclusion in quantitative syntheses (i.e., meta-analysis).

Evaluating Results in SSED Research

Statistical analysis and ssed.

The issue of when, if ever, the data generated from SSEDs should be statistically analyzed has a long and, at times, contentious history ( Iwata, Neef, Wacker, Mace, & Vollmer, 2000 ). We approach this issue by breaking it into four related but distinct parts that include detecting effects, determining their magnitude and the quality of the causal inference, and data-based decision making. Subsequently, relevant considerations for research and practice are delineated. Space considerations preclude treating any one aspect of this issue exhaustively (suggestions for further reading are provided).

Effect detection

Conventional approaches to single-subject data analysis rely on visual inspection (as reviewed earlier in this article). From the perspective of clinical significance, supporting a “visual inspection–only” approach is warranted because the practitioner (and, ultimately, the field of practice) is interested in identifying only those variables that lead to large, unambiguous changes in behavior. One argument against the exclusive reliance on visual inspection is that it is prone to Type 1 errors (inferring an effect when there is none), particularly if the effects are small to medium ( Franklin, Gorman, Beasley, & Allison, 1996 ; Todman & Dugard, 2001 ). Evidence for experimental control is not always as compelling from a visual analysis perspective. This was showcased in the Tincani et al. (2006) study discussed previously. In many cases, the clinical significance of behavior change between conditions is less clear and, therefore, is open to interpretation.

From the perspective of scientific significance, one can argue that statistical analysis may be warranted as a judgment aid for determining whether there were any effects, regardless of size, because knowing this would help determine whether to continue investigating the variable (i.e., intervention). If it is decided that, under some circumstances, it is scientifically sensible to use statistical analyses (e.g., t tests, analyses of variance [ANOVAs], etc.) as judgment aids for effect detection within single case data sets, the next question is a very practical one—can we? In other words, can parametric inferential statistical techniques be applied safely? In this context, the term safely refers to whether the outcome variables are sufficiently robust that they withstand violating the assumptions underlying the statistical test. The short answer seems to be “no,” with the qualifier “under almost all circumstances.” The key limitation and common criticism of generating statistics based on single-subject data is auto-correlation (any given data point is dependent or interacts with the data point preceding it). Because each data point is generated by the same person, the data points are not independent of one another (violating a core assumption of statistical analysis—technically, that the error terms are not independent of one another). Thus, performance represented in each data point may likely be influencing the next ( Todman & Dugard, 2001 ). Autocorrelated data will, in turn, artificially inflate p values and affect Type 1 error rates.

One argument for statistically analyzing single-subject data sets, mentioned above, is that visual inspection is prone to Type 1 error in the presence of medium to small effects ( Franklin et al., 1996 ). Unfortunately, the proposed solution of implementing conventional inferential statistical tests with single-subject data based on repeated measurement of the same subject is equally prone to Type 1 error because of autocorrelation. Traditional nonparametric approaches have been advocated, but they do not necessarily avoid the autocorrelation problem and, depending on the size of the data array, there are power issues. Alternatively, if single-subject data are regarded as time-series data, there have been some novel applications of bootstrapping methodologies relying on using the data set itself along with resampling approaches to determine exact probabilities rather than probability estimates ( Wilcox, 2001 ). For example, Borckardt et al. (2008) described a “simulation modeling analysis” for time-series data, which allows a statistical comparison between phases of a single-subject experiment while controlling for serial dependency in the data (i.e., quantifying the autocorrelation and modeling it in the analysis). In the end, effect detection is determined by data patterns in relation to the phases of the experimental design. It seems that the clearer one is about the logic of the design and the criteria that will be used to determine an effect in advance, the less one needs to rely on searching for a “just-in-case” test after the fact.

Magnitude of effect

An emphasis on accountability is embodied in the term evidence-based practice . One of the tools used to help answer the question of “what works” that forms the basis for the evidence in evidence-based practice is meta-analysis —the quantitative synthesis of studies from which standardized and weighted effect sizes can be derived. Meta-analysis methodology provides an objective estimate of the magnitude of an intervention's effect. One of the main problems of SSEDs is that the evidence generated is not always included in meta-analyses. Alternatively, if studies based on SSEDs are used in meta-analysis, there is no agreement on the correct metric to estimate and quantify the effect size.

An obvious corollary to the issue of effect magnitude is that visual inspection, per se—although sensitive to a range of holistic information embodied in a data display (trend, recurrent pattern, delayed/lagged response, variability, etc.; Parker & Hagan-Burke, 2007 )—does not generate a quantitative index of intervention strength (i.e., effect magnitude) that is recognizable to the broader scientific community. The determination of which practices and interventions are evidence based (and which will, therefore, be promoted and funded) increasingly involves quantitative synthesis of data and exposes the need for a single, agreed-upon effect size metric to reflect magnitude in SSEDs ( Parker, Hagan-Burke, & Vannest, 2007 ). Accordingly, the changing scientific standards across practice communities (e.g., ASHA, American Psychological Association, American Educational Research Association) are reflected in the organization's editorial policies and publication practices, which increasingly require effect sizes to be reported.

There has been a small but steady body of work addressing effect size calculation and interpretation for SSEDs. Space precludes an exhaustive review of all the metrics (for comprehensive reviews, see Parker & Hagan-Burke, 2007 , and related papers from this group). There are, however, a number of points that can be made regarding the use (derivation, interpretation) of effect size indices that are common to all. The simplest and most common effect size metric is the percentage of nonoverlapping data (PND; Scruggs, Mastropieri, & Casto, 1987 ). It is easy to calculate by hand and, therefore, is easily accessible to practitioners. The most extreme positive (the term positive is used in relation to the clinical problem being addressed; therefore, it could be the highest or lowest score) baseline data point is selected, from which a straight line is drawn across the intervention phase of the graph (for simplicity's sake, assume an AB-only design). Then, the number of data points that fall above (or below) the line is tallied and divided by the total number of intervention data points. If, for example, in a study of a treatment designed to improve (i.e., increase) communication fluency, eight of 10 data points in the intervention phase are greater in value than the largest baseline data point value, the resulting PND would equal 80%.

Although the clinical/educational appeal of such a metric seems obvious (easy to calculate, it is consistent with visual inspection of graphic data), there are potential problems with the approach. For example, there are ceiling effects for PND, making comparisons across or between interventions difficult ( Parker & Hagan-Burke, 2007 ; Parker et al., 2007 ), and PND is based on a single data point, making it sensitive to outliers ( Riley-Tillman & Burns, 2009 ). In addition, there is no known sampling distribution, making it impossible to derive a confidence interval (CI). CIs are important because they help create an interpretive context for the dependability of the effect by providing upper and lower bounds for the estimate. As a result, PND is a statistic of unknown reliability.

Most work on effect sizes for SSEDs has been conducted implicitly or explicitly to address the limits of PND. Some work has conserved the approach by continuing to calculate some form of descriptive degrees of overlap , including percentage of data points exceeding the median (PEM; Ma, 2006 ), percentage of zero data points (PZD; Johnson, Reichle, & Monn, 2009 ), and the percentage of all nonover-lapping data (PAND; Parker et al., 2007 ). Olive and Smith (2005) compared a set of descriptive effect size statistics (including a regression-based effect size, PND, standard mean difference, and mean baseline reduction) to visual analysis of several data sets and found that each consistently estimated relative effect size. Other investigators have attempted to integrate degree of overlap with general linear model approaches such as linear regression. The regression-based techniques (e.g., Gorman & Allison, 1996 , pp. 159–214) make use of predicted values derived from baseline data to remove the effects of trend (i.e., predicted values are subtracted from observed data). Subsequently, adjusted mean treatment scores can be used in calculating familiar effect size statistics (e.g., Cohen's d , Hedge's g ). This application may be more commonly accepted among those familiar with statistical procedures associated with group design.

As with each of the issues discussed in this section, there are advantages and disadvantages to the regression and non-regression methods for determining effect size for SSEDs. Nonregression methods involve simpler hand calculations, map on to visual inspection of the data, and are less biased in the presence of small numbers of observations ( Scruggs & Mastropieri, 1998 ). But, as recently argued by Wolery, Busick, Reichow, and Barton (2010) , the overlap approaches for calculating effect sizes do not produce metrics that adequately reflect magnitude (i.e., in cases where the intervention was effective and there is no overlap between baseline and treatment, the degree of the nonoverlap of the data—the magnitude—is not indexed by current overlap-based effect sizes). Regression methods are less sensitive to outliers, control for trend in the data, and may be more sensitive to detecting treatment effects in slope and intercept ( Gorman & Allison, 1996 ). As work in this area continues, novel effect size indices will likely emerge. Parker and Hagan-Burke (2007) , for example, demonstrated that the improvement rate difference metric (IRD—an index frequently used in evidenced-based medicine) was superior to both PND and PEM (it produces a CI and discriminates among cases [i.e., reduced floor/ceiling effects]) but conserved many of their clinically appealing features (hand calculation, based on nonoverlapping data) without requiring any major assumptions of the data.

Although effect sizes may not be a requirement for databased decision making for a given specific case—because the decision about effect is determined primarily by the degree of differentiation within the data set as ascertained through visual inspection and by the logical ordering of conditions (see also the Practice and data-based decisions section below)— their calculation and reporting may be worth considering with respect to changing publication standards and facilitating future meta-analyses. Note also that lost in the above discussion concerning effect size metrics is the issue of statistical versus clinical significance. Although one of the scientific goals of research is to discover functional relations between independent and dependent variables, the purpose of applied research is discovering the relations that lead to clinically meaningful outcomes (i.e., clinical significance; see Barlow & Hersen, 1973 ) or socially relevant behavior changes (i.e., social validity; see Wolf, 1978 ). From a practice perspective, one of the problems of statistical significance is that it can over- or underestimate clinical significance ( Chassan, 1979 ). In principle, the notion of quantifying how large (i.e., magnitude) of an effect was obtained is in keeping with the spirit of clinical significance and social validity, but the effect size interpretation should not blindly lead to assertions of clinically significant results divorced from judgments about whether the changes were clinically or socially meaningful.

Quality of inference

One of the great scientific strengths of SSEDs is the premium placed on internal validity and the reliance on effect replication within and across participants. One of the great clinical strengths of SSEDs is the ability to use a response-guided intervention approach such that phase or condition changes (i.e., changes in the independent variable) are made based on the behavior of the participant. This notion has a long legacy and reflects Skinner's (1948) early observation that the subject (“organism”) is always right. In contrast with these two strengths, there is a line of thinking that argues for incorporating randomization into SSEDs ( Kratochwill & Levin, 2009 ). This notion has a relatively long history ( Edgington, 1975 ) and continues to be mentioned in contemporary texts ( Todman & Dugard, 2001 ). The advantages and disadvantages of the practice are worth addressing (albeit briefly).

The argument for incorporating randomization into SSEDs is to further improve the quality of the causal inference (i.e., strengthening internal validity) by randomizing phase order or condition start times (there are numerous approaches to randomizing within SSEDs; see Kratochwill & Levin, 2009 , or almost any of Edgington's work). However, doing so comes at the cost of practitioner flexibility in making phase/condition changes based on patterns in the data (i.e., how the participant is responding). This cost, it is argued, is worth the expense because randomization is superior to replication for reducing plausible threats to internal validity. The within-series intervention conditions are compared in an unbiased (i.e., randomized) manner rather than in a manner that is researcher determined and, hence, prone to bias. The net effect is to further enhance the scientific credibility of the findings from SSEDs. At this point, it seems fair to conclude that it remains an open question about whether randomization is superior to replication with regard to producing clinically meaningful effects for any given participant in an SSED.

One potential additional advantage to incorporating randomization into an SSED is that the data series can be analyzed using randomization tests ( Bulte & Onghena, 2008 ; Edgington, 1996 ; Todman & Dugard, 2001 ) that leverage the ease and availability of computer-based resampling for likelihood estimation. Exact p values are generated, and the tests appear to be straightforward ways to supplement the visual analysis of single-subject data. It should be noted, however, that randomization tests in and of themselves do not necessarily address the problem of autocorrelation.

Practice and data-based decisions

Finally, related to several different comments in the preceding sections regarding practical significance, there is the issue of interpreting effects directly in relation to practice in terms of eventual empirically based decision making for a given client or participant. At issue here is not determining whether there was an effect and its standardized size but whether there is change in behavior or performance over time—and the rate of that change. Riley-Tillman and Burns (2009) argued that effect size estimates may make valuable contributions for future quantitative syntheses; however, for a given practitioner, data interpretation and subsequent practice decisions are driven more by slope changes, not by average effect sizes. Nontrivial practice issues, such as special education eligibility, entitlement decisions, and instructional modification, depend on repeated measurement of student growth (i.e., time series data) that is readily translatable into single-subject design logic with judgment aids in the form of numerical slope values and aim lines.

Key advantages of relying on visual inspection and quantifying slope are not only that student growth rates can be interpreted for an individual student in relation to an intervention but also that the growth rate values can be compared to a given student's respective grade or class (or other local norms). For a clear example, interested readers are referred to Silberglitt and Gibbons’ (2005) documentation of a slope-standard approach to identifying, intervening, and monitoring reading fluency and at-risk students. Of course, the approach (relying on slope values from serially collected single-subject data) is not without its problems. Depending on the frequency and duration of data collection, the standard error of the estimate for slope values can vary widely ( Christ, 2006 ), leading to interpretive problems for practice. Thus, consistent with all of the points made above, sound methodology (design, measurement) is the biggest determinant of valid decision making. Overall, the four issues discussed above—effect detection, magnitude of effect, quality of the inference, and practice decisions—reflect the critical dimensions involved in the analysis of SSED. The importance of any one dimension over the other will likely depend on the purpose of the study and the state of the scientific knowledge about the problem being addressed.

Conclusions

Unlike the research questions often addressed by studies using traditional group designs, studies employing SSEDs can address the effects that intervention strategies and environmental variables have on performance at the individual level. SSED methodology permits flexibility within a study to modify the independent variable when it does not lead to the desired or expected effect, and it does not compromise the integrity of the experimental design. As a result, SSED methodology provides a useful alternative to RCTs (and quasi-experimental group designs) for the goal of empirically demonstrating that an intervention is effective, or alternatively, determining the better of two or more potential interventions. SSEDs are ideal for both researchers and clinicians working with small or very heterogeneous populations in the development and implementation of evidence-based practice. The strong internal validity of well-implemented SSED studies allows for visual and, under some circumstances, statistical data analyses to support confident conclusions about—in the words of U.S. Department of Education—“what works.”

Kazdin (2010) , Horner et al. (2005) , and others have highlighted the issue of RCTs within traditional probabilistic group design research being favored among policymakers, granting agencies, and practitioners in the position of selecting interventions from the evidence base. They also highlight the important role that SSEDs can and should play in this process. The specific criteria developed by the WWCH panel emphasize the importance of strong experimental designs—and replication, if SSEDs are to be taken seriously as a tool within the establishment of evidence-based practice. Speech, language, and hearing interventions, by their nature, strive to improve outcomes for individual clients or research participants. Evaluating those interventions within SSEDs and associated visual and statistical data analyses lends rigor to clinical work, is logically and methodologically consistent with intervention research in the field, and can serve as a common framework for decision making with colleagues within and outside the CSD field.

American Speech-Language-Hearing Association Evidence-based practice in communication disorders [Position statement] 2005 Available from www.asha.org/policy .
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10.2 Single-Subject Research Designs

Learning objectives.

Describe the basic elements of a single-subject research design.
Design simple single-subject studies using reversal and multiple-baseline designs.
Explain how single-subject research designs address the issue of internal validity.
Interpret the results of simple single-subject studies based on the visual inspection of graphed data.

General Features of Single-Subject Designs

Before looking at any specific single-subject research designs, it will be helpful to consider some features that are common to most of them. Many of these features are illustrated in Figure 10.3 “Results of a Generic Single-Subject Study Illustrating Several Principles of Single-Subject Research” , which shows the results of a generic single-subject study. First, the dependent variable (represented on the y -axis of the graph) is measured repeatedly over time (represented by the x -axis) at regular intervals. Second, the study is divided into distinct phases, and the participant is tested under one condition per phase. The conditions are often designated by capital letters: A, B, C, and so on. Thus Figure 10.3 “Results of a Generic Single-Subject Study Illustrating Several Principles of Single-Subject Research” represents a design in which the participant was tested first in one condition (A), then tested in another condition (B), and finally retested in the original condition (A). (This is called a reversal design and will be discussed in more detail shortly.)

Figure 10.3 Results of a Generic Single-Subject Study Illustrating Several Principles of Single-Subject Research

Another important aspect of single-subject research is that the change from one condition to the next does not usually occur after a fixed amount of time or number of observations. Instead, it depends on the participant’s behavior. Specifically, the researcher waits until the participant’s behavior in one condition becomes fairly consistent from observation to observation before changing conditions. This is sometimes referred to as the steady state strategy (Sidman, 1960). The idea is that when the dependent variable has reached a steady state, then any change across conditions will be relatively easy to detect. Recall that we encountered this same principle when discussing experimental research more generally. The effect of an independent variable is easier to detect when the “noise” in the data is minimized.

Reversal Designs

The most basic single-subject research design is the reversal design , also called the ABA design . During the first phase, A, a baseline is established for the dependent variable. This is the level of responding before any treatment is introduced, and therefore the baseline phase is a kind of control condition. When steady state responding is reached, phase B begins as the researcher introduces the treatment. There may be a period of adjustment to the treatment during which the behavior of interest becomes more variable and begins to increase or decrease. Again, the researcher waits until that dependent variable reaches a steady state so that it is clear whether and how much it has changed. Finally, the researcher removes the treatment and again waits until the dependent variable reaches a steady state. This basic reversal design can also be extended with the reintroduction of the treatment (ABAB), another return to baseline (ABABA), and so on.

The study by Hall and his colleagues was an ABAB reversal design. Figure 10.4 “An Approximation of the Results for Hall and Colleagues’ Participant Robbie in Their ABAB Reversal Design” approximates the data for Robbie. The percentage of time he spent studying (the dependent variable) was low during the first baseline phase, increased during the first treatment phase until it leveled off, decreased during the second baseline phase, and again increased during the second treatment phase.

Figure 10.4 An Approximation of the Results for Hall and Colleagues’ Participant Robbie in Their ABAB Reversal Design

Why is the reversal—the removal of the treatment—considered to be necessary in this type of design? Why use an ABA design, for example, rather than a simpler AB design? Notice that an AB design is essentially an interrupted time-series design applied to an individual participant. Recall that one problem with that design is that if the dependent variable changes after the treatment is introduced, it is not always clear that the treatment was responsible for the change. It is possible that something else changed at around the same time and that this extraneous variable is responsible for the change in the dependent variable. But if the dependent variable changes with the introduction of the treatment and then changes back with the removal of the treatment, it is much clearer that the treatment (and removal of the treatment) is the cause. In other words, the reversal greatly increases the internal validity of the study.

There are close relatives of the basic reversal design that allow for the evaluation of more than one treatment. In a multiple-treatment reversal design , a baseline phase is followed by separate phases in which different treatments are introduced. For example, a researcher might establish a baseline of studying behavior for a disruptive student (A), then introduce a treatment involving positive attention from the teacher (B), and then switch to a treatment involving mild punishment for not studying (C). The participant could then be returned to a baseline phase before reintroducing each treatment—perhaps in the reverse order as a way of controlling for carryover effects. This particular multiple-treatment reversal design could also be referred to as an ABCACB design.

Multiple-Baseline Designs

One solution to these problems is to use a multiple-baseline design , which is represented in Figure 10.5 “Results of a Generic Multiple-Baseline Study” . In one version of the design, a baseline is established for each of several participants, and the treatment is then introduced for each one. In essence, each participant is tested in an AB design. The key to this design is that the treatment is introduced at a different time for each participant. The idea is that if the dependent variable changes when the treatment is introduced for one participant, it might be a coincidence. But if the dependent variable changes when the treatment is introduced for multiple participants—especially when the treatment is introduced at different times for the different participants—then it is extremely unlikely to be a coincidence.

Figure 10.5 Results of a Generic Multiple-Baseline Study

Results of a Generic Multiple-Baseline Study: The multiple baselines can be for different participants, dependent variables, or settings. The treatment is introduced at a different time on each baseline

The multiple baselines can be for different participants, dependent variables, or settings. The treatment is introduced at a different time on each baseline.

As an example, consider a study by Scott Ross and Robert Horner (Ross & Horner, 2009). They were interested in how a school-wide bullying prevention program affected the bullying behavior of particular problem students. At each of three different schools, the researchers studied two students who had regularly engaged in bullying. During the baseline phase, they observed the students for 10-minute periods each day during lunch recess and counted the number of aggressive behaviors they exhibited toward their peers. (The researchers used handheld computers to help record the data.) After 2 weeks, they implemented the program at one school. After 2 more weeks, they implemented it at the second school. And after 2 more weeks, they implemented it at the third school. They found that the number of aggressive behaviors exhibited by each student dropped shortly after the program was implemented at his or her school. Notice that if the researchers had only studied one school or if they had introduced the treatment at the same time at all three schools, then it would be unclear whether the reduction in aggressive behaviors was due to the bullying program or something else that happened at about the same time it was introduced (e.g., a holiday, a television program, a change in the weather). But with their multiple-baseline design, this kind of coincidence would have to happen three separate times—a very unlikely occurrence—to explain their results.

Data Analysis in Single-Subject Research

In visually inspecting their data, single-subject researchers take several factors into account. One of them is changes in the level of the dependent variable from condition to condition. If the dependent variable is much higher or much lower in one condition than another, this suggests that the treatment had an effect. A second factor is trend , which refers to gradual increases or decreases in the dependent variable across observations. If the dependent variable begins increasing or decreasing with a change in conditions, then again this suggests that the treatment had an effect. It can be especially telling when a trend changes directions—for example, when an unwanted behavior is increasing during baseline but then begins to decrease with the introduction of the treatment. A third factor is latency , which is the time it takes for the dependent variable to begin changing after a change in conditions. In general, if a change in the dependent variable begins shortly after a change in conditions, this suggests that the treatment was responsible.

In the top panel of Figure 10.6 , there are fairly obvious changes in the level and trend of the dependent variable from condition to condition. Furthermore, the latencies of these changes are short; the change happens immediately. This pattern of results strongly suggests that the treatment was responsible for the changes in the dependent variable. In the bottom panel of Figure 10.6 , however, the changes in level are fairly small. And although there appears to be an increasing trend in the treatment condition, it looks as though it might be a continuation of a trend that had already begun during baseline. This pattern of results strongly suggests that the treatment was not responsible for any changes in the dependent variable—at least not to the extent that single-subject researchers typically hope to see.

Figure 10.6

Visual inspection of the data suggests an effective treatment in the top panel but an ineffective treatment in the bottom panel.

The results of single-subject research can also be analyzed using statistical procedures—and this is becoming more common. There are many different approaches, and single-subject researchers continue to debate which are the most useful. One approach parallels what is typically done in group research. The mean and standard deviation of each participant’s responses under each condition are computed and compared, and inferential statistical tests such as the t test or analysis of variance are applied (Fisch, 2001). (Note that averaging across participants is less common.) Another approach is to compute the percentage of nonoverlapping data (PND) for each participant (Scruggs & Mastropieri, 2001). This is the percentage of responses in the treatment condition that are more extreme than the most extreme response in a relevant control condition. In the study of Hall and his colleagues, for example, all measures of Robbie’s study time in the first treatment condition were greater than the highest measure in the first baseline, for a PND of 100%. The greater the percentage of nonoverlapping data, the stronger the treatment effect. Still, formal statistical approaches to data analysis in single-subject research are generally considered a supplement to visual inspection, not a replacement for it.

Key Takeaways

Single-subject research designs typically involve measuring the dependent variable repeatedly over time and changing conditions (e.g., from baseline to treatment) when the dependent variable has reached a steady state. This approach allows the researcher to see whether changes in the independent variable are causing changes in the dependent variable.
In a reversal design, the participant is tested in a baseline condition, then tested in a treatment condition, and then returned to baseline. If the dependent variable changes with the introduction of the treatment and then changes back with the return to baseline, this provides strong evidence of a treatment effect.
In a multiple-baseline design, baselines are established for different participants, different dependent variables, or different settings—and the treatment is introduced at a different time on each baseline. If the introduction of the treatment is followed by a change in the dependent variable on each baseline, this provides strong evidence of a treatment effect.
Single-subject researchers typically analyze their data by graphing them and making judgments about whether the independent variable is affecting the dependent variable based on level, trend, and latency.

Practice: Design a simple single-subject study (using either a reversal or multiple-baseline design) to answer the following questions. Be sure to specify the treatment, operationally define the dependent variable, decide when and where the observations will be made, and so on.

Does positive attention from a parent increase a child’s toothbrushing behavior?
Does self-testing while studying improve a student’s performance on weekly spelling tests?
Does regular exercise help relieve depression?
Practice: Create a graph that displays the hypothetical results for the study you designed in Exercise 1. Write a paragraph in which you describe what the results show. Be sure to comment on level, trend, and latency.

Fisch, G. S. (2001). Evaluating data from behavioral analysis: Visual inspection or statistical models. Behavioural Processes , 54 , 137–154.

Ross, S. W., & Horner, R. H. (2009). Bully prevention in positive behavior support. Journal of Applied Behavior Analysis , 42 , 747–759.

Scruggs, T. E., & Mastropieri, M. A. (2001). How to summarize single-participant research: Ideas and applications. Exceptionality , 9 , 227–244.

Sidman, M. (1960). Tactics of scientific research: Evaluating experimental data in psychology . Boston, MA: Authors Cooperative.

Research Methods in Psychology Copyright © 2016 by University of Minnesota is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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What is ABA and ABAB Design in Applied Behavior Analysis?

Psychology has been criticized for many years as an inexact science. Critics say its weakness is that it doesn’t rely on empirical data. The introduction of different types of ABA research designs have done much to dispel that idea. The ABA and ABAB design are especially useful in applied behavioral analysis (ABA) as they help therapists identify and concentrate on interventions that are successful. Therapists can avoid wasting time with strategies that do little to alter behavior.

Related resource: Top 20 Online Applied Behavior Analysis Bachelor’s Degree and BCaBA Coursework Programs

This model is a form of a research protocol called Single Subject Experimental Design (SSED). Single Subject Research Designs are common in special education and in clinical settings. In a SSED, the individual serves as their own control. Their performance is not compared to a group or another individual.

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ABAB and ABA are not acronyms as such but refer to the stages of the model.

“A” is the dependent variable. It represents the initial unaltered behavior, and that becomes a baseline for the study.
“B” is the independent variable or the treatment phase

The rationale behind a single subject designs are:

Verification
Replication

Even though an SSED implies there is only one subject, in a research study, there are many different subjects using the same design. It is still considered a single subject design though since the individual is their own control.

In a basic AB design psychology experiment, there is a baseline (A) and an intervention (B). If A changes after the implementation of B, a researcher could conclude that B caused a change in A. Unfortunately, this is oversimplified thinking, and a strong conclusion is difficult to make. The AB design does a poor job of controlling for threats to internal validity.

So, in an ABA research design , the initial behavior is altered by the intervention and then the intervention is withdrawn to see if the behavior returns to the baseline level. This is also known as a reversal design. If the dependent variable changes when the intervention takes place and then returns to baseline, there is further evidence of a treatment effect. Since the ABA design has a high degree of experimental control, there is confidence that treatment effects are actually the result of the treatment and not something else.

ABAB Design

The ABAB design is the reintroduction of the intervention after the return to the baseline to judge the strength of the intervention and determine if there is a functional relationship between A and B. The ABAB design definition includes:

A- Baseline period and data collection
B- Intervention
A- Removal of the intervention, back to baseline
B- Introduction of the intervention again

Some interventions may increase over time while others grow weaker as the person being studied becomes accustomed to the intervention.

The ABAB design can be considered a type of time-series design. This means researchers can use the same statistical procedures with ABAB that they do with a time series analysis.

Related Resource: Understanding the Difference between an ABA Therapist and a BCBA

How the ABA Model is Used

These research methods are also by therapists to discover treatments for patients with target behavior that affects their life activities. It is especially helpful when working with individuals with intellectual and developmental disabilities. It is also used in the treatment of individuals with autism spectrum disorder because it isolates one behavior to address.

An example cited in one article is that of children asked to read a paragraph that included text only. The children were tested on their understanding of the information. Then, another paragraph including an illustration was given to the children to read. Again, they were tested to see if their level of understanding increased. Finally, they were given another paragraph that contained only text and retested to see if their grasp of the information returned to the initial test results. Using the ABA design, the therapist can evaluate the effects of treatment related to baseline responding.

According to an article in the US National Library of Medicine , the primary requirement to judge the effectiveness of this model is the ability of the researcher to replicate the results. A study of the same behavior in several different people should elicit the same results. That replication becomes the basis for identifying the intervention as a universal method of treatment.

How the ABAB Model is Used

An ABAB reversal design can also work when trying an intervention to help reduce self-injurious behavior. The individual engages in hair pulling and biting. After the initial baseline phase, the therapist begins the intervention program. The therapist continues to collect data on the self injurious behavior. The therapist then stops the intervention phase, but still continues to collect data on the same behavior. Finally, the therapist reintroduces the intervention and completes their statistical analysis. If the behavior improves with the intervention and reverts back to the initial baseline numbers when the intervention is removed, then it is easy to verify treatment effects on the behavior. The intended behavior modification is likely strengthened. This type of experiment can also be used for anxiety disorders and feeding disorders.

Advantages of ABA and ABAB Design in Applied Behavior Analysis

The ABA design psychology experiment allows researchers to isolate one behavior for study and intervention. That decreases the chances of other variables influencing the results. It is also a simple way to assess an intervention. If only one thing is changing at a time, it is easy to decipher if an intervention is working. If the behavior doesn’t after the intervention is removed, then something else must be causing the change in behavior. The design is pretty straightforward. The model allows therapists to identify successful interventions quickly.

The main advantage of the ABAB model is that it ends “on a positive note” with the intervention in place instead of with its withdrawal. Another advantage is that the ABAB design psychology experiment has an additional piece of experimental control with the reintroduction of the intervention at the end of the study. Some researchers believe ABAB is a stronger design since it has multiple reversals.

Disadvantages

One of the major drawbacks to this model is contained in the question, “what if the behavior does not change with the intervention?” In the Randomized Control Trials, that outcome would be supported by similar findings among many people, but the lack of results invalidates a study of one individual. For instance, the researcher would not know if other variables had been introduced.

The other major disadvantage is the ethical problem of identifying a successful intervention and then withdrawing it. The ABA and ABAB design can’t be used with variables that could cause irreversible effects. It also can’t be used when it would be unethical or unsafe for an individual to revert back to their baseline condition. It can also be hard to rule out a history effect if the dependent variable doesn’t return to its original state when the treatment or therapy is removed.

Fortunately, there are options when an ABA or ABAB design isn’t feasible. A multiple baseline design can be used when there is more than one individual or behavior in need of treatment. This design can also be used if the effects of the independent variable can’t be reversed. The alternating treatments design can be used when you want to determine the effectiveness of more than one treatment. The changing conditions design can be used to study the effect of two or more treatments on the behavior of an individual.

Conclusion

Behavioral analysis is a therapy used with people of different ages and cognitive abilities. Often, therapists work with a patient for a long time to find an intervention that succeeds in modifying a troublesome behavior. The use of the ABA and the ABAB models can shorten the time of treatment and increase the chances of a good outcome for clients of mental health practitioners.

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Single-Subject Research Designs

Rajiv S. Jhangiani; I-Chant A. Chiang; Carrie Cuttler; and Dana C. Leighton

Learning Objectives

Describe the basic elements of a single-subject research design.
Design simple single-subject studies using reversal and multiple-baseline designs.
Explain how single-subject research designs address the issue of internal validity.
Interpret the results of simple single-subject studies based on the visual inspection of graphed data.

General Features of Single-Subject Designs

Before looking at any specific single-subject research designs, it will be helpful to consider some features that are common to most of them. Many of these features are illustrated in Figure 10.1, which shows the results of a generic single-subject study. First, the dependent variable (represented on the y -axis of the graph) is measured repeatedly over time (represented by the x -axis) at regular intervals. Second, the study is divided into distinct phases, and the participant is tested under one condition per phase. The conditions are often designated by capital letters: A, B, C, and so on. Thus Figure 10.1 represents a design in which the participant was tested first in one condition (A), then tested in another condition (B), and finally retested in the original condition (A). (This is called a reversal design and will be discussed in more detail shortly.)

Another important aspect of single-subject research is that the change from one condition to the next does not usually occur after a fixed amount of time or number of observations. Instead, it depends on the participant’s behavior. Specifically, the researcher waits until the participant’s behavior in one condition becomes fairly consistent from observation to observation before changing conditions. This is sometimes referred to as the steady state strategy (Sidman, 1960) [1] . The idea is that when the dependent variable has reached a steady state, then any change across conditions will be relatively easy to detect. Recall that we encountered this same principle when discussing experimental research more generally. The effect of an independent variable is easier to detect when the “noise” in the data is minimized.

Reversal Designs

The most basic single-subject research design is the reversal design , also called the ABA design . During the first phase, A, a baseline is established for the dependent variable. This is the level of responding before any treatment is introduced, and therefore the baseline phase is a kind of control condition. When steady state responding is reached, phase B begins as the researcher introduces the treatment. There may be a period of adjustment to the treatment during which the behavior of interest becomes more variable and begins to increase or decrease. Again, the researcher waits until that dependent variable reaches a steady state so that it is clear whether and how much it has changed. Finally, the researcher removes the treatment and again waits until the dependent variable reaches a steady state. This basic reversal design can also be extended with the reintroduction of the treatment (ABAB), another return to baseline (ABABA), and so on.

There are close relatives of the basic reversal design that allow for the evaluation of more than one treatment. In a multiple-treatment reversal design , a baseline phase is followed by separate phases in which different treatments are introduced. For example, a researcher might establish a baseline of studying behavior for a disruptive student (A), then introduce a treatment involving positive attention from the teacher (B), and then switch to a treatment involving mild punishment for not studying (C). The participant could then be returned to a baseline phase before reintroducing each treatment—perhaps in the reverse order as a way of controlling for carryover effects. This particular multiple-treatment reversal design could also be referred to as an ABCACB design.

Multiple-Baseline Designs

There are two potential problems with the reversal design—both of which have to do with the removal of the treatment. One is that if a treatment is working, it may be unethical to remove it. For example, if a treatment seemed to reduce the incidence of self-injury in a child with an intellectual delay, it would be unethical to remove that treatment just to show that the incidence of self-injury increases. The second problem is that the dependent variable may not return to baseline when the treatment is removed. For example, when positive attention for studying is removed, a student might continue to study at an increased rate. This could mean that the positive attention had a lasting effect on the student’s studying, which of course would be good. But it could also mean that the positive attention was not really the cause of the increased studying in the first place. Perhaps something else happened at about the same time as the treatment—for example, the student’s parents might have started rewarding him for good grades. One solution to these problems is to use a multiple-baseline design , which is represented in Figure 10.3. There are three different types of multiple-baseline designs which we will now consider.

Multiple-Baseline Design Across Participants

As an example, consider a study by Scott Ross and Robert Horner (Ross & Horner, 2009) [2] . They were interested in how a school-wide bullying prevention program affected the bullying behavior of particular problem students. At each of three different schools, the researchers studied two students who had regularly engaged in bullying. During the baseline phase, they observed the students for 10-minute periods each day during lunch recess and counted the number of aggressive behaviors they exhibited toward their peers. After 2 weeks, they implemented the program at one school. After 2 more weeks, they implemented it at the second school. And after 2 more weeks, they implemented it at the third school. They found that the number of aggressive behaviors exhibited by each student dropped shortly after the program was implemented at the student’s school. Notice that if the researchers had only studied one school or if they had introduced the treatment at the same time at all three schools, then it would be unclear whether the reduction in aggressive behaviors was due to the bullying program or something else that happened at about the same time it was introduced (e.g., a holiday, a television program, a change in the weather). But with their multiple-baseline design, this kind of coincidence would have to happen three separate times—a very unlikely occurrence—to explain their results.

Multiple-Baseline Design Across Behaviors

Multiple-Baseline Design Across Settings

Data Analysis in Single-Subject Research

In addition to its focus on individual participants, single-subject research differs from group research in the way the data are typically analyzed. As we have seen throughout the book, group research involves combining data across participants. Group data are described using statistics such as means, standard deviations, correlation coefficients, and so on to detect general patterns. Finally, inferential statistics are used to help decide whether the result for the sample is likely to generalize to the population. Single-subject research, by contrast, relies heavily on a very different approach called visual inspection . This means plotting individual participants’ data as shown throughout this chapter, looking carefully at those data, and making judgments about whether and to what extent the independent variable had an effect on the dependent variable. Inferential statistics are typically not used.

In visually inspecting their data, single-subject researchers take several factors into account. One of them is changes in the level of the dependent variable from condition to condition. If the dependent variable is much higher or much lower in one condition than another, this suggests that the treatment had an effect. A second factor is trend , which refers to gradual increases or decreases in the dependent variable across observations. If the dependent variable begins increasing or decreasing with a change in conditions, then again this suggests that the treatment had an effect. It can be especially telling when a trend changes directions—for example, when an unwanted behavior is increasing during baseline but then begins to decrease with the introduction of the treatment. A third factor is latency , which is the time it takes for the dependent variable to begin changing after a change in conditions. In general, if a change in the dependent variable begins shortly after a change in conditions, this suggests that the treatment was responsible.

The results of single-subject research can also be analyzed using statistical procedures—and this is becoming more common. There are many different approaches, and single-subject researchers continue to debate which are the most useful. One approach parallels what is typically done in group research. The mean and standard deviation of each participant’s responses under each condition are computed and compared, and inferential statistical tests such as the t test or analysis of variance are applied (Fisch, 2001) [3] . (Note that averaging across participants is less common.) Another approach is to compute the percentage of non-overlapping data (PND) for each participant (Scruggs & Mastropieri, 2001) [4] . This is the percentage of responses in the treatment condition that are more extreme than the most extreme response in a relevant control condition. In the study of Hall and his colleagues, for example, all measures of Robbie’s study time in the first treatment condition were greater than the highest measure in the first baseline, for a PND of 100%. The greater the percentage of non-overlapping data, the stronger the treatment effect. Still, formal statistical approaches to data analysis in single-subject research are generally considered a supplement to visual inspection, not a replacement for it.

Image Description

Sidman, M. (1960). Tactics of scientific research: Evaluating experimental data in psychology . Boston, MA: Authors Cooperative. ↵
Ross, S. W., & Horner, R. H. (2009). Bully prevention in positive behavior support. Journal of Applied Behavior Analysis, 42 , 747–759. ↵
Fisch, G. S. (2001). Evaluating data from behavioral analysis: Visual inspection or statistical models. Behavioral Processes, 54 , 137–154. ↵
Scruggs, T. E., & Mastropieri, M. A. (2001). How to summarize single-participant research: Ideas and applications. Exceptionality, 9 , 227–244. ↵

When the researcher waits until the participant’s behavior in one condition becomes fairly consistent from observation to observation before changing conditions.

Another term for reversal design.

The beginning phase of an ABA design which acts as a kind of control condition in which the level of responding before any treatment is introduced.

In this design the baseline phase is followed by separate phases in which different treatments are introduced.

In this design two or more treatments are alternated relatively quickly on a regular schedule.

In this design, multiple baselines are either established for one participant or one baseline is established for many participants.

This is the percentage of responses in the treatment condition that are more extreme than the most extreme response in a relevant control condition.

Single-Subject Research Designs Copyright © 2022 by Rajiv S. Jhangiani; I-Chant A. Chiang; Carrie Cuttler; and Dana C. Leighton is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Developing ash-free high-strength spherical carbon catalyst supports

Domestic Catalysts
Published: 28 June 2013
Volume 5 , pages 156–163, ( 2013 )

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V. V. Gur’yanov 1 ,
V. M. Mukhin 1 &
A. A. Kurilkin 1

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The possibility of using furfurol for the production of ash-free high-strength active carbons with spheroidal particles as adsorbents and catalyst supports is substantiated. A single-stage process that incorporates the resinification of furfurol, the molding of a spherical product, and its hardening while allowing the process cycle time and the cost of equipment to be reduced is developed. Derivatographic, X-ray diffraction, mercury porometric, and adsorption studies of the carbonization of the molded spherical product are performed to characterize the development of the primary and porous structures of carbon residues. Ash-free active carbons with spheroidal particles, a full volume of sorbing micro- and mesopores (up to 1.50 cm 3 /g), and a uniquely high mechanical strength (its abrasion rate is three orders of magnitude lower than that of industrial active carbons) are obtained via the vapor-gas activation of a carbonized product. The obtained active carbons are superior to all known foreign and domestic analogues and are promising for the production of catalysts that operate under severe regimes, i.e., in moving and fluidized beds.

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Optimization of the preparation conditions for cocoa shell-based activated carbon and its evaluation as salts adsorbent material

A. Y. León, J. R. Rincón, … D. R. Molina

Carbon adsorbents for methane storage: genesis, synthesis, porosity, adsorption

Ilya Men’shchikov, Andrey Shiryaev, … Anatoly Fomkin

Hierarchical nanostructured carbons as CO2 adsorbents

Kiara Montiel-Centeno, Deicy Barrera, … Karim Sapag

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10.2: Single-Subject Research Designs

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Learning Objectives

Describe the basic elements of a single-subject research design.
Design simple single-subject studies using reversal and multiple-baseline designs.
Explain how single-subject research designs address the issue of internal validity.
Interpret the results of simple single-subject studies based on the visual inspection of graphed data.

General Features of Single-Subject Designs

Before looking at any specific single-subject research designs, it will be helpful to consider some features that are common to most of them. Many of these features are illustrated in Figure \(\PageIndex{1}\), which shows the results of a generic single-subject study. First, the dependent variable (represented on the y -axis of the graph) is measured repeatedly over time (represented by the x -axis) at regular intervals. Second, the study is divided into distinct phases , and the participant is tested under one condition per phase. The conditions are often designated by capital letters: A, B, C, and so on. Thus Figure \(\PageIndex{1}\) represents a design in which the participant was tested first in one condition (A), then tested in another condition (B), and finally retested in the original condition (A). (This is called a reversal design and will be discussed in more detail shortly.)

Another important aspect of single-subject research is that the change from one condition to the next does not usually occur after a fixed amount of time or number of observations. Instead, it depends on the participant’s behavior. Specifically, the researcher waits until the participant’s behavior in one condition becomes fairly consistent from observation to observation before changing conditions. This is sometimes referred to as the steady state strategy (Sidman, 1960) [1] . The idea is that when the dependent variable has reached a steady state, then any change across conditions will be relatively easy to detect. Recall that we encountered this same principle when discussing experimental research more generally. The effect of an independent variable is easier to detect when the “noise” in the data is minimized.

Reversal Designs

The most basic single-subject research design is the reversal design , also called the ABA design . During the first phase, A, a baseline is established for the dependent variable. This is the level of responding before any treatment is introduced, and therefore the baseline phase is a kind of control condition. When steady state responding is reached, phase B begins as the researcher introduces the treatment. There may be a period of adjustment to the treatment during which the behavior of interest becomes more variable and begins to increase or decrease. Again, the researcher waits until that dependent variable reaches a steady state so that it is clear whether and how much it has changed. Finally, the researcher removes the treatment and again waits until the dependent variable reaches a steady state. This basic reversal design can also be extended with the reintroduction of the treatment (ABAB), another return to baseline (ABABA), and so on.

The study by Hall and his colleagues employed an ABAB reversal design. Figure \(\PageIndex{2}\) approximates the data for Robbie. The percentage of time he spent studying (the dependent variable) was low during the first baseline phase, increased during the first treatment phase until it leveled off, decreased during the second baseline phase, and again increased during the second treatment phase.

There are close relatives of the basic reversal design that allow for the evaluation of more than one treatment. In a multiple-treatment reversal design , a baseline phase is followed by separate phases in which different treatments are introduced. For example, a researcher might establish a baseline of studying behavior for a disruptive student (A), then introduce a treatment involving positive attention from the teacher (B), and then switch to a treatment involving mild punishment for not studying (C). The participant could then be returned to a baseline phase before reintroducing each treatment—perhaps in the reverse order as a way of controlling for carryover effects. This particular multiple-treatment reversal design could also be referred to as an ABCACB design.

Multiple-Baseline Designs

There are two potential problems with the reversal design—both of which have to do with the removal of the treatment. One is that if a treatment is working, it may be unethical to remove it. For example, if a treatment seemed to reduce the incidence of self-injury in a child with an intellectual delay, it would be unethical to remove that treatment just to show that the incidence of self-injury increases. The second problem is that the dependent variable may not return to baseline when the treatment is removed. For example, when positive attention for studying is removed, a student might continue to study at an increased rate. This could mean that the positive attention had a lasting effect on the student’s studying, which of course would be good. But it could also mean that the positive attention was not really the cause of the increased studying in the first place. Perhaps something else happened at about the same time as the treatment—for example, the student’s parents might have started rewarding him for good grades. One solution to these problems is to use a multiple-baseline design , which is represented in Figure \(\PageIndex{3}\). There are three different types of multiple-baseline designs which we will now consider.

Multiple-Baseline Design Across Participants

As an example, consider a study by Scott Ross and Robert Horner (Ross & Horner, 2009) [2] . They were interested in how a school-wide bullying prevention program affected the bullying behavior of particular problem students. At each of three different schools, the researchers studied two students who had regularly engaged in bullying. During the baseline phase, they observed the students for 10-minute periods each day during lunch recess and counted the number of aggressive behaviors they exhibited toward their peers. After 2 weeks, they implemented the program at one school. After 2 more weeks, they implemented it at the second school. And after 2 more weeks, they implemented it at the third school. They found that the number of aggressive behaviors exhibited by each student dropped shortly after the program was implemented at his or her school. Notice that if the researchers had only studied one school or if they had introduced the treatment at the same time at all three schools, then it would be unclear whether the reduction in aggressive behaviors was due to the bullying program or something else that happened at about the same time it was introduced (e.g., a holiday, a television program, a change in the weather). But with their multiple-baseline design, this kind of coincidence would have to happen three separate times—a very unlikely occurrence—to explain their results.

Multiple-Baseline Design Across Behaviors

Multiple-Baseline Design Across Settings

Data Analysis in Single-Subject Research

In addition to its focus on individual participants, single-subject research differs from group research in the way the data are typically analyzed. As we have seen throughout the book, group research involves combining data across participants. Group data are described using statistics such as means, standard deviations, correlation coefficients, and so on to detect general patterns. Finally, inferential statistics are used to help decide whether the result for the sample is likely to generalize to the population. Single-subject research, by contrast, relies heavily on a very different approach called visual inspection . This means plotting individual participants’ data as shown throughout this chapter, looking carefully at those data, and making judgments about whether and to what extent the independent variable had an effect on the dependent variable. Inferential statistics are typically not used.

In visually inspecting their data, single-subject researchers take several factors into account. One of them is changes in the level of the dependent variable from condition to condition. If the dependent variable is much higher or much lower in one condition than another, this suggests that the treatment had an effect. A second factor is trend , which refers to gradual increases or decreases in the dependent variable across observations. If the dependent variable begins increasing or decreasing with a change in conditions, then again this suggests that the treatment had an effect. It can be especially telling when a trend changes directions—for example, when an unwanted behavior is increasing during baseline but then begins to decrease with the introduction of the treatment. A third factor is latency , which is the time it takes for the dependent variable to begin changing after a change in conditions. In general, if a change in the dependent variable begins shortly after a change in conditions, this suggests that the treatment was responsible.

In the top panel of Figure \(\PageIndex{4}\), there are fairly obvious changes in the level and trend of the dependent variable from condition to condition. Furthermore, the latencies of these changes are short; the change happens immediately. This pattern of results strongly suggests that the treatment was responsible for the changes in the dependent variable. In the bottom panel of Figure \(\PageIndex{4}\), however, the changes in level are fairly small. And although there appears to be an increasing trend in the treatment condition, it looks as though it might be a continuation of a trend that had already begun during baseline. This pattern of results strongly suggests that the treatment was not responsible for any changes in the dependent variable—at least not to the extent that single-subject researchers typically hope to see.

The results of single-subject research can also be analyzed using statistical procedures—and this is becoming more common. There are many different approaches, and single-subject researchers continue to debate which are the most useful. One approach parallels what is typically done in group research. The mean and standard deviation of each participant’s responses under each condition are computed and compared, and inferential statistical tests such as the t test or analysis of variance are applied (Fisch, 2001) [3] . (Note that averaging across participants is less common.) Another approach is to compute the percentage of non-overlapping data (PND) for each participant (Scruggs & Mastropieri, 2001) [4] . This is the percentage of responses in the treatment condition that are more extreme than the most extreme response in a relevant control condition. In the study of Hall and his colleagues, for example, all measures of Robbie’s study time in the first treatment condition were greater than the highest measure in the first baseline, for a PND of 100%. The greater the percentage of non-overlapping data, the stronger the treatment effect. Still, formal statistical approaches to data analysis in single-subject research are generally considered a supplement to visual inspection, not a replacement for it.

Key Takeaways

Single-subject research designs typically involve measuring the dependent variable repeatedly over time and changing conditions (e.g., from baseline to treatment) when the dependent variable has reached a steady state. This approach allows the researcher to see whether changes in the independent variable are causing changes in the dependent variable.
In a reversal design, the participant is tested in a baseline condition, then tested in a treatment condition, and then returned to baseline. If the dependent variable changes with the introduction of the treatment and then changes back with the return to baseline, this provides strong evidence of a treatment effect.
In a multiple-baseline design, baselines are established for different participants, different dependent variables, or different settings—and the treatment is introduced at a different time on each baseline. If the introduction of the treatment is followed by a change in the dependent variable on each baseline, this provides strong evidence of a treatment effect.
Single-subject researchers typically analyze their data by graphing them and making judgments about whether the independent variable is affecting the dependent variable based on level, trend, and latency.
Does positive attention from a parent increase a child’s tooth-brushing behavior?
Does self-testing while studying improve a student’s performance on weekly spelling tests?
Does regular exercise help relieve depression?
Practice: Create a graph that displays the hypothetical results for the study you designed in Exercise 1. Write a paragraph in which you describe what the results show. Be sure to comment on level, trend, and latency.
Sidman, M. (1960). Tactics of scientific research: Evaluating experimental data in psychology . Boston, MA: Authors Cooperative.
Ross, S. W., & Horner, R. H. (2009). Bully prevention in positive behavior support. Journal of Applied Behavior Analysis, 42 , 747–759.
Fisch, G. S. (2001). Evaluating data from behavioral analysis: Visual inspection or statistical models. Behavioral Processes, 54 , 137–154.
Scruggs, T. E., & Mastropieri, M. A. (2001). How to summarize single-participant research: Ideas and applications. Exceptionality, 9 , 227–244.

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Home
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/ Vladimir Soloviev, prophet of Russia's conversion

VLADIMIR SOLOVIEV prophet of Russia’s conversion

Vladimir Soloviev, à l'âge de vingt ans.

T HE conversion of Russia will not be the work of man, no matter how gifted he may be, but that of the Immaculate Heart of the Virgin Mary, the Mediatrix of all graces, because this is God’s wish, which he revealed to the world in 1917. The life and works of Vladimir Soloviev are a perfect illustration of this truth of Fatima. He whom our Father regards as « the greatest Russian genius of the 19th century », was in his own way a prophet of the “ conversion ” of his beloved Country, announcing the necessity of her returning to the bosom of the Roman Church. « Rome or chaos », such was his catchphrase, Rome whose anagram is not a matter of chance, but a providential sign, a definition: ROMA , AMOR . Led by this incomparable guide, we would like « to anticipate in our thoughts, our hearts and our prayers this consecration, this long-awaited conversion, which must mark the beginning of a time of sacred peace throughout the world, the beginning of the universal reign of the Most Blessed and Immaculate Heart of Mary, and through Her, of God’s Kingdom » (English CRC, December 1982, p. 23).

A PERSONAL CONVERSION

Through the example of his life, Soloviev recalls the indispensable means of this immense work: self-renunciation, personal and collective sacrifice, in Russian the podwig , the only way in which the Church, nations, saints and heroes can become the instruments of God’s designs. If he managed to surpass his master Dostoyevsky by his « truly universal Catholicism and far superior mystical vision », this was not without without a conversion of mind and heart on his part.

Our Father summarises the principal stages of his life as follows: « Born of an honourable Muscovite family, of part Kievian ancestry, Vladimir Soloviev began, in a world where only Germany counted, by being a victim of all the poisons of the West. He himself relates how he was a zealous materialist at the age of thirteen, had read Renan’s Life of Jesus at fifteen, and had become an evolutionist and therefore (!) an atheist and a nihilist at eighteen, in « It was Spinoza and then Schopenhauer who pulled him out of this bottomless void. Whereupon in 1872 a mysterious encounter with “  Wisdom  ” suddenly shook him out of the scientific naturalism in which he had been vegetating and made him aware, as he says, of invisible Beauty, the “  Sophia tou théou  ”, the daughter of God. He thus became the fervent witness of Wisdom’s indwelling in the world and of Her desire for total incarnation and universal queenship. His quest for wisdom, scientific, aesthetic and mystical, had commenced. He was nineteen years old. The quest would never end for this new style Russian pilgrim ; it would be of an unparalleled fruitfulness despite its touching brevity. He died of exhaustion in 1900, at the age ! » (English CRC, December 1982, p. 35)

We will limit ourselves in this article to his prophetic insights on the Union of the Churches. In his Lessons on Theandry (1878) – he was then twenty-five ! – our philosopher applies himself to contemplating the Wisdom of God at work in history, perfectly incarnated in Jesus and His virginal Mother, as well as in the Church as she awaits her eschatological transfiguration. The most serious sin, throughout this history, has been that of schism. Who is responsible for this vast Vladimir Soloviev began by throwing all responsibility for it on the Catholic Church, so much so that he provided the inspiration for Dostoyevsky’s famous “ myth of the Grand Inquisitor ” in The Brothers Karamazov . But, at the beginning of the 1880’s, through studying the question more closely, he understood that the sin of schism was in fact that of the East. This was a stroke of genius on his part for which our Father commends him greatly:

« I must beg pardon of my master Msgr. Jean Rupp, of Solzhenitsyn, Volkoff and so many others, but it seems obvious to to me, as it did to Soloviev in the end, that the schism of Moscow in setting itself up as the third Rome was the beginning of all the ills suffered by these admirable Christian peoples of European Russia . And I must say so because this rupture still weighs heavily on the world of today and because it is precisely of this rupture that Our Lady of Fatima speaks when She foretells “  the conversion of Russia  ”. (English CRC, December 1982, p. 24)

Let us follow Soloviev in his commendable mystical conversion which has opened up a path of light for his people, allowing a spring of grace and mercy to gush forth.

AN EVANGELICAL DISCOURSE

In 1881, Soloviev published a long article, still very antipapist, entitled Spiritual power in Russia . There the pope was presented as Antichrist institutionalised ! Our theorist placed all his hope in the regenerative mission of Holy Russia and in the Tsar who was to be her « divine figure, religious guide and animating wisdom ». But were the Russian people still capable of accomplishing such One particular event was to shake Soloviev’s patriotic faith. On March 1, 1881, Alexander II was assassinated by revolutionaries. A few days later, Soloviev gave a Discourse in which he recommended that his successor, Alexander III, show mercy to the regicides. Certainly not as a matter of weakness or abdication before the Revolution, even less out of the spirit of non-violence that a certain Tolstoy was already preaching, but « as an example of Russian piety », that famous podwig « which lies at the heart of the Russian people’s evangelical soul, of which the tsar is the living icon ». Alas, Soloviev was not understood... This was a painful stage in his life, the first step he had taken beyond his master Dostoyevsky.

The following year, he published another article entitled “  Schism in the Russian people and society  ”. Delving deep into the past, he accused Metropolitan Nikon of having broken, at the time of Peter the Great, the communion, the Sobornost , so beloved of the Russian people, by excommunicating Raskol, the fierce guardian of traditional popular religion... Ever since then, the Orthodox hierarchy, enslaved to the imperial power, had proved powerless to govern and sanctify Orthodoxy. It was nothing now but a shrunken, secularized “ local Church ” which, if it were to be restored and revived, would need to open itself up to “ the universal Church ”.

In the spring of 1882, Soloviev was powerfully affected by an unusual dream. In his dream he met a high-ranking Catholic ecclesiastic and entreated him to give him his blessing. The priest refused, so Soloviev insisted, declaring, « The separation of the Churches is the most disastrous thing possible. » Finally, the ecclesiastic agreed to give him his blessing.

This premonitory dream was to awaken in Vladimir Soloviev a burning desire for reconciliation with Catholicism, and to stimulate him to write a series of articles to be published every month in his friend Aksakov’s slavophile newspaper Rouss and then to be collected together in a work with the resonant title: The Great Controversy and Christian Politics . One particular maxim constantly reappeared under the Russian writer’s pen:

« FIRST AND FOREMOST WE MUST WORK TO RESTORE THE UNITY OF THE CHURCH, AND TO MAKE THE FIRE OF LOVE BURN IN THE HEART OF CHRIST’S SPOUSE . »

By an irony of fate, the term “ Controversy ”, which for Soloviev referred to the conflict between Rome and the East, was going to give place to a bitter controversy between himself and his Orthodox and slavophile friends.

A MARVELLOUS AND ADORABLE WISDOM

T HE world’s beauty appeared to Soloviev as a living figure, a real existence, changing and yet immortal. He saw her and held her as the queen of his spiritual universe under her venerable name of Sancta Sophia . At the end of his life, in 1898, he celebrated the Three Encounters he had had with this Beauty which for him was Wisdom.

“ Three times in his life he had been overwhelmed by the radiant visit of Wisdom who appeared to him in the form of an absolutely heavenly female being, dazzling him and enlightening him profoundly. Not without reason certain authors think that all his religious and even philosophical works derive from this illumination. ”

And let us immediately point out, in order to acclimatize the Western reader who is highly likely to be disconcerted by these accounts, that trustworthy interpreters of Soloviev have attributed a marian character to these visions. For them, the whole of the Philosopher’s work derives from the AVE MARIA GRATIA PLENA . “ It is a marvellous perspective ”, adds Msgr. Rupp. “ Wisdom is closely allied to the Immaculate who is its seat. ” ( Le message ecclésial de Soloviev , p. 340)...

What I am going to say next will perhaps surprise my reader. Nothing is more biblical than this vision, and I am astonished at the astonishment of theologians and their impatient criticisms. This Sophia was already well known, hymned and even boldly adored by the scribes of the Old Testament under this very name of Wisdom. Far from being “ pantheist ”, this idea, this vision touches the essence of created beings, and is clearly poles apart from the Platonic idea and far more profound than Aristotle’s substance; it lies at the very heart of being, there where nothing exists except relationship to God, the term of a will and a wisdom that are infinite, there where exists a pure reflection, a fragment of the image of God’s beauty.

George de Nantes , A mysticism for our time , French CRC no. 133, p. 7.

THE GREAT CONTROVERSY

In January 1883, he fired the opening shots with an open letter to Aksakov: « As I reflected on the means of curing this interior disease (of Christianity), I became convinced that the origin of all these evils lies in the general weakening of the earthly organisation of the visible Church, following her division into two disunited parts. » He demonstrated that, in order to establish herself on earth and to endure throughout history, the Christian religion had need of a higher authority, and he explained that it was therefore essential to restore « the union of all Christian and ecclesiastical forces under the standard and under the power of one central ecclesiastical authority ».

On February 19, Soloviev gave a talk in homage to his master Dostoyevsky. It was almost a panegyric of the Roman Church ! He declared his ardent hope for the reconciliation of the two Churches, for the two parts of the universal Church which should never have been separated and whose centre lay in... Rome . As a result of this speech, he saw himself banned from speaking in public. The newspapers made no mention of his speech. For the first time, and it would not be the last, Soloviev was the victim of the censure of Constantin Petrowitch Pobiedonostev, Russia’s Grand Inquisitor and the Tsar’s adviser on religious matters. Pobiedonostev championed a sacral conception of political power, akin to that of the French legitimists of the time, but he was fiercely Orthodox, and any opening towards the Catholic religion was pitilessly censured.

Soloviev responded to this censure with a smile. So his speech had been described as « infantile chattering » ? « If we are not converted », he said to his friends, « and become like little children again, we will not enter the Kingdom of Heaven. » He went on: « When I was a pretentious little boy [teaching German philosophy: Kant, Hegel, Fichte, Schopenhauer and Nietzsche], people listened with great respect to my “ truly infantile ” prattling. And now it is fitting that the only way I can attain the perfection of humility is by everyone ! »

At the same time, he wrote to Aksakov: « It is necessary to defend Catholicism against the false accusations being brought against it... Consequently, in advocating a reconciliation with Catholicism, I assume that Catholicism is not in principle erroneous, for one cannot be reconciled with error . » Now there we have a true ecumenism ! The life of Soloviev, writes our Father, « was ».

To the charge of “ papism ” levelled against him, Soloviev responded in March 1883 with an admirable profession of faith, already Catholic:

« It seems to to me that you concentrate only on “ papism ” whereas I focus first and foremost on the great, holy and eternal Rome, a fundamental and integral part of the universal Church. I believe in this Rome, I bow before it, I love it with all my heart, and with all the strength of my soul I desire its rehabilitation for the unity and integrality of the universal Church. And may I be accursed as a parricide should I ever utter one word of condemnation against the Holy Church of Rome . »

THE REALISATION OF THE DREAM

In May 1883, on the occasion of the coronation of the Emperor Alexander III, the Moscow press complained that too many concessions were being made to restore diplomatic relations with the Vatican broken in 1866, but Soloviev protested: such an agreement was necessary, were it only to improve relations with the Catholics of Poland. The Pope was represented at the ceremony by his special envoy Msgr. Vincenzo Vanutelli. Had not Alexander III written to Leo XIII shortly beforehand: « Never has unity between all Churches and all States been so necessary, in order to realise the wish expressed by Your Holiness of seeing the peoples abandoning the disastrous errors responsible for the social malaise and returning to the holy laws of the Gospel... »

A few days after the ceremony, Soloviev was crossing Moscow in a hired car. Suddenly, he recognized the route he had followed in his dream the previous year. Soon he came to a stop in front of a house from which a Catholic prelate was just leaving: it was Msgr. Vanutelli in person... There was the same hesitation of this latter to give his blessing to a schismatic, and the same entreaties of Soloviev, who finally !

In the summer of 1883, our author wrote two articles on The Catholic Question . According to Soloviev, it was for Russia to take the first step towards the Catholic Church. Imagine !

His articles were not of the sort to leave his readers indifferent. On the Orthodox side, there was an increasing irritation, while on the Catholic side, surprise soon gave way to enthusiasm. The news crossed the borders, spreading to Poland and even to Croatia, where Msgr. Strossmayer was finally seeing his desires realised. The jurisdiction of his diocese of Djakovo extended into Bosnia and Serbia, that is into Orthodox territory. Endowed with a superior intelligence and animated by great apostolic zeal, this Croatian bishop keenly felt the need for a true, intelligent and benevolent ecumenism. He wrote in 1883 to one of his friends, Father Martynov:

« In my opinion, the principal task of the Catholic Church and of the Holy See this century is to draw as closely as possible to the Slav nation, principally the Russian nation . By winning it over to the divine unity of the Catholic Church, we would at the same time win over everyone in the world who still possess a positive faith. »

Bishop Strossmayer and the cathedral of Djakovo

IN THE RADIANCE OF THE IMMACULATE

In the summer of 1883, Soloviev wrote five long letters to a Russian Uniate priest on the subject of The Immaculate Conception of the Most Blessed Virgin Mary . At the same time he translated Petrarch’s “ Praise and prayer to the Most Blessed Virgin ”, wherein he contemplated Her “ clothed in the Sun, crowned with stars... Her glance radiating infinity ! ” It is highly significant that Soloviev was simultaneously attracted by the mystery of the Catholic Church and the mystery of the Immaculate Virgin. The dogma of the Immaculate Conception was the first Catholic dogma which he embraced, and his favourite painting was the Immaculate Conception by Murillo.

In The Foundations of the Spiritual Life (1884), he exalted the « All Holy and Immaculate » Virgin Mary. In Russia and the Church Universal (1889), he would praise Pope Pius IX for having quoted, in support of his dogmatic definition, the Old Testament texts referring to Wisdom, the “  Sophia  ” of his personal intuitions:

« If, by the substantial Wisdom of God, we were exclusively meant to understand the Person of Jesus Christ, how could we apply to the Blessed Virgin all those texts in the Wisdom books which speak of this Wisdom ? However, this application, which has existed from the very earliest times in the offices of both the Latin and Greek Churches, has today received doctrinal confirmation in the bull of Pius IX on the Immaculate Conception of the Most Blessed Virgin. » (quoted by Msgr. Rupp, Le message ecclésial de Soloviev, p. 338)

In September 1883, when the sixth chapter of The Great Controversy was published, a rumour spread through Moscow that Soloviev had “ passed over ” to Catholicism, but there was no truth in it. Moreover, curious though this may seem to us, he was not looking “ to pass over to Catholicism ”, but only to open Orthodoxy up to the universality of the Roman Church.

His seventh and final chapter aroused a lively debate, one that is ever topical. The question turned on the attitude of the Byzantine Greeks in conflict with the Crusaders of the West. Soloviev wrote: « On the day that Constantinople fell, seeing the Turkish armies poised to attack, the final spontaneously expressed cry of the Greeks was, “ Better Islamic slavery than any agreement with the Latins. ” I do not mention this as a reproach to the unfortunate Greeks. If, in this cry of implacable hatred, there was nothing Christian, then neither has there been anything especially Christian in all the formal and artificial attempts to reunite the Churches… »

Aksakov, his Orthodox pride deeply irritated by this remark, retorted: « What does he mean, nothing Christian ? May the Greeks be blessed a hundred times over for having preferred a foreign yoke and bodily torture to the abandonment of the purity of their faith in Christ and for having thus preserved us from the distortions of papism at the precise moment [ the beginning of the 13th century ! ] when it had reached the height of its deformity. May they win eternal glory for this ! »

Nonetheless, Soloviev continued his search for truth, surmounting every obstacle. His article “  Nine Questions to Father Ivantsov-Platonov  ” published in December 1883, created a deep stir even in the West. Here he put nine questions to his former master in Orthodoxy on those points of controversy which set the Church of the East against the Church of Rome. Here is the setting:

« How is it that the countries of the East are separated from the Roman Church ? Did the latter proclaim an heretical proposition ? One would be hard pushed to maintain this, for the addition of the Filioque to the Creed, which is put forward to justify the separation, does not have the character of a heresy. Furthermore, it is absurd to say that the Roman Church is in a state of schism with regard to the Eastern Churches. Thus, the latter’s separation from the former has no basis. Let us acknowledge this and, putting aside all human viewpoints, let us work towards Unity or rather let us work so that Unity, which already has a virtual existence, may become a reality. »

THE THREAD OF AN ANCIENT TRADITION

During 1884, the Russian philosopher studied Catholic dogmatics. He read the works of Perrone, the theologian of Gregory XVI and Pius IX, as well as the texts of the Councils. He was particularly interested in Popes Gregory VII and Innocent III, whom he read in the original text.

At the same time he had a great enthusiasm for the Croatian priest George Krijanich who « had come from Zagreb to Moscow in the 17th century to spread the ideal of the Holy Kingdom of God, Roman Catholic and panslavic, gathering together under the sceptre of the tsars and the crook of the Pope all the Slav peoples who would thereby be freed and protected from the twofold burden pressing them on both sides like a vice, the Germanic powers and the Turks. Thus the Croats would work to free themselves from Austrian control and at the same time they would assist the Serbs, their Orthodox brothers, to shake off Moslem domination.

« To realise this grand design, capable at one blow of powerfully advancing the Kingdom of God on earth, Krijanich came to Moscow and preached on the subject of Russia’s reconciliation with Rome . This should not be difficult, he said, because the Russians had only fallen into schism through ignorance and not through heresy or malice. He himself was already preaching that everyone should recognise their own individual faults, be they unconscious or involuntary, and the need for expiation. God’s blessings would follow as a result, immense and eternal blessings. Sergius Mikhailovich Soloviev, our great man’s father, a historian and the author of a monumental history of Russia, admired Krijanich as “ the first of the Slavophiles ” and also, in his eyes, “ the most paradoxical ”, so alien did Catholicism then appear to the Russian consciousness. » (English CRC, December 1982, p. 32)

Soloviev intended to prove the contrary. And it was just at this time that he entered into friendly relations with the Croatian Bishop Strossmayer, thereby resuming the thread of an ancient tradition, one which was apparently marginal but which in reality was pregnant with a splendid future. Early in December 1885, Soloviev for the first time received a letter from the Croatian bishop. He replied to him on December 8, “  the blessed Day of the Immaculate Conception of the Most Blessed Virgin  ”:

« On the reunion of the Churches », he wrote, « depends the fate of Russia, the Slavs and the whole world. We Russian Orthodox, and indeed the whole of the East, are incapable of achieving anything before we have expiated the ecclesiastical sin of schism and rendered papal authority its due . » And he ended with these words: « My heart burns with joy at the thought that I have a guide like you. May God long preserve your precious leadership for the good of the Church and the Slav people. » In his pastoral letter of January 1886, the bishop of Djakovo quoted large extracts from this letter.

Encouraged by such support, in 1886 Soloviev undertook a study on Dogmatic development and the question of the reunion of the Churches , which provoked the fury of Orthodoxy. However, at a conference given at the ecclesiastical Academy of Saint Petersburg, Soloviev attempted to justify himself: « I can assure you that I will never pass over to Latinism. » He thereby sought to register his attachment to the Eastern rite. No question for him of adopting the Latin rite ! After that, he set out on a journey to Europe.

FIRST STAY IN ZAGREB (1886)

At the beginning of July, he was the guest of the honourable Canon Racki, President of the Yugoslav Academy of Zagreb, founded by Msgr. Strossmayer, and a personal friend of the latter. Every morning the Orthodox Soloviev assisted at the Catholic Mass with great enthusiasm. He made the sign of the cross in the Catholic manner, but prayed in the Greek manner, crossing his arms on his chest. He willingly admitted to his host – and this was not due to any desire to please on his part – that Croatian Catholics, like the Ukrainians, were more religious than his Orthodox compatriots !

Following an article published in the Croatian journal Katolicki List , Soloviev for the first time encountered opposition from a Catholic priest.

During his stay in Zagreb, he also published a letter in the Russian newspaper Novoie Vremia , wherein he refuted the widespread opinion in Russia that the Croats were the instruments of the Austro-Hungarian government’s attempt to Latinize the Eastern Slavs.

In August, he joined Msgr. Strossmayer in the Styrian Alps, and spent ten marvellous days with him. These two minds were truly made to get along. The mutual admiration they felt for one another reinforced their spiritual friendship. But Soloviev continued to receive Holy Communion at the hands of the Orthodox priest of the Serb parish of Zagreb... Rising above the inevitable criticisms, he then wrote a letter to Msgr. Strossmayer, summarising their initial conversations:

« The reunion of the Churches would be advantageous to both sides . Rome would gain a devout people enthusiastic for the religious idea, she would gain a faithful and powerful defender. Russia for her part, she who through the will of God holds in her hands the destinies of the East, would not only rid herself of the involuntary sin of schism but, what is more, she would thereby become free to fulfil her great universal mission of uniting around herself all the Slav nations and of founding a new and truly Christian civilisation, a civilisation uniting the characteristics of the one truth and of religious liberty in the supreme principle of charity, encompassing everything in its unity and distributing to everyone the plenitude of the one unique good. »

Such was his transcription of the well known Catholic principle: « In necessariis unitas, in dubiis libertas, in omnibus caritas : unity in essentials, liberty in matters of doubt, and in all things charity . Such must be the Charter of Catholic ecumenism under the crook of the one Shepherd. From the start of this crisis, such has been the invitation we have made to our bishops and to our brothers. Today, it is also the will of the Holy Father », wrote our Father in his editorial for September 1978, dedicated to John Paul I, another Saint Pius X without knowing it (English CRC no. 102, p. 6).

When he informed his friends of Soloviev’s letter, Msgr. Strossmayer presented its author as « a candid and truly holy soul ».

Msgr. Strossmayer and Soloviev had agreed to meet again in Rome for the jubilee pilgrimage of 1888. The Croatian bishop decided to pave the way in Rome by writing to Leo XIII’s Secretary of State, Cardinal Rampolla. He presented his Russian friend as « toto corde et animo catholicus ». The Pope at first took a personal interest in the affair: « Here is a sheep », he said, « who will soon be clearing the gate of the sheepfold. » But curiously, there was to be no follow-up. It seems that Leo XIII failed to appreciate Soloviev’s genius... However, things were different in France, where an unassuming and ardent rural parish priest latched on to everything that his apostolic zeal could extract from the lightning advances made by the Russian thinker ( see inset , p. 19).

Soloviev returned to Russia at the beginning of October 1886, rather discouraged by the criticisms directed against him on all sides: there were the Orthodox, some of whom had accused him of bringing Orthodoxy into disrepute abroad... and certain Catholics, like Fr. Guettée in France, a modernist priest with little to commend him, whom he had met in Paris in 1876 and who had recently published an article of rare violence against him !

THE “ RETURN OF THE DISSIDENTS ”

June 18, 1887: a young Capuchin, Leopold Mandic, from Herzeg Novi in Bosnia, under the jurisdiction of Msgr. Strossmayer, and studying at the friary in Padua, heard the voice of God inviting him to pray for and promote the return of the Orthodox to the bosom of the one Church of Christ. « The goal of my life , he would later say, must be the return of the Eastern dissidents to Catholic unity; I must therefore employ all my energies, as far as my littleness allows, to co-operate in such a task through the sacrifice of my life . » Fifty years later, he would still remember this grace: « June 18, for the record: 1887-1937. Today, I offered the Holy Sacrifice for the Eastern dissidents, for their return to Catholic unity . » Thus the Heart of Jesus and the Immaculate united, in this one same “ ecumenical ” work, the ardent heart of a young Capuchin destined for the altars, the apostolic wisdom of a bishop and the brilliant intuitions of a great thinker.

In January 1887, from the Monastery of Saint Sergius where he had celebrated Christmas, Soloviev wrote an article in which he provided philosophic justification for the three Catholic dogmas which the Orthodox reject, namely the Filioque, the Immaculate Conception and papal infallibility . Here is a « basis for working towards the reunion of the Churches », he explained. A few months later, he published in Zagreb (on account of the censure directed against him in Russia) his book The History and Future of Theocracy .

There he retraced the vast movement of history towards the establishment of the Kingdom of God. Universal Theocracy, the successor of Jewish Theocracy, cannot be conceived, he explained, without an integrally Christian politics, and he concluded with a splendid anthem to Christ Pantocrator receiving from His Father all power on earth and in Heaven and acting through His emissaries, the Apostles and their successors. Soloviev always believed in the privileged vocation of Russia within the Catholic community of Christian nations, even if he stigmatized what he called “ the sin of Russia ”, which was to oppress and hate all those it dominated, in particular Polish Catholics, Greek Uniates, Ruthenians and Jews !

Like a true prophet, he was vigorous in preaching repentance to his people . In order that they might be faithful to their vocation within the great Slav family, Soloviev asked them to give up their inordinate ambitions, to return to a truer and more Christian conception of their destiny, and to accomplish this within the only international organization which could direct its course, Catholicism, that is to say Roman universalism.

« One of my theses is that the cause of the Reunion of the Churches in Russia demands a podwig (sacrifice) even heavier to bear than that which, already demanding great self-denial, was needed to ensure Russia’s receptivity to Western culture, an event truly disagreeable to the national sentiment of our ancestors .

« Well ! this sacrifice consists in drawing closer to Rome and it must be attained at all costs. In this lies the remedy for the Russian sin . »

It goes without saying that Soloviev earned himself new enemies with his book. It cost him great personal suffering, but he could not fail the Truth, which he contemplated with ever greater clarity... What greatness of soul this universal genius possessed !

SAINT VLADIMIR AND THE CHRISTIAN STATE

1888 marked the ninth centenary of the baptism of Saint Vladimir, the first prince of Kiev, whose kingdom after his conversion became « the model of Christian States, with evangelical morals », writes our Father (English CRC, December 1982, p. 23). Soloviev used the occasion to give a conference in Moscow, where he reaffirmed that Russia’s destiny was to turn towards Rome, as King Vladimir had ! However, having hardened itself in its schism, the Muscovite hierarchy was no longer animated by the spirit of St. Vladimir. Hence the fury of the Orthodox hierarchs !

At the same time, Msgr. Strossmayer had gone to Rome for the Jubilee. In vain did he wait for Soloviev there. The latter, fearing perhaps that he had made a definitive break with the Orthodox world which he dreamed on the contrary of winning for the Union, had given up the idea of making this journey. It must also be said that Vatican diplomacy hardly inspired more confidence in him. Leo XIII was revealing himself less and less slavophile, reserving his favours for the Germany of old Bismarck and the young William II ! Msgr. Strossmayer lamented this in a letter to Fr. Martynov: « The Pope is acting against the Slavs. The Roman prelates are like people insane and think only of temporal power ! »

What a difference between Leo XIII and his successor, St. Pius X, who was, in the words of Msgr. Rupp and our Father, the greatest slavophile pope of our times !

Early in May 1888, Soloviev was on a visit to Paris. To explain his thinking to the French public, he gave a conference on the Russian Idea , « the true national idea eternally fixed in the design of God », who longs to spread His light over the whole world. However, Soloviev remained lucid about his own Church: « If the unity of the universal Church founded by Christ only exists among us in a latent state, it is because the official institution represented by our ecclesiastical government and our theological school is not a living part of the universal Church. »

In passing, he described the destruction of the Greek-Uniate Church by the Orthodox as a « veritable national sin weighing on Russia and paralysing her moral strength ». That is still the case today...

In July, Kiev celebrated the feast of the baptism of St. Vladimir. From Zagreb Msgr. Strossmayer sent a telegram in which he exalted Russia’s future role in the manner of his friend Soloviev. Scandal ! His remarks were universally reported by the press. Cardinal Rampolla informed the Croatian bishop that Leo XIII was seriously displeased ! The bishop of Djakovo also earned himself the bitter reproaches of Emperor Francis Joseph of Austria, which is more understandable given the rivalry existing between the two Empires.

In the summer of 1887, Soloviev published in the Universe , the newspaper of Louis Veuillot, three articles on St. Vladimir and the Christian State which caused a great stir. Then he journeyed to Croatia where he remained for one whole month with Msgr. Strossmayer. This meeting was rather sad, for the two friends were increasingly aware that their attempt to reunite the Churches would not succeed, at least in their lifetime.

It was in Djakovo that Soloviev finished the immense prologue to his magisterial book, Russia and the Church Universal , in which one can already glimpse signs of the discouragement that would overwhelm the thinker in the latter part of his life. We know from Fatima that the work of the conversion of Russia, something humanly impossible, has been entrusted to the Immaculate Heart of Mary who has a particular love for this Nation such as to inspire jealousy in others. But this only makes it all the more extraordinary that our prophet should have traced out the course of this conversion, like a true Precursor !

« RUSSIA AND THE CHURCH UNIVERSAL »

Soloviev does not hesitate to delve deep, extremely deep, into the past. To realise its designs in the world, divine Wisdom wished to become incarnate, and the Verb to take flesh like our own. As that was not enough, He also wished to unite to Himself a social and historical body, one that could reach the universality of mankind and communicate to all men His own divine Life. In this magnificent perspective, Soloviev compares the formation of that Body through which God wishes to be united with humanity to that effected in the womb of the Virgin Mary at the time of the Incarnation, and to that which operates every day in the Eucharistic mystery... What was needed for this work was a solid foundation, a Rock:

« This bedrock has been found », he writes, « it is Rome. It is only on the Rock [of Peter and his successors] that the Church is founded. This is not an opinion, it is an imposing historical reality . »

It is also an evangelical truth: « You are Peter, and on this Rock I will build my Church . » Here Soloviev addresses the Protestants who seek to outbid each other in their attacks against the Primacy of Peter by quoting Jesus’ own words to His Apostle when he was obstructing the Master’s path: « Get behind me, Satan ! » Soloviev’s response once again shows the clarity of his intelligence and his perfect knowledge of Catholic dogma:

« There is only one way of harmonising these texts which the inspired Evangelist did not juxtapose without reason. Simon Peter, as supreme pastor and doctor of the universal Church , assisted by God and speaking for all, is, in this capacity, the unshakeable foundation of the House of God and the holder of the keys of the heavenly Kingdom. The same Simon Peter, as a private person, speaking and acting through his own natural forces and an understanding that is purely human , can say and do things that are unworthy, scandalous and even satanic. But personal defects and sins are passing, whereas the social function of the ecclesiastical monarch is permanent. “ Satan ” and the scandal have disappeared, but Peter has remained. »

Soloviev’s doctrine agrees with that of Vatican Council I and with that of our Father who, at the same time as he makes us venerate Peter’s magisterium, magnificently illustrated by Blessed Pius IX, St. Pius X and John Paul I, accuses John XXIII, Paul VI and John Paul II of being instruments of “ Satan ” for the ruin of the Church.

However, Christ wished that it should be around Peter that the unity of faith and charity should be formed: « Since the unity of the faith does not presently exist in the totality of believers, seeing that not all of them are unanimous in matters of religion, it must lie in the legal authority of a single head, an authority assured by divine assistance and the trust of all the faithful . This is the ROCK on which Christ founded His Church and against which the gates of hell will never prevail. »

Why did this ROCK settle in Rome, and not in Jerusalem, Constantinople or Moscow ? Here we have a further brilliant response from Soloviev: historically Rome represented the order, civilization and terrestrial Empire that would best allow the Church to become the universal spiritual Empire desired by Christ. In a mystical view of the history of Salvation – we would say divine “ orthodromy ” – Soloviev shows how God, wishing to extend salvation to the whole world, decided one day that His Kingdom should leave Israel for Rome, so that the capital of the pagan Empire should become “ the conjoint instrument ” of His designs:

« The universal monarchy was to stay put; the centre of unity was not to move. But central power itself, its character, its source and its sanction were to be renewed... Instead of an Empire of Might, there was to be a Church of Love. » One thinks of Constantine’s conversion and his imposition throughout the Roman Empire of laws favouring Christianity, and of Theodosius declaring the Christian religion the religion of State. What decisive support for the Gospel ! The remarkable Roman civilization, already the heir of Greece, was put at the service of the Cross of Christ !

Soloviev had some wonderful expressions to describe this, as for example the following: « Jesus unthroned Caesar... By unthroning the false and impious absolutism of the pagan Caesars, Jesus confirmed and immortalised the universal monarchy of Rome and gave it its true theocratic foundation . »

« Let us not think », comments our Father, « that our theosophist loses his way in a contemplation of evangelical love and freedom. Fully aware of the frailty and shortcomings of humanity, he declares that it is essential, for its effective salvation, that supreme divine power be joined to the firmest social structure, to the virile principle , and not as formerly to the female principle of a virginal flesh for the Incarnation. This firm principle is the imperial monarchical institution which is Rome and Caesar. Converted, elevated and unabolished, the Power of Rome continues in the Pope for the service of the universal community.

« It is only this divino-human pontifical paternity that is capable of forming the basis of the universal fraternity of the peoples, not only through its spiritual influence but also through its authority and its supranational organization. In this monarchy, sacred but popular, the Pope, the Universal Emperor, clearly remains the servant of the servants of God and is, for that very reason, the sovereign Head of the Nations. Opposed to any kind of papolatry, antagonistic to all the encroachments of papism, and quite capable of denouncing such a Pope as Satan, Soloviev raised an imperishable monument to the glory of Rome and pointed out – him, a member of the Orthodox Church – the path of the world’s salvation, which lay in one place only, in the universal Christian order of a restored Roman Catholic Church ... » (French CRC no. 131, July 1978, p. 6)

In his lifetime, Soloviev ran up against a wall of hostility and incomprehension: « I am not so naive », he said, « to seek to convince minds whose private interests are greater than their desire for religious truth. In presenting the general evidence for the permanent primacy of Peter as the basis of the universal Church, I have simply wanted to assist those who are opposed to this truth, not because of their interests and passions, but merely because of their unwitting errors and hereditary prejudices. »

The final period of his life might seem to some like a decline and a renunciation of his prophetic insights, but our Father writes: « Soloviev was too great a mind to be discouraged or to modify his ideas in accordance with the fluctuations of his worldly success. What is certainly true is that his bitter experiences gave him a better knowledge of the Evil that was at work in the world, throwing up formidable obstacles to God’s designs and going so far as to erect a kind of caricature of them. This he denounced as the power of the Antichrist, the Prince of this world, announced in the Scriptures. » (French CRC no. 132, August 1978, p. 12)

At the beginning of the 1890’s, relations between Soloviev and the Orthodox Church deteriorated. « Given the papaphobia reigning among us , he wrote to a friend, sometimes revealing its underhand character and at other times its stupidity, and always in any event unchristian, I considered and I continue to consider that it is necessary to draw people’s attention to the Rock of the Church laid by Christ Himself and to its positive significance . »

As he persisted in his criticisms, even going so far as to compare the Greco-Russian Church with « the Synagogue », the Orthodox hierarchy, in the person of Pobiedonostev, the Holy Synod’s prosecutor, employed the ultimate weapon at its disposal: it deprived him of the sacraments. One day in 1894, being seriously ill, Soloviev asked to receive the sacraments. His Orthodox confessor refused to give him absolution unless he renounced his Catholic views. Soloviev refused to yield, preferring to forego confession and Holy Communion.

AN AUTHENTIC CONVERSION

The moment had come. On February 18, 1896, he went to see Fr. Nicholas Alexeyevich Tolstoy, a Catholic priest of the Eastern rite exercising his ministry in Moscow. This priest, a former officer, owed him his vocation, his formation (Soloviev having been his teacher) and his conversion to Catholicism. That February 18 was the feast day of Pope St. Leo so dear to Soloviev. Before Mass, he read on his knees the Tridentine symbol of the faith containing the Filioque and a formula declaring that the Church of Rome must be regarded as the head of all the particular Churches. Then he received the Body of Christ at the hands of the Catholic priest.

On the following day, Fr. Tolstoy was denounced and arrested. He managed to escape and to reach Rome first, then France. It was only in 1910 that he would give an account in the Universe of the authentic conversion of Soloviev, and in 1917 that the two witnesses present at the scene would confirm the celebrated Russian’s profession of the Catholic faith. Nevertheless, this conversion was disputed not only by the Orthodox but also by Catholics imbued with a false ecumenism like Msgr. d’Herbigny of sinister memory. But in this matter the facts are indubitable. His entry into the Catholic Church did not, however, in Soloviev’s mind, exclude him from what he called « the true and authentic Eastern or Greco-Russian Church ». Never did he embrace the Latin rite. After the exile of Fr. Tolstoy, as there were no longer any Catholic priests in Moscow apart from those belonging to the Latin rite, Soloviev decided to refrain from receiving the sacraments...

In 1897, a census of the whole of Russia was carried out in which a question was asked about religion. « I am both Catholic and Orthodox; let the police work that out ! » Soloviev answered.

« Self-important people from Rome and Moscow declared themselves scandalized », writes our Father. « The hour had not yet come for the podwig , for self-renunciation and reconciliation in truth and justice ( pravda ), and for the restoration of the wholly divine unity of communion in love ( sobornost ). Msgr. Rupp thinks that we achieved it with Vatican II. Alas, no ! I hope for and expect it to come with Vatican III... but only after the trial, after conversion and expiation... and after Our Lady’s humble requests have been met. » (English CRC, December 1982, p. 36)

UNDER THE SIGN OF MARY

« This glow from Heaven emanates from Mary, And vain remains the attraction of the serpent’s venom. »

On July 17, 1900, sensing death approaching, Soloviev sent for a priest. He was most insistent about this: « Will it be morning soon ? When will the priest come ? » The next day, he made his confession and received Holy Communion at the hands of an Orthodox priest. He died peacefully a few days later, on July 31, « in the communion of Russian Orthodoxy to which he had ever been faithful, without however disowning the Catholicism of his heart, assured by the example of the Fathers of Russian Christianity, Saints Cyril and Methodius, Saint Vladimir, and so many strastoterptsi , innocents who had suffered the passion , and startsi , slavophiles and romanophiles at the same time, without schism or constraint, in the love of Holy Church and Holy Russia, the Kingdom of God to come ! »

But all this is too beautiful for us not to revisit it, so our Father has decided that we will study in more depth the work of this great Russian thinker, in three parts to appear in subsequent editions of Resurrection , Deo volente:

The vocation of Russia in the designs of God and the concert of the Christian nations: up to and including Putin ?

The Immaculate Virgin Mary , throne of Wisdom, essential beauty of the created world, our ultimate recourse !

The Antichrist unmasked by Soloviev . This was the last service the “ inspired prophet ” rendered to his beloved Russia: that of putting her on her guard against the seductions of the Antichrist. In Rome, at the same time, St. Pius X was also announcing his advent in his encyclical E supremi Apostolatus of October 4, 1903: « The Antichrist is present among us. The Evil shaking the world should not affright us, it will only last a short while. What must fall will fall, and the Church will be reborn from the trial, assisted by her Saviour and ready for extraordinary developments. »

Brother Thomas of Our Lady of Perpetual Help He is risen ! n° 8, August 2001, pp. 13-22

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Single-Subject Research Designs
The most basic single-subject research design is the ... Figure 10.5 long description: Two graphs showing the results of a generic single-subject study with an ABA design. In the first graph, under condition A, level is high and the trend is increasing. Under condition B, level is much lower than under condition A and the trend is decreasing.
Single Subject Experimental Designs
When choosing a single-subject experimental design, ABA researchers are looking for certain characteristics that fit their study. First, individuals serve as their own control in single subject research. In other words, the results of each condition are compared to the participant's own data. If 3 people participate in the study, each will ...
10.2 Single-Subject Research Designs
The most basic single-subject research design is the reversal design, also called the ABA design. During the first phase, A, a baseline is established for the dependent variable. This is the level of responding before any treatment is introduced, and therefore the baseline phase is a kind of control condition.
Types of Single-Subject Research Designs
This blog post will cover D-5 of Section 1 in the BCBA/BCaBA Fifth Edition Task List. You will learn about how to "use single-subject experimental designs" and the different types of single-subject research designs (Beha...
Single-Subject Research Designs
The most basic single-subject research design is the ... Figure 10.4 long description: Two graphs showing the results of a generic single-subject study with an ABA design. In the first graph, under condition A, level is high and the trend is increasing. Under condition B, level is much lower than under condition A and the trend is decreasing.
Applied Behavior Analysis: Single Subject Research Design
Single case design (SCD), often referred to as single subject design, is an evaluation method that can be used to rigorously test the success of an intervention or treatment on a particular case (i.e., a person, school, community) and to also provide evidence about the general effectiveness of an intervention using a relatively small sample size.
10.3: Single-Subject Research Designs
The most basic single-subject research design is the reversal design, also called the ABA design. During the first phase, A, a baseline is established for the dependent variable. This is the level of responding before any treatment is introduced, and therefore the baseline phase is a kind of control condition. When steady state responding is ...
Creating Single-Subject Research Design Graphs with Google Applications
Several technical articles for the development of single-subject research design graphs have been published to assist ABA practitioners and researchers in their usage. ... Journal of Applied Behavior Analysis, 52(1), 188-204. 10.1002/jaba.522. Blair BJ, Shawler LA. Developing and implementing emergent responding training systems with ...
Single Subject Research Designs
Single-subject design research uses a rigorous, experimental research methodology to identify functional or causal relationships between variables, also making it a useful methodology to define basic principles of behavior and establish evidence-based practices (Horner et al., 2005). ... Three studies (7%) utilized an ABA design integrating a ...
15.2 Types of Single-Systems Research Designs
This is called a withdrawal design and is represented as A-B-A or A-B-A-B. Reversal Designs: It is the most single-subject research design, also known as ABA design. During the first phase, A, a baseline is established for the dependent variable. This is the level of responding before any treatment is introduced, and therefore the baseline ...
Single-Subject Experimental Design for Evidence-Based Practice
The use of single-subject research to identify evidence-based practice in special education. Exceptional Children. 2005; 71:165-179. [Google Scholar] Iwata BA, Neef NA, Wacker DP, Mace FC, Vollmer TR, editors. Methodological and conceptual issues in applied behavior analysis. 2nd ed Society for the Experimental Analysis of Behavior; Lawrence ...
10.2 Single-Subject Research Designs
Reversal Designs. The most basic single-subject research design is the reversal design, also called the ABA design. During the first phase, A, a baseline is established for the dependent variable. This is the level of responding before any treatment is introduced, and therefore the baseline phase is a kind of control condition.
Creating Single-Subject Research Design Graphs with Google ...
Several technical articles for the development of single-subject research design graphs have been published to assist ABA practitioners and researchers in their usage. For example, Carr and Burkholder ( 1998 ), Dixon et al. ( 2009 ), and Pritchard ( 2008 ) published tutorials on generating graphs with Microsoft Excel whereas Berkman et al ...
Advanced Single Subject Research Designs in ABA
Active. This course will feature a review of quantitative skills and methods required to produce scientific research. Single-subject design formats often used in behavior analytic research will be reviewed in detail. Single-subject designs will be compared and contrasted with group designs and issues of generality will be explored.
What is ABA and ABAB Design in Applied Behavior Analysis?
Related resource: Top 20 Online Applied Behavior Analysis Bachelor's Degree and BCaBA Coursework Programs . Definition. This model is a form of a research protocol called Single Subject Experimental Design (SSED). Single Subject Research Designs are common in special education and in clinical settings.
Single-Subject Research Designs
This blog post will cover D-3 of Section 1 in the BCBA/BCaBA Fifth Edition Task List. You will learn about "defining features of single-subject research experimental designs" (Behavior Analyst Certification Board, 2017)....
Single-Subject Research Designs
The most basic single-subject research design is the ... Figure 10.4 long description: Two graphs showing the results of a generic single-subject study with an ABA design. In the first graph, under condition A, level is high and the trend is increasing. Under condition B, level is much lower than under condition A and the trend is decreasing.
Developing ash-free high-strength spherical carbon catalyst supports
The possibility of using furfurol for the production of ash-free high-strength active carbons with spheroidal particles as adsorbents and catalyst supports is substantiated. A single-stage process that incorporates the resinification of furfurol, the molding of a spherical product, and its hardening while allowing the process cycle time and the cost of equipment to be reduced is developed ...
10.2: Single-Subject Research Designs
The most basic single-subject research design is the reversal design, also called the ABA design. During the first phase, A, a baseline is established for the dependent variable. This is the level of responding before any treatment is introduced, and therefore the baseline phase is a kind of control condition. When steady state responding is ...
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They perform local market research to determine whether the prospective homesites make sense in the Elektrostal', Moscow Oblast, Russia market, as well as survey the land on which the custom house will be built to make sure it is suitable for construction. Custom house building companies also obtain the necessary permits.
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Because the entire project is happening within one company, Elektrostal' design-build services are able to overlap the design and construction phases of the project, which often speeds up the project significantly. In addition, these firms work to minimize risks for the project owner through single-point responsibility contracts.
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This blog post will cover D-4 of Section 1 in the BCBA/BCaBA Fifth Edition Task List. You will learn about how to "describe the advantages of single-subject experimental designs compared to group designs" (Behavior Analy...
Vladimir Soloviev, prophet of Russia's conversion
Vladimir Soloviev, aged twenty. T HE conversion of Russia will not be the work of man, no matter how gifted he may be, but that of the Immaculate Heart of the Virgin Mary, the Mediatrix of all graces, because this is God's wish, which he revealed to the world in 1917. The life and works of Vladimir Soloviev are a perfect illustration of this ...