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Types of Variables in Research | Definitions & Examples

Published on 19 September 2022 by Rebecca Bevans . Revised on 28 November 2022.

In statistical research, a variable is defined as an attribute of an object of study. Choosing which variables to measure is central to good experimental design .

You need to know which types of variables you are working with in order to choose appropriate statistical tests and interpret the results of your study.

You can usually identify the type of variable by asking two questions:

• What type of data does the variable contain?
• What part of the experiment does the variable represent?

Table of contents

Types of data: quantitative vs categorical variables, parts of the experiment: independent vs dependent variables, other common types of variables, frequently asked questions about variables.

Data is a specific measurement of a variable – it is the value you record in your data sheet. Data is generally divided into two categories:

• Quantitative data represents amounts.
• Categorical data represents groupings.

A variable that contains quantitative data is a quantitative variable ; a variable that contains categorical data is a categorical variable . Each of these types of variable can be broken down into further types.

Quantitative variables

When you collect quantitative data, the numbers you record represent real amounts that can be added, subtracted, divided, etc. There are two types of quantitative variables: discrete and continuous .

Categorical variables

Categorical variables represent groupings of some kind. They are sometimes recorded as numbers, but the numbers represent categories rather than actual amounts of things.

There are three types of categorical variables: binary , nominal , and ordinal variables.

*Note that sometimes a variable can work as more than one type! An ordinal variable can also be used as a quantitative variable if the scale is numeric and doesn’t need to be kept as discrete integers. For example, star ratings on product reviews are ordinal (1 to 5 stars), but the average star rating is quantitative.

Example data sheet

To keep track of your salt-tolerance experiment, you make a data sheet where you record information about the variables in the experiment, like salt addition and plant health.

To gather information about plant responses over time, you can fill out the same data sheet every few days until the end of the experiment. This example sheet is colour-coded according to the type of variable: nominal , continuous , ordinal , and binary .

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Experiments are usually designed to find out what effect one variable has on another – in our example, the effect of salt addition on plant growth.

You manipulate the independent variable (the one you think might be the cause ) and then measure the dependent variable (the one you think might be the effect ) to find out what this effect might be.

You will probably also have variables that you hold constant ( control variables ) in order to focus on your experimental treatment.

In this experiment, we have one independent and three dependent variables.

The other variables in the sheet can’t be classified as independent or dependent, but they do contain data that you will need in order to interpret your dependent and independent variables.

What about correlational research?

When you do correlational research , the terms ‘dependent’ and ‘independent’ don’t apply, because you are not trying to establish a cause-and-effect relationship.

However, there might be cases where one variable clearly precedes the other (for example, rainfall leads to mud, rather than the other way around). In these cases, you may call the preceding variable (i.e., the rainfall) the predictor variable and the following variable (i.e., the mud) the outcome variable .

Once you have defined your independent and dependent variables and determined whether they are categorical or quantitative, you will be able to choose the correct statistical test .

But there are many other ways of describing variables that help with interpreting your results. Some useful types of variable are listed below.

A confounding variable is closely related to both the independent and dependent variables in a study. An independent variable represents the supposed cause , while the dependent variable is the supposed effect . A confounding variable is a third variable that influences both the independent and dependent variables.

Failing to account for confounding variables can cause you to wrongly estimate the relationship between your independent and dependent variables.

Discrete and continuous variables are two types of quantitative variables :

• Discrete variables represent counts (e.g., the number of objects in a collection).
• Continuous variables represent measurable amounts (e.g., water volume or weight).

You can think of independent and dependent variables in terms of cause and effect: an independent variable is the variable you think is the cause , while a dependent variable is the effect .

In an experiment, you manipulate the independent variable and measure the outcome in the dependent variable. For example, in an experiment about the effect of nutrients on crop growth:

• The  independent variable  is the amount of nutrients added to the crop field.
• The  dependent variable is the biomass of the crops at harvest time.

Defining your variables, and deciding how you will manipulate and measure them, is an important part of experimental design .

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Research Methodologies

Quantitative research methodologies.

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What is quantitative research.

Quantitative methodologies use statistics to analyze numerical data gathered by researchers to answer their research questions. Quantitative methods can be used to answer questions such as:

• What are the relationships between two or more variables? 
• What factors are at play in an environment that might affect the behavior or development of the organisms in that environment?

Quantitative methods can also be used to test hypotheses by conducting quasi-experimental studies or designing experiments.

Independent and Dependent Variables

In quantitative research, a variable is something (an intervention technique, a pharmaceutical, a temperature, etc.) that changes. There are two kinds of variables:  independent variables and dependent variables . In the simplest terms, the independent variable is whatever the researchers are using to attempt to make a change in their dependent variable.

* This is a real, repeatable experiment you can try on your plants.

Correlational

Researchers will compare two sets of numbers to try and identify a relationship (if any) between two things.

• Köse S., & Murat, M. (2021). Examination of the relationship between smartphone addiction and cyberchondria in adolescents. Archives of Psychiatric Nursing, 35(6): 563-570.
• Pilger et al. (2021). Spiritual well-being, religious/spiritual coping and quality of life among the elderly undergoing hemodialysis: a correlational study. Journal of Religion, Spirituality & Aging, 33(1): 2-15.

Descriptive

Researchers will attempt to quantify a variety of factors at play as they study a particular type of phenomenon or action. For example, researchers might use a descriptive methodology to understand the effects of climate change on the life cycle of a plant or animal. 

• Lakshmi, E. (2021). Food consumption pattern and body mass index of adolescents: A descriptive study. International Journal of Nutrition, Pharmacology, Neurological Diseases, 11(4), 293–297.
• Lin, J., Singh, S., Sha, L., Tan, W., Lang, D., Gašević, D., & Chen, G. (2022). Is it a good move? Mining effective tutoring strategies from human–human tutorial dialogues. Future Generation Computer Systems, 127, 194–207.

Experimental

To understand the effects of a variable, researchers will design an experiment where they can control as many factors as possible. This can involve creating control and experimental groups. The experimental group will be exposed to the variable to study its effects. The control group provides data about what happens when the variable is absent. For example, in a study about online teaching, the control group might receive traditional face-to-face instruction while the experimental group would receive their instruction virtually. 

• Jinzhang Jia, Yinuo Chen, Guangbo Che, Jinchao Zhu, Fengxiao Wang, & Peng Jia. (2021). Experimental study on the explosion characteristics of hydrogen-methane premixed gas in complex pipe networks. Scientific Reports, 11(1), 1–11.
• Sasaki, R. et al. (2021). Effects of cryotherapy applied at different temperatures on inflammatory pain during the acute phase of arthritis in rats. Physical Therapy, 101(2), 1–9.

Quasi-Experimental/Quasi-Comparative

Researchers will attempt to determine what (if any) effect a variable can have. These studies may have multiple independent variables (causes) and multiple dependent variables (effects), but this can complicate researchers' efforts to find out if A can cause B or if X, Y,  and  Z are also playing a role.

• Jafari, A., Alami, A., Charoghchian, E., Delshad Noghabi, A., & Nejatian, M. (2021). The impact of effective communication skills training on the status of marital burnout among married women. BMC Women’s Health, 21(1), 1-10.
• Phillips, S. W., Kim, D.-Y., Sobol, J. J., & Gayadeen, S. M. (2021). Total recall?: A quasi-experimental study of officer’s recollection in shoot - don’t shoot simulators. Police Practice and Research, 22(3), 1229–1240.

Surveys can be considered a quantitative methodology if the researchers require their respondents to choose from pre-determined responses. 

• Harries et al. (2021). Effects of the COVID-19 pandemic on medical students: A multicenter quantitative study. BMC Medical Education, 21(14), 1-8.
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Research Methods Simplified

• Quantitative Research
• Qualitative Research
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Quantitative

Quantitative research - concerned with precise measurement, replicable, controlled and used to predict events. It is a formal, objective, systematic process. N umerical data are used to obtain information about the subject under study.

-uses data that are numeric

- primarily intended to test theories

-it is deductive and outcome orientated

-examples of statistical techniques used for quantitative data analysis are random sampling, regression analysis, factor analysis, correlation, cluster analysis, causal modeling and standardized tests

For comparative information on qualitative v.s. quantitative see: The University of Arkansas University Library Lib Guides

Related Information

Control group - the group of subjects or elements NOT exposed to the experimental treatment in a study where the sample is randomly selected

Experimental group - the group of subjects receiving the experimental treatment, i.e., the independent variable ( controlled measure or cause ) in an experiment.

Independent variable - the variable or measure being manipulated or controlled by the experimenter. The independent variable is assigned to participants by random assignment.

Dependent variable or dependent measure - the factor that the experimenter predicts is affected by the independent variable, i.e., the response, outcome or effect from the participants that the experimenter is measuring.

Four types of Quantitative Research

Descriptive  

1) Descriptive - provides a description and exploration of phenomena in real-life situations and characteristics. Correlational of particular individuals, situations or groups are described.  

Comparative

2) Comparative - a systematic investigation of relationships between two or more variables used to explain the nature of relationships in the world. Correlations may be positive (e.g., if one variable increases, so does the other), or negative (correlation occurs when one variable increases and the other decreases).

Quasi-experimental

3) Quasi-experimental - a study that resembles an experiment but random assignment had no role in determining which participants were placed on a specific level of treatment. Generally would have less validity than experiments.

Experimental (empirical)

4) Experimental (empirical) method- the scientific method used to test an experimental hypothesis or premise. Consists of a control group (not exposed to the experimental treatment, i.e.. is dependent) and the experimental group (is exposed to the treatment, i.e., independent)

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Home Market Research

Quantitative Research: What It Is, Practices & Methods

Quantitative research involves analyzing and gathering numerical data to uncover trends, calculate averages, evaluate relationships, and derive overarching insights. It’s used in various fields, including the natural and social sciences. Quantitative data analysis employs statistical techniques for processing and interpreting numeric data.

Research designs in the quantitative realm outline how data will be collected and analyzed with methods like experiments and surveys. Qualitative methods complement quantitative research by focusing on non-numerical data, adding depth to understanding. Data collection methods can be qualitative or quantitative, depending on research goals. Researchers often use a combination of both approaches to gain a comprehensive understanding of phenomena.

What is Quantitative Research?

Quantitative research is a systematic investigation of phenomena by gathering quantifiable data and performing statistical, mathematical, or computational techniques. Quantitative research collects statistically significant information from existing and potential customers using sampling methods and sending out online surveys , online polls , and questionnaires , for example.

One of the main characteristics of this type of research is that the results can be depicted in numerical form. After carefully collecting structured observations and understanding these numbers, it’s possible to predict the future of a product or service, establish causal relationships or Causal Research , and make changes accordingly. Quantitative research primarily centers on the analysis of numerical data and utilizes inferential statistics to derive conclusions that can be extrapolated to the broader population.

An example of a quantitative research study is the survey conducted to understand how long a doctor takes to tend to a patient when the patient walks into the hospital. A patient satisfaction survey can be administered to ask questions like how long a doctor takes to see a patient, how often a patient walks into a hospital, and other such questions, which are dependent variables in the research. This kind of research method is often employed in the social sciences, and it involves using mathematical frameworks and theories to effectively present data, ensuring that the results are logical, statistically sound, and unbiased.

Data collection in quantitative research uses a structured method and is typically conducted on larger samples representing the entire population. Researchers use quantitative methods to collect numerical data, which is then subjected to statistical analysis to determine statistically significant findings. This approach is valuable in both experimental research and social research, as it helps in making informed decisions and drawing reliable conclusions based on quantitative data.

Quantitative Research Characteristics

Quantitative research has several unique characteristics that make it well-suited for specific projects. Let’s explore the most crucial of these characteristics so that you can consider them when planning your next research project:

• Structured tools: Quantitative research relies on structured tools such as surveys, polls, or questionnaires to gather quantitative data . Using such structured methods helps collect in-depth and actionable numerical data from the survey respondents, making it easier to perform data analysis.
• Sample size: Quantitative research is conducted on a significant sample size  representing the target market . Appropriate Survey Sampling methods, a fundamental aspect of quantitative research methods, must be employed when deriving the sample to fortify the research objective and ensure the reliability of the results.
• Close-ended questions: Closed-ended questions , specifically designed to align with the research objectives, are a cornerstone of quantitative research. These questions facilitate the collection of quantitative data and are extensively used in data collection processes.
• Prior studies: Before collecting feedback from respondents, researchers often delve into previous studies related to the research topic. This preliminary research helps frame the study effectively and ensures the data collection process is well-informed.
• Quantitative data: Typically, quantitative data is represented using tables, charts, graphs, or other numerical forms. This visual representation aids in understanding the collected data and is essential for rigorous data analysis, a key component of quantitative research methods.
• Generalization of results: One of the strengths of quantitative research is its ability to generalize results to the entire population. It means that the findings derived from a sample can be extrapolated to make informed decisions and take appropriate actions for improvement based on numerical data analysis.

Quantitative Research Methods

Quantitative research methods are systematic approaches used to gather and analyze numerical data to understand and draw conclusions about a phenomenon or population. Here are the quantitative research methods:

• Primary quantitative research methods
• Secondary quantitative research methods

Primary Quantitative Research Methods

Primary quantitative research is the most widely used method of conducting market research. The distinct feature of primary research is that the researcher focuses on collecting data directly rather than depending on data collected from previously done research. Primary quantitative research design can be broken down into three further distinctive tracks and the process flow. They are:

A. Techniques and Types of Studies

There are multiple types of primary quantitative research. They can be distinguished into the four following distinctive methods, which are:

01. Survey Research

Survey Research is fundamental for all quantitative outcome research methodologies and studies. Surveys are used to ask questions to a sample of respondents, using various types such as online polls, online surveys, paper questionnaires, web-intercept surveys , etc. Every small and big organization intends to understand what their customers think about their products and services, how well new features are faring in the market, and other such details.

By conducting survey research, an organization can ask multiple survey questions , collect data from a pool of customers, and analyze this collected data to produce numerical results. It is the first step towards collecting data for any research. You can use single ease questions . A single-ease question is a straightforward query that elicits a concise and uncomplicated response.

This type of research can be conducted with a specific target audience group and also can be conducted across multiple groups along with comparative analysis . A prerequisite for this type of research is that the sample of respondents must have randomly selected members. This way, a researcher can easily maintain the accuracy of the obtained results as a huge variety of respondents will be addressed using random selection. 

Traditionally, survey research was conducted face-to-face or via phone calls. Still, with the progress made by online mediums such as email or social media, survey research has also spread to online mediums.There are two types of surveys , either of which can be chosen based on the time in hand and the kind of data required:

Cross-sectional surveys: Cross-sectional surveys are observational surveys conducted in situations where the researcher intends to collect data from a sample of the target population at a given point in time. Researchers can evaluate various variables at a particular time. Data gathered using this type of survey is from people who depict similarity in all variables except the variables which are considered for research . Throughout the survey, this one variable will stay constant.

• Cross-sectional surveys are popular with retail, SMEs, and healthcare industries. Information is garnered without modifying any parameters in the variable ecosystem.
• Multiple samples can be analyzed and compared using a cross-sectional survey research method.
• Multiple variables can be evaluated using this type of survey research.
• The only disadvantage of cross-sectional surveys is that the cause-effect relationship of variables cannot be established as it usually evaluates variables at a particular time and not across a continuous time frame.

Longitudinal surveys: Longitudinal surveys are also observational surveys , but unlike cross-sectional surveys, longitudinal surveys are conducted across various time durations to observe a change in respondent behavior and thought processes. This time can be days, months, years, or even decades. For instance, a researcher planning to analyze the change in buying habits of teenagers over 5 years will conduct longitudinal surveys.

• In cross-sectional surveys, the same variables were evaluated at a given time, and in longitudinal surveys, different variables can be analyzed at different intervals.
• Longitudinal surveys are extensively used in the field of medicine and applied sciences. Apart from these two fields, they are also used to observe a change in the market trend analysis , analyze customer satisfaction, or gain feedback on products/services.
• In situations where the sequence of events is highly essential, longitudinal surveys are used.
• Researchers say that when research subjects need to be thoroughly inspected before concluding, they rely on longitudinal surveys.

02. Correlational Research

A comparison between two entities is invariable. Correlation research is conducted to establish a relationship between two closely-knit entities and how one impacts the other, and what changes are eventually observed. This research method is carried out to give value to naturally occurring relationships, and a minimum of two different groups are required to conduct this quantitative research method successfully. Without assuming various aspects, a relationship between two groups or entities must be established.

Researchers use this quantitative research design to correlate two or more variables using mathematical analysis methods. Patterns, relationships, and trends between variables are concluded as they exist in their original setup. The impact of one of these variables on the other is observed, along with how it changes the relationship between the two variables. Researchers tend to manipulate one of the variables to attain the desired results.

Ideally, it is advised not to make conclusions merely based on correlational research. This is because it is not mandatory that if two variables are in sync that they are interrelated.

Example of Correlational Research Questions :

• The relationship between stress and depression.
• The equation between fame and money.
• The relation between activities in a third-grade class and its students.

03. Causal-comparative Research

This research method mainly depends on the factor of comparison. Also called quasi-experimental research , this quantitative research method is used by researchers to conclude the cause-effect equation between two or more variables, where one variable is dependent on the other independent variable. The independent variable is established but not manipulated, and its impact on the dependent variable is observed. These variables or groups must be formed as they exist in the natural setup. As the dependent and independent variables will always exist in a group, it is advised that the conclusions are carefully established by keeping all the factors in mind.

Causal-comparative research is not restricted to the statistical analysis of two variables but extends to analyzing how various variables or groups change under the influence of the same changes. This research is conducted irrespective of the type of relationship that exists between two or more variables. Statistical analysis plan is used to present the outcome using this quantitative research method.

Example of Causal-Comparative Research Questions:

• The impact of drugs on a teenager. The effect of good education on a freshman. The effect of substantial food provision in the villages of Africa.

04. Experimental Research

Also known as true experimentation, this research method relies on a theory. As the name suggests, experimental research is usually based on one or more theories. This theory has yet to be proven before and is merely a supposition. In experimental research, an analysis is done around proving or disproving the statement. This research method is used in natural sciences. Traditional research methods are more effective than modern techniques.

There can be multiple theories in experimental research. A theory is a statement that can be verified or refuted.

After establishing the statement, efforts are made to understand whether it is valid or invalid. This quantitative research method is mainly used in natural or social sciences as various statements must be proved right or wrong.

• Traditional research methods are more effective than modern techniques.
• Systematic teaching schedules help children who struggle to cope with the course.
• It is a boon to have responsible nursing staff for ailing parents.

B. Data Collection Methodologies

The second major step in primary quantitative research is data collection. Data collection can be divided into sampling methods and data collection using surveys and polls.

01. Data Collection Methodologies: Sampling Methods

There are two main sampling methods for quantitative research: Probability and Non-probability sampling .

Probability sampling: A theory of probability is used to filter individuals from a population and create samples in probability sampling . Participants of a sample are chosen by random selection processes. Each target audience member has an equal opportunity to be selected in the sample.

There are four main types of probability sampling:

• Simple random sampling: As the name indicates, simple random sampling is nothing but a random selection of elements for a sample. This sampling technique is implemented where the target population is considerably large.
• Stratified random sampling: In the stratified random sampling method , a large population is divided into groups (strata), and members of a sample are chosen randomly from these strata. The various segregated strata should ideally not overlap one another.
• Cluster sampling: Cluster sampling is a probability sampling method using which the main segment is divided into clusters, usually using geographic segmentation and demographic segmentation parameters.
• Systematic sampling: Systematic sampling is a technique where the starting point of the sample is chosen randomly, and all the other elements are chosen using a fixed interval. This interval is calculated by dividing the population size by the target sample size.

Non-probability sampling: Non-probability sampling is where the researcher’s knowledge and experience are used to create samples. Because of the researcher’s involvement, not all the target population members have an equal probability of being selected to be a part of a sample.

There are five non-probability sampling models:

• Convenience sampling: In convenience sampling , elements of a sample are chosen only due to one prime reason: their proximity to the researcher. These samples are quick and easy to implement as there is no other parameter of selection involved.
• Consecutive sampling: Consecutive sampling is quite similar to convenience sampling, except for the fact that researchers can choose a single element or a group of samples and conduct research consecutively over a significant period and then perform the same process with other samples.
• Quota sampling: Using quota sampling , researchers can select elements using their knowledge of target traits and personalities to form strata. Members of various strata can then be chosen to be a part of the sample as per the researcher’s understanding.
• Snowball sampling: Snowball sampling is conducted with target audiences who are difficult to contact and get information. It is popular in cases where the target audience for analysis research is rare to put together.
• Judgmental sampling: Judgmental sampling is a non-probability sampling method where samples are created only based on the researcher’s experience and research skill .

02. Data collection methodologies: Using surveys & polls

Once the sample is determined, then either surveys or polls can be distributed to collect the data for quantitative research.

Using surveys for primary quantitative research

A survey is defined as a research method used for collecting data from a pre-defined group of respondents to gain information and insights on various topics of interest. The ease of survey distribution and the wide number of people it can reach depending on the research time and objective makes it one of the most important aspects of conducting quantitative research.

Fundamental levels of measurement – nominal, ordinal, interval, and ratio scales

Four measurement scales are fundamental to creating a multiple-choice question in a survey. They are nominal, ordinal, interval, and ratio measurement scales without the fundamentals of which no multiple-choice questions can be created. Hence, it is crucial to understand these measurement levels to develop a robust survey.

Use of different question types

To conduct quantitative research, close-ended questions must be used in a survey. They can be a mix of multiple question types, including multiple-choice questions like semantic differential scale questions , rating scale questions , etc.

Survey Distribution and Survey Data Collection

In the above, we have seen the process of building a survey along with the research design to conduct primary quantitative research. Survey distribution to collect data is the other important aspect of the survey process. There are different ways of survey distribution. Some of the most commonly used methods are:

• Email: Sending a survey via email is the most widely used and effective survey distribution method. This method’s response rate is high because the respondents know your brand. You can use the QuestionPro email management feature to send out and collect survey responses.
• Buy respondents: Another effective way to distribute a survey and conduct primary quantitative research is to use a sample. Since the respondents are knowledgeable and are on the panel by their own will, responses are much higher.
• Embed survey on a website: Embedding a survey on a website increases a high number of responses as the respondent is already in close proximity to the brand when the survey pops up.
• Social distribution: Using social media to distribute the survey aids in collecting a higher number of responses from the people that are aware of the brand.
• QR code: QuestionPro QR codes store the URL for the survey. You can print/publish this code in magazines, signs, business cards, or on just about any object/medium.
• SMS survey: The SMS survey is a quick and time-effective way to collect a high number of responses.
• Offline Survey App: The QuestionPro App allows users to circulate surveys quickly, and the responses can be collected both online and offline.

Survey example

An example of a survey is a short customer satisfaction (CSAT) survey that can quickly be built and deployed to collect feedback about what the customer thinks about a brand and how satisfied and referenceable the brand is.

Using polls for primary quantitative research

Polls are a method to collect feedback using close-ended questions from a sample. The most commonly used types of polls are election polls and exit polls . Both of these are used to collect data from a large sample size but using basic question types like multiple-choice questions.

C. Data Analysis Techniques

The third aspect of primary quantitative research design is data analysis . After collecting raw data, there must be an analysis of this data to derive statistical inferences from this research. It is important to relate the results to the research objective and establish the statistical relevance of the results.

Remember to consider aspects of research that were not considered for the data collection process and report the difference between what was planned vs. what was actually executed.

It is then required to select precise Statistical Analysis Methods , such as SWOT, Conjoint, Cross-tabulation, etc., to analyze the quantitative data.

• SWOT analysis: SWOT Analysis stands for the acronym of Strengths, Weaknesses, Opportunities, and Threat analysis. Organizations use this statistical analysis technique to evaluate their performance internally and externally to develop effective strategies for improvement.
• Conjoint Analysis: Conjoint Analysis is a market analysis method to learn how individuals make complicated purchasing decisions. Trade-offs are involved in an individual’s daily activities, and these reflect their ability to decide from a complex list of product/service options.
• Cross-tabulation: Cross-tabulation is one of the preliminary statistical market analysis methods which establishes relationships, patterns, and trends within the various parameters of the research study.
• TURF Analysis: TURF Analysis , an acronym for Totally Unduplicated Reach and Frequency Analysis, is executed in situations where the reach of a favorable communication source is to be analyzed along with the frequency of this communication. It is used for understanding the potential of a target market.

Inferential statistics methods such as confidence interval, the margin of error, etc., can then be used to provide results.

Secondary Quantitative Research Methods

Secondary quantitative research or desk research is a research method that involves using already existing data or secondary data. Existing data is summarized and collated to increase the overall effectiveness of the research.

This research method involves collecting quantitative data from existing data sources like the internet, government resources, libraries, research reports, etc. Secondary quantitative research helps to validate the data collected from primary quantitative research and aid in strengthening or proving, or disproving previously collected data.

The following are five popularly used secondary quantitative research methods:

• Data available on the internet: With the high penetration of the internet and mobile devices, it has become increasingly easy to conduct quantitative research using the internet. Information about most research topics is available online, and this aids in boosting the validity of primary quantitative data.
• Government and non-government sources: Secondary quantitative research can also be conducted with the help of government and non-government sources that deal with market research reports. This data is highly reliable and in-depth and hence, can be used to increase the validity of quantitative research design.
• Public libraries: Now a sparingly used method of conducting quantitative research, it is still a reliable source of information, though. Public libraries have copies of important research that was conducted earlier. They are a storehouse of valuable information and documents from which information can be extracted.
• Educational institutions: Educational institutions conduct in-depth research on multiple topics, and hence, the reports that they publish are an important source of validation in quantitative research.
• Commercial information sources: Local newspapers, journals, magazines, radio, and TV stations are great sources to obtain data for secondary quantitative research. These commercial information sources have in-depth, first-hand information on market research, demographic segmentation, and similar subjects.

Quantitative Research Examples

Some examples of quantitative research are:

• A customer satisfaction template can be used if any organization would like to conduct a customer satisfaction (CSAT) survey . Through this kind of survey, an organization can collect quantitative data and metrics on the goodwill of the brand or organization in the customer’s mind based on multiple parameters such as product quality, pricing, customer experience, etc. This data can be collected by asking a net promoter score (NPS) question , matrix table questions, etc. that provide data in the form of numbers that can be analyzed and worked upon.
• Another example of quantitative research is an organization that conducts an event, collecting feedback from attendees about the value they see from the event. By using an event survey , the organization can collect actionable feedback about the satisfaction levels of customers during various phases of the event such as the sales, pre and post-event, the likelihood of recommending the organization to their friends and colleagues, hotel preferences for the future events and other such questions.

What are the Advantages of Quantitative Research?

There are many advantages to quantitative research. Some of the major advantages of why researchers use this method in market research are:

Collect Reliable and Accurate Data:

Quantitative research is a powerful method for collecting reliable and accurate quantitative data. Since data is collected, analyzed, and presented in numbers, the results obtained are incredibly reliable and objective. Numbers do not lie and offer an honest and precise picture of the conducted research without discrepancies. In situations where a researcher aims to eliminate bias and predict potential conflicts, quantitative research is the method of choice.

Quick Data Collection:

Quantitative research involves studying a group of people representing a larger population. Researchers use a survey or another quantitative research method to efficiently gather information from these participants, making the process of analyzing the data and identifying patterns faster and more manageable through the use of statistical analysis. This advantage makes quantitative research an attractive option for projects with time constraints.

Wider Scope of Data Analysis:

Quantitative research, thanks to its utilization of statistical methods, offers an extensive range of data collection and analysis. Researchers can delve into a broader spectrum of variables and relationships within the data, enabling a more thorough comprehension of the subject under investigation. This expanded scope is precious when dealing with complex research questions that require in-depth numerical analysis.

Eliminate Bias:

One of the significant advantages of quantitative research is its ability to eliminate bias. This research method leaves no room for personal comments or the biasing of results, as the findings are presented in numerical form. This objectivity makes the results fair and reliable in most cases, reducing the potential for researcher bias or subjectivity.

In summary, quantitative research involves collecting, analyzing, and presenting quantitative data using statistical analysis. It offers numerous advantages, including the collection of reliable and accurate data, quick data collection, a broader scope of data analysis, and the elimination of bias, making it a valuable approach in the field of research. When considering the benefits of quantitative research, it’s essential to recognize its strengths in contrast to qualitative methods and its role in collecting and analyzing numerical data for a more comprehensive understanding of research topics.

Best Practices to Conduct Quantitative Research

Here are some best practices for conducting quantitative research:

• Differentiate between quantitative and qualitative: Understand the difference between the two methodologies and apply the one that suits your needs best.
• Choose a suitable sample size: Ensure that you have a sample representative of your population and large enough to be statistically weighty.
• Keep your research goals clear and concise: Know your research goals before you begin data collection to ensure you collect the right amount and the right quantity of data.
• Keep the questions simple: Remember that you will be reaching out to a demographically wide audience. Pose simple questions for your respondents to understand easily.

Quantitative Research vs Qualitative Research

Quantitative research and qualitative research are two distinct approaches to conducting research, each with its own set of methods and objectives. Here’s a comparison of the two:

Quantitative Research

• Objective: The primary goal of quantitative research is to quantify and measure phenomena by collecting numerical data. It aims to test hypotheses, establish patterns, and generalize findings to a larger population.
• Data Collection: Quantitative research employs systematic and standardized approaches for data collection, including techniques like surveys, experiments, and observations that involve predefined variables. It is often collected from a large and representative sample.
• Data Analysis: Data is analyzed using statistical techniques, such as descriptive statistics, inferential statistics, and mathematical modeling. Researchers use statistical tests to draw conclusions and make generalizations based on numerical data.
• Sample Size: Quantitative research often involves larger sample sizes to ensure statistical significance and generalizability.
• Results: The results are typically presented in tables, charts, and statistical summaries, making them highly structured and objective.
• Generalizability: Researchers intentionally structure quantitative research to generate outcomes that can be helpful to a larger population, and they frequently seek to establish causative connections.
• Emphasis on Objectivity: Researchers aim to minimize bias and subjectivity, focusing on replicable and objective findings.

Qualitative Research

• Objective: Qualitative research seeks to gain a deeper understanding of the underlying motivations, behaviors, and experiences of individuals or groups. It explores the context and meaning of phenomena.
• Data Collection: Qualitative research employs adaptable and open-ended techniques for data collection, including methods like interviews, focus groups, observations, and content analysis. It allows participants to express their perspectives in their own words.
• Data Analysis: Data is analyzed through thematic analysis, content analysis, or grounded theory. Researchers focus on identifying patterns, themes, and insights in the data.
• Sample Size: Qualitative research typically involves smaller sample sizes due to the in-depth nature of data collection and analysis.
• Results: Findings are presented in narrative form, often in the participants’ own words. Results are subjective, context-dependent, and provide rich, detailed descriptions.
• Generalizability: Qualitative research does not aim for broad generalizability but focuses on in-depth exploration within a specific context. It provides a detailed understanding of a particular group or situation.
• Emphasis on Subjectivity: Researchers acknowledge the role of subjectivity and the researcher’s influence on the Research Process . Participant perspectives and experiences are central to the findings.

Researchers choose between quantitative and qualitative research methods based on their research objectives and the nature of the research question. Each approach has its advantages and drawbacks, and the decision between them hinges on the particular research objectives and the data needed to address research inquiries effectively.

Quantitative research is a structured way of collecting and analyzing data from various sources. Its purpose is to quantify the problem and understand its extent, seeking results that someone can project to a larger population.

Companies that use quantitative rather than qualitative research typically aim to measure magnitudes and seek objectively interpreted statistical results. So if you want to obtain quantitative data that helps you define the structured cause-and-effect relationship between the research problem and the factors, you should opt for this type of research.

At QuestionPro , we have various Best Data Collection Tools and features to conduct investigations of this type. You can create questionnaires and distribute them through our various methods. We also have sample services or various questions to guarantee the success of your study and the quality of the collected data.

Quantitative research is a systematic and structured approach to studying phenomena that involves the collection of measurable data and the application of statistical, mathematical, or computational techniques for analysis.

Quantitative research is characterized by structured tools like surveys, substantial sample sizes, closed-ended questions, reliance on prior studies, data presented numerically, and the ability to generalize findings to the broader population.

The two main methods of quantitative research are Primary quantitative research methods, involving data collection directly from sources, and Secondary quantitative research methods, which utilize existing data for analysis.

1.Surveying to measure employee engagement with numerical rating scales. 2.Analyzing sales data to identify trends in product demand and market share. 4.Examining test scores to assess the impact of a new teaching method on student performance. 4.Using website analytics to track user behavior and conversion rates for an online store.

1.Differentiate between quantitative and qualitative approaches. 2.Choose a representative sample size. 3.Define clear research goals before data collection. 4.Use simple and easily understandable survey questions.

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Quantitative Research

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Quantitative research methods are concerned with the planning, design, and implementation of strategies to collect and analyze data. Descartes, the seventeenth-century philosopher, suggested that how the results are achieved is often more important than the results themselves, as the journey taken along the research path is a journey of discovery. High-quality quantitative research is characterized by the attention given to the methods and the reliability of the tools used to collect the data. The ability to critique research in a systematic way is an essential component of a health professional’s role in order to deliver high quality, evidence-based healthcare. This chapter is intended to provide a simple overview of the way new researchers and health practitioners can understand and employ quantitative methods. The chapter offers practical, realistic guidance in a learner-friendly way and uses a logical sequence to understand the process of hypothesis development, study design, data collection and handling, and finally data analysis and interpretation.

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Babbie ER. The practice of social research. 14th ed. Belmont: Wadsworth Cengage; 2016.

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Wilson, L.A. (2019). Quantitative Research. In: Liamputtong, P. (eds) Handbook of Research Methods in Health Social Sciences. Springer, Singapore. https://doi.org/10.1007/978-981-10-5251-4_54

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3.4 - Two Quantitative Variables

Later in the course, we will devote an entire lesson to analyzing two quantitative variables. In this lesson, you will be introduced to scatterplots, correlation, and simple linear regression. A scatterplot is a graph used to display data concerning two quantitative variables. Correlation is a measure of the direction and strength of the relationship between two quantitative variables. Simple linear regression uses one quantitative variable to predict a second quantitative variable. You will not need to compute correlations or regression models by hand in this course. There is one example of computing a correlation by hand in the notes to show you how it relates to  z  scores, but for all assignments, you should be using Minitab to compute these statistics.

3.4.1 - Scatterplots

Recall from Lesson 1.1.2 , in some research studies one variable is used to predict or explain differences in another variable. In those cases, the  explanatory variable  is used to predict or explain differences in the  response variable .

Variable that is used to explain variability in the response variable, also known as an  independent variable  or  predictor variable ; in an experimental study, this is the variable that is manipulated by the researcher.

The outcome variable, also known as a  dependent variable .

A scatterplot can be used to display the relationship between the explanatory and response variables. Or, a scatterplot can be used to examine the association between two variables in situations where there is not a clear explanatory and response variable. For example, we may want to examine the relationship between height and weight in a sample but have no hypothesis as to which variable impacts the other; in this case, it does not matter which variable is on the x-axis and which is on the y-axis.

When examining a scatterplot, we need to consider the following:

• Direction (positive or negative)
• Form (linear or non-linear) 
• Strength (weak, moderate, strong)
• Bivariate outliers

In this class, we will focus on linear relationships. This occurs when the line-of-best-fit for describing the relationship between  x  and  y  is a straight line. The linear relationship between two variables is positive when both increase together; in other words, as values of  x  get larger values of  y  get larger. This is also known as a direct relationship. The linear relationship between two variables is negative when one increases as the other decreases. For example, as values of  x  get larger values of  y  get smaller. This is also known as an indirect relationship.

A bivariate outlier is an observation that does not fit with the general pattern of the other observations. 

Example: Baseball

Data concerning baseball statistics and salaries from the 1991 and 1992 seasons is available at:

•   http://www.amstat.org/publications/jse/datasets/baseball.dat.txt

The scatterplot below shows the relationship between salary and batting average for the 337 baseball players in this sample.

From this scatterplot, we can see that there does not appear to be a meaningful relationship between baseball players' salaries and batting averages. We can also see that more players had salaries at the low end and fewer had salaries at the high end.

Example: Height and Shoe Size

Data concerning the heights and shoe sizes of 408 students were retrieved from:

• http://www.amstat.org/publications/jse/v20n3/mclaren/shoesize.xls

The scatterplot below was constructed to show the relationship between height and shoe size.

There is a positive linear relationship between height and shoe size in this sample. The magnitude of the relationship appears to be strong. There do not appear to be any outliers. 

Example: Height and Weight

Data concerning body measurements from 507 individuals retrieved from:

• https://ww2.amstat.org/publications/jse/datasets/body.dat.txt

For more information see:

• https://ww2.amstat.org/publications/jse/datasets/body.txt

The scatterplot below shows the relationship between height and weight.

There is a positive linear relationship between height and weight. The magnitude of the relationship is moderately strong.

Example: Cafés

Data concerning sales at student-run café were retrieved from:

• http://www.amstat.org/publications/jse/v19n1/cafedata.xls

For more information about this data set, visit:

• http://www.amstat.org/publications/jse/v19n1/cafedata_documentation.txt

The scatterplot below shows the relationship between maximum daily temperature and coffee sales.

There is a negative linear relationship between the maximum daily temperature and coffee sales. The magnitude is moderately strong. There do not appear to be any outliers.

3.4.1.1 - Minitab: Simple Scatterplot

Minitab ®  – simple scatterplot.

The file below contains data concerning students' quiz averages and final exam scores. Let's construct a scatterplot with the quiz averages on the horizontal axis and final exam scores on the vertical axis.

• Open the data file in Minitab 
• From the tool bar, select Graphs > Scatterplot  >  One Y Variable  >  Simple
• Double click the variable  Final  on the left to move it to the  Y variable  box on the right
• Double click the variable  Quiz_Average on the left to move it to the   X variable  box on the right

This should result in the scatterplot below:

  Watch Video

3.4.2 - Correlation

In this course, we will be using Pearson's \(r\) as a measure of the linear relationship between two quantitative variables. In a sample, we use the symbol \(r\). In a population, we use the Greek letter \(\rho\) ("rho"). Pearson's \(r\) can easily be computed using statistical software.

• \(-1\leq r \leq +1\)
• For a positive association, \(r>0\), for a negative association \(r<0\), if there is no relationship \(r=0\)
• The closer \(r\) is to \(0\) the weaker the relationship and the closer to \(+1\) or \(-1\) the stronger the relationship (e.g., \(r=-0.88\) is a stronger relationship than \(r=+0.60\)); the sign of the correlation provides direction only
• Correlation is unit free; the \(x\) and \(y\) variables do NOT need to be on the same scale (e.g., it is possible to compute the correlation between height in centimeters and weight in pounds)
• It does not matter which variable you label as \(x\) and which you label as \(y\). The correlation between \(x\) and \(y\) is equal to the correlation between \(y\) and \(x\). 

The following table may serve as a guideline when evaluating correlation coefficients:

• Correlation does NOT equal causation. A strong relationship between \(x\) and \(y\) does not necessarily mean that \(x\) causes \(y\). It is possible that \(y\) causes \(x\), or that a confounding variable causes both \(x\) and \(y\). 
• Pearson's \(r\) should only be used when there is a linear relationship between \(x\) and \(y\). A scatterplot should be constructed before computing Pearson's \(r\) to confirm that the relationship is not non-linear. 
• Pearson's \(r\) is not resistant to outliers.  Figure 1 below provides an example of an influential outlier. Influential outliers are points in a data set that increase the correlation coefficient. In Figure 1 the correlation between \(x\) and \(y\) is strong (\(r=0.979\)). In Figure 2 below, the outlier is removed. Now, the correlation between \(x\) and \(y\) is lower (\(r=0.576\)) and the slope is less steep.

Note that the scale on both the x and y axes has changed. In addition to the correlation changing, the y-intercept changed from 4.154 to 70.84 and the slope changed from 6.661 to 1.632.

3.4.2.1 - Formulas for Computing Pearson's r

There are a number of different versions of the formula for computing Pearson's \(r\). You should get the same correlation value regardless of which formula you use.  Note that you will not have to compute Pearson's \(r\) by hand in this course.  These formulas are presented here to help you understand what the value means. You should always be using technology to compute this value. 

First, we'll look at the conceptual formula which uses \(z\) scores. To use this formula we would first compute the  \(z\) score for every \(x\) and \(y\) value. We would multiply each case's \(z_x\) by their \(z_y\).  If their  \(x\) and  \(y\) values were both above the mean then this product would be positive. If their x and y values were both below the mean this product would be positive. If one value was above the mean and the other was below the mean this product would be negative. Think of how this relates to the correlation being positive or negative. The sum of all of these products is divided by \(n-1\) to obtain the correlation. 

\(r=\dfrac{\sum{z_x z_y}}{n-1}\) where \(z_x=\dfrac{x - \overline{x}}{s_x}\) and \(z_y=\dfrac{y - \overline{y}}{s_y}\)

When we replace \(z_x\) and \(z_y\) with the \(z\) score formulas and move the \(n-1\) to a separate fraction we get the formula in your textbook: \(r=\frac{1}{n-1}\Sigma{\left(\frac{x-\overline x}{s_x}\right) \left( \frac{y-\overline y}{s_y}\right)}\)

3.4.2.2 - Example of Computing r by Hand (Optional)

Again, you will  not  need to compute \(r\) by hand in this course. This example is meant to show you how \(r\)   is computed with the intention of enhancing your understanding of its meaning. In this course, you will always be using Minitab or StatKey to compute correlations. 

In this example we have data from a random sample of \(n = 9\) World Campus STAT 200 students from the Spring 2017 semester. WileyPlus scores had a maximum possible value of 100. Midterm exam scores had a maximum possible value of 50. Remember, the \(x\) and \(y\) variables do not need to be on the same metric to compute a correlation. 

Minitab was used to construct a scatterplot of these two variables. We need to examine the shape of the relationship before determining if Pearson's \(r\) is the appropriate correlation coefficient to use. Pearson's \(r\) can only be used to check for a linear relationship. For this example I am going to call WileyPlus grades the \(x\) variable and midterm exam grades the \(y\) variable because students completed WileyPlus assignments before the midterm exam.

Summary Statistics

From this scatterplot we can determine that the relationship may be weak, but that it is reasonable to consider a linear relationship. If we were to draw a line of best fit through this scatterplot we would draw a straight line with a slight upward slope. Now, we'll compute Pearson's \(r\) using the \(z\) score formula. The first step is to convert every WileyPlus score to a \(z\) score and every midterm score to a \(z\) score. When we constructed the scatterplot in Minitab we were also provided with summary statistics including the mean and standard deviation for each variable which we need to compute the \(z\) scores.

A positive value in the \(z_x\) column means that the student's WileyPlus score is above the mean. Now, we'll do the same for midterm exam scores.

Our next step is to multiply each student's WileyPlus \(z\) score with his or her midterm exam score.

A positive "cross product" (i.e., \(z_x z_y\)) means that the student's WileyPlus and midterm score were both either above or below the mean. A negative cross product means that they scored above the mean on one measure and below the mean on the other measure. If there is no relationship between \(x\) and \(y\) then there would be an even mix of positive and negative cross products; when added up these would equal around zero signifying no relationship. If there is a relationship between \(x\) and \(y\) then these cross products would primarily be going in the same direction. If the correlation is positive then these cross products would primarily be positive. If the correlation is negative then these cross products would primarily be negative; in other words, students with higher \(x\) values would have lower \(y\) values and vice versa. Let's add the cross products here and compute our \(r\) statistic.

\(\sum z_x z_y = 0.758+0.714-0.624-0.411-0.425+1.631+1.124+0.988+0.123=3.878\)

\(r=\frac{3.878}{9-1}=0.485\)

There is a positive, moderately strong, relationship between WileyPlus scores and midterm exam scores in this sample.

3.4.2.3 - Minitab: Compute Pearson's r

Minitab ®  – pearson's r.

We previously created a scatterplot of quiz averages and final exam scores and observed a linear relationship. Here, we will compute the correlation between these two variables.

• Open the data file in Minitab: Exam.mwx (or Exam.csv )
• Choose Stat > Basic Statistics > Correlation .
• In Variables , enter Double click the  Quiz_Average  and  Final  in the box on the left to insert them into the  Variables  box
• Click Graphs.
• In Statistics to display on plot , choose Correlations and intervals .

This should result in the following:

3.4.3 - Simple Linear Regression

Regression uses one or more explanatory variables (\(x\)) to predict one response variable (\(y\)). In this course, we will be learning specifically about simple linear regression. The "simple" part is that we will be using only one explanatory variable. If there are two or more explanatory variables, then multiple linear regression is necessary. The "linear" part is that we will be using a straight line to predict the response variable using the explanatory variable. Unlike in correlation, in regression is does matter which variable is called \(x\) and which is called \(y\). In regression, the explanatory variable is always \(x\) and the response variable is always \(y\). Both \(x\) and \(y\) must be quantitative variables.

You may recall from an algebra class that the formula for a straight line is \(y=mx+b\), where \(m\) is the slope and \(b\) is the y-intercept. The slope is a measure of how steep the line is; in algebra, this is sometimes described as "change in y over change in x," (\(\frac{\Delta y}{\Delta x}\)), or "rise over run." A positive slope indicates a line moving from the bottom left to top right. A negative slope indicates a line moving from the top left to bottom right. The  y-intercept is the location on the y-axis where the line passes through. In other words, when \(x=0\) then \(y=y - intercept\).

In statistics, we use similar formulas:

\(\widehat{y}\) = predicted value of \(y\) for a given value of \(x\) \(a\) = \(y\)-intercept \(b\) = slope

In a population, the y-intercept is denoted as \(\beta_0\) ("beta sub 0") or \(\alpha\) ("alpha"). The slope is denoted as \(\beta_1\) ("beta sub 1") or just \(\beta\) ("beta").

Simple linear regression uses data from a sample to construct the line of best fit. But what makes a line “best fit”? The most common method of constructing a simple linear regression line, and the only method that we will be using in this course, is the least squares method. The least squares method finds the values of the y-intercept and slope that make the sum of the squared residuals (also know as the sum of squared errors or SSE) as small as possible.

\(y\) = actual value of \(y\) \(\widehat{y}\) = predicted value of \(y\)

The plot below shows the line \(\widehat{y}=6.5+1.8x\)

Identify and interpret the y-intercept.

The y-intercept is 6.5. When \(x=0\) the predicted value of y is 6.5.

Identify and interpret the slope.

The slope is 1.8. For every one unit increase in x, the predicted value of y increases by 1.8.

Compute and interpret the residual for the point (-0.2, 5.1).

The observed x value is -0.2 and the observed y value is 5.1.

The formula for the residual is \(e=y-\widehat{y}\)

We can compute \(\widehat{y}\) using the regression equation that we have and \(x=-0.2\)

\(\widehat{y}=6.5+1.8(-0.2)=6.14\)

Given an x value of -0.2, we would predict this observation to have a y value of 6.14. In reality, they had a y value of 5.1. The residual is the difference between these two values.

\(e=y-\widehat{y}=5.1-6.14=-1.04\)

The residual for this observation is -1.04. This observation's y value is 1.04 less than predicted given their x value.

• Avoid extrapolation. This means that a regression line should not be used to make a prediction about someone from a population different from the one that the sample used to define the model was from. 
• Make a scatterplot of your data before running a regression model to confirm that a linear relationship is reasonable. Simple linear regression constructs a straight line. If the relationship between x and y is not linear, then a linear model is not the most appropriate. 
• Outliers can heavily influence a regression model. Recall the plots that we looked at when learning about correlation. The addition of one outlier can greatly change the line of best fit. In addition to examining a scatterplot for linearity, you should also be looking for outliers. 

Later in the course, we will devote a week to correlation and regression.

3.4.3.1 - Minitab: SLR

Minitab ®  – simple linear regression.

We previously created a scatterplot of quiz averages and final exam scores and observed a linear relationship. Here, we will use quiz scores to predict final exam scores.

• Open the Minitab file: Exam.mwx (or Exam.csv )
• Select  Stat > Regression > Regression > Fit Regression Model...
• Double click  Final  in the box on the left to insert it into the  Responses (Y)  box on the right
• Double click  Quiz_Average  in the box on the left to insert it into the Continuous Predictors (X)  box on the right
• Click  OK

This should result in the following output:

Regression Equation

Final = 12.1 + 0.751 Quiz_Average

Coefficients

Model summary, analysis of variance, fits and diagnostics for unusual observations.

R Large residual

Interpretation

In the output in the above example we are given a simple linear regression model of Final = 12.1 + 0.751 Quiz_Average

This means that the y-intercept is 12.1 and the slope is 0.751. 

3.4.3.2 - Example: Interpreting Output

This example uses the "CAOSExam" dataset available from http://www.lock5stat.com/datapage.html.

CAOS stands for Comprehensive Assessment of Outcomes in a First Statistics course. It is a measure of students' statistical reasoning skills. Here we have data from 10 students who took the CAOS at the beginning (pre-test) and end (post-test) of a statistics course. 

Research question:  How can we use students' pre-test scores to predict their post-test scores?

Minitab was used to construct a simple linear regression model. The two pieces of output that we are going to interpret here are the regression equation and the scatterplot containing the regression line.

Let's work through a few common questions.

What is the regression model?

The "regression model" refers to the regression equation. This is \(\widehat {posttest}=21.43 + 0.8394(Pretest)\)

The slope is 0.8394. For every one point increase in a student's pre-test score, their predicted post-test score increases by 0.8394 points.

Identify and interpret the y-intercept. 

The y-intercept is 21.43. A student with a pre-test score of 0 would have a predicted post-test score of 21.43.  However, in this scenario, we should not actually use this model to predict the post-test score of someone who scored 0 on the pre-test because that would be extrapolation. This model should only be used to predict the post-test score of students from a comparable population whose pre-test scores were between approximately 35 and 65.

One student scored 60 on the pre-test and 65 on the post-test. Calculate and interpret that student's residual. 

This student's observed x value was 60 and their observed y value was 65. 

\(e=y- \widehat y\)

We have y.  We can compute \(\widehat y\) using the x value and regression equation that we have.

\(\widehat y = 21.43 + 0.8394(60) = 71.794\)

\(e=65-71.794=-6.794\)

This student's residual is -6.794. They scored 6.794 points lower on the post-test than we predicted given their pre-test score. 

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Home » Quantitative Variable – Definition, Types and Examples

Quantitative Variable – Definition, Types and Examples

Table of Contents

Quantitative Variable

Definition:

Quantitative variable is a type of variable in statistics that measures a numerical quantity or amount. It is a variable that can be measured on a numeric or quantitative scale, where each value has a specific numerical meaning.

Types of Quantitative Variables

There are two types of quantitative variables:

Discrete Variable

A discrete variable is a variable that can take only specific values. It cannot take on any value between two specific points. Examples of discrete variables include the number of children in a family, the number of students in a class, and the number of cars in a parking lot.

Continuous Variable

A continuous variable is a variable that can take on any value within a certain range. It can be measured on a continuous scale, and there are no gaps or interruptions between the values. Examples of continuous variables include age, weight, height, and temperature. Continuous variables are often measured using instruments that provide a high level of precision, such as a scale or a thermometer.

Quantitative Variable Measuring Scales

There are four types of quantitative variable measuring scales:

Nominal Scale

A nominal scale is a scale in which data are classified into mutually exclusive categories with no inherent order or ranking. Examples of nominal scale variables include gender, race, and occupation.

Ordinal Scale

An ordinal scale is a scale in which data are classified into categories that can be ranked or ordered. However, the intervals between the categories may not be equal. Examples of ordinal scale variables include education level (high school, college, graduate school), and socioeconomic status (low, middle, high).

Interval Scale

An interval scale is a scale in which data are classified into categories with equal intervals between them, but there is no true zero point. Examples of interval scale variables include temperature (measured in Celsius or Fahrenheit) and IQ scores.

Ratio Scale

A ratio scale is a scale in which data are classified into categories with equal intervals between them and a true zero point. Examples of ratio scale variables include weight, height, and income. With ratio scales, we can make meaningful comparisons between the numbers, and we can multiply or divide them to create meaningful ratios. For example, if someone’s income is twice that of someone else, we can say that their income ratio is 2:1.

Quantitative Variable Examples

Here are some examples of quantitative variables:

• Age : Age is a quantitative variable that can be measured on a continuous scale. It can be measured in years, months, or days.
• Income : Income is a quantitative variable that can be measured on a continuous scale. It can be measured in dollars, pounds, euros, or any other currency.
• Height : Height is a quantitative variable that can be measured on a continuous scale. It can be measured in inches, centimeters, or any other unit of measurement.
• Weight : Weight is a quantitative variable that can be measured on a continuous scale. It can be measured in pounds, kilograms, or any other unit of measurement.
• Test Scores : Test scores are quantitative variables that can be measured on a continuous scale. They can be measured as a percentage, a fraction, or a raw score.
• Number of Siblings : Number of siblings is a quantitative variable that can be measured on a discrete scale. It can take on specific values such as 0, 1, 2, 3, etc.
• Time to Complete a Task : Time to complete a task is a quantitative variable that can be measured on a continuous scale. It can be measured in seconds, minutes, or hours.
• Distance Traveled : Distance traveled is a quantitative variable that can be measured on a continuous scale. It can be measured in miles, kilometers, or any other unit of measurement.

Applications of Quantitative Variable

Quantitative variables have numerous applications in a wide range of fields, including:

• Social Sciences: In social sciences such as sociology, psychology, and economics, quantitative variables are used to measure and analyze social and economic phenomena such as income inequality, poverty rates, and education levels.
• Health Sciences: In health sciences, quantitative variables are used to measure and analyze health-related phenomena such as body mass index, blood pressure, and cholesterol levels.
• Physical Sciences: In physical sciences such as physics, chemistry, and engineering, quantitative variables are used to measure and analyze physical phenomena such as velocity, temperature, and mass.
• Business: In business, quantitative variables are used to measure and analyze financial and economic phenomena such as sales figures, profits, and market trends.
• Education: In education, quantitative variables are used to measure and analyze student achievement, learning outcomes, and teacher effectiveness.
• Environmental Science : In environmental science, quantitative variables are used to measure and analyze environmental phenomena such as pollution levels, climate change, and natural resource depletion.

When to use Quantitative Variable

Quantitative variables are used when we need to measure or analyze a numerical quantity, and the data can be expressed on a scale. Here are some situations where quantitative variables are appropriate:

• When we need to measure a physical characteristic: Quantitative variables are often used to measure physical characteristics such as height, weight, and blood pressure.
• When we need to analyze economic or financial data: Quantitative variables are often used in finance and economics to analyze financial and economic data such as income, expenditures, and market trends.
• When we need to analyze social phenomena: Quantitative variables are often used in social sciences such as sociology and psychology to analyze social phenomena such as educational attainment, poverty rates, and crime statistics.
• When we need to make precise comparisons: Quantitative variables provide a precise way to make comparisons between different groups or individuals.
• When we need to conduct statistical analysis: Quantitative variables are often used in statistical analysis to test hypotheses and make inferences about populations based on samples.

Purpose of Quantitative Variable

The purpose of a quantitative variable is to provide a numerical measurement of a phenomenon or attribute. It allows us to obtain precise and accurate data that can be analyzed and interpreted using statistical methods. Quantitative variables are used to:

• Measure and describe a phenomenon : Quantitative variables allow us to describe a phenomenon or attribute using numerical measurements. For example, height, weight, and age are all quantitative variables that allow us to describe physical characteristics of individuals.
• Test hypotheses and make inferences : Quantitative variables are often used in statistical analysis to test hypotheses and make inferences about populations based on samples. This allows us to draw conclusions about a larger group based on a smaller sample.
• Compare and contrast: Quantitative variables provide a structured and precise way to make comparisons and draw conclusions about differences and similarities between individuals, groups, or populations.
• Monitor changes over time : Quantitative variables can be used to monitor changes in a phenomenon over time, such as changes in economic indicators or health outcomes.

Characteristics of Quantitative Variable

The main characteristics of quantitative variables are:

• Numerical measurement: Quantitative variables are measured using numerical values, which can be expressed on a continuous or discrete scale.
• Precise and objective: Quantitative variables are typically more precise and objective than qualitative variables, as they can be measured using standardized instruments and methods.
• Statistical analysis: Quantitative variables are often used in statistical analysis, allowing for testing of hypotheses, making inferences, and drawing conclusions based on data.
• Different levels of measurement: Quantitative variables can be measured at different levels, including nominal, ordinal, interval, and ratio scales, which provide different levels of precision and allow for different types of statistical analysis.
• Continuous or discrete : Quantitative variables can be either continuous or discrete. Continuous variables can take on any value within a range, while discrete variables can only take on certain values.
• Mean and standard deviation : Quantitative variables are often described using summary statistics such as mean and standard deviation, which provide information about the central tendency and spread of the data.

Advantages of Quantitative Variable

• Precise measurements : Quantitative variables provide precise and measurable data, as they are measured using numerical values. This helps to reduce errors and make accurate conclusions.
• Statistical analysis: Quantitative variables are easier to analyze statistically, as numerical data can be easily graphed, compared, and manipulated.
• Easy to compare: Quantitative variables can be compared more easily than qualitative variables, as they are based on numerical values that can be ordered and compared.
• More objective : Quantitative variables are generally considered to be more objective than qualitative variables, as they are based on numerical data rather than subjective opinions or observations.
• Useful in modeling and prediction: Quantitative variables are often used in modeling and prediction, as they can be used to make mathematical models and projections based on numerical data.
• Can be used in scientific research: Quantitative variables are commonly used in scientific research, as they can provide precise and objective data that can be used to make empirical conclusions.

Limitation of Quantitative Variable

• Limited understanding of context: Quantitative variables may provide precise numerical measurements, but they often do not provide a full understanding of the context in which the data was collected. This can lead to misinterpretation or incomplete analysis of the data.
• May not capture qualitative aspects : Quantitative variables may not capture the full range of qualitative aspects of a phenomenon or attribute. For example, a quantitative variable such as income may not fully capture the quality of life of an individual or a community.
• May not capture unique experiences: Quantitative variables may not capture unique experiences or perspectives of individuals or groups. For example, a quantitative variable such as satisfaction with a product may not capture the unique experiences or perspectives of individual consumers.
• Potential for measurement error: Quantitative variables can be affected by measurement error, which can be introduced through faulty instruments or human error. This can lead to inaccurate or incomplete data.
• Limited to measurable phenomena: Quantitative variables are limited to phenomena that can be measured and expressed in numerical form. This means that some phenomena may not be fully captured by quantitative variables.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

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• Research article
• Open access
• Published: 06 May 2024

Evaluating lumbar disc degeneration by MRI quantitative metabolic indicators: the perspective of factor analysis

• Boxin Zheng 1 , 2   na1 ,
• Lin Ouyang 1 , 3   na1 ,
• Jianhua Shi 2 , 4 ,
• Xiaochan Shen 1 , 2 &
• Hanbin Lei 1 , 2  

Journal of Orthopaedic Surgery and Research volume  19 , Article number:  281 ( 2024 ) Cite this article

17 Accesses

Metrics details

This study aimed to investigate an early diagnostic method for lumbar disc degeneration (LDD) and improve its diagnostic accuracy.

Quantitative biomarkers of the lumbar body (LB) and lumbar discs (LDs) were obtained using nuclear magnetic resonance (NMR) detection technology. The diagnostic weights of each biological metabolism indicator were screened using the factor analysis method.

Through factor analysis, common factors such as the LB fat fraction, fat content, and T2* value of LDs were identified as covariates for the diagnostic model for the evaluation of LDD. This model can optimize the accuracy and reliability of LDD diagnosis.

The application of biomarker quantification methods based on NMR detection technology combined with factor analysis provides an effective means for the early diagnosis of LDD, thereby improving diagnostic accuracy and reliability.

Introduction

The intervertebral disc (ID), located between two vertebral bodies, is a dynamic fluid structure composed of three parts: the nucleus pulposus (NP), annulus pulposus (AF), and cartilage endplate (CEP) [ 1 , 2 ]. The nucleus pulposus is located in the central region and is rich in proteoglycans (PGs), which maintain the water content and height of the ID. Its main function is to buffer the axial load of the spine [ 3 , 4 ]. The AF is composed of organic collagen fibres and some fibroblast-like cells [ 5 , 6 ], and it supports the gel-like structure of the NP by wrapping the ID in a layered structure to resist the external force imposed on ID components [ 7 ]. The CEP is two transparent cartilages located on the upper and lower sides of the ID that are directly connected to the vertebral bone tissue [ 5 ]. As an individual ages, the IDs undergo a degradation cycle that begins earlier and progresses faster than other tissues in the body [ 8 ]. Therefore, the ID is one of the most sensitive organs in the ageing process of the human body and can reflect changes in human function.

Lumbar disc degeneration (LDD) is the pathological and physiological process in which significant changes occur in the shape, structure, and physiological function of the lumbar disc (LD), ultimately leading to a decrease in its ability to withstand pressure and torsional load. The pathogenesis of LDD is complex and closely related to age, genetics, excessive mechanical loading, trauma, and other factors. LDD is an important cause of low back pain in adults, and it is also the pathological and physiological basis for degenerative diseases such as lumbar spinal stenosis and lumbar disc herniation. In severe cases, it can even lead to the loss of a patient’s ability to work. If the signs of LDD can be detected in a timely manner at an early stage, early intervention and treatment can be carried out, which can effectively prevent the escalation of the lesion level and avoid the occurrence of irreversible consequences. Pfirrmann et al. [ 9 ] first proposed a method based on morphological and structural MRI indicators to determine the severity of LDD termed the Pfirrmann grading method. This method divides LDD into five progressive regression levels, I to V, and is recognized as the gold standard for determining the degree of LDD. With these criteria, doctors can determine the severity of LDD in a patient based on indicators such as morphological changes in the LD and the degree of MRI signal reduction. These MRI techniques often rely on the experience of diagnostic doctors to determine the severity of LDD. However, in patients with unclear symptoms of early LDD, the accurate detection of LDD using traditional diagnostic methods is difficult.

Previous studies have shown that abnormal tissue metabolism occurs earlier than changes in tissue structure. In the early stages of LDD, the biochemical metabolism of the LB and LDs changes [ 10 , 11 ]. These changes can be used to assist in earlier LDD evaluation, improve diagnostic accuracy, and provide more accurate treatment. To address this issue, this article used a technical method based on quantitative detection of biochemical metabolites by MRI to observe characteristic metabolic changes during LDD.

Materials and methods

Study population.

This study was approved by the Medical Ethics Committee of the 909th Hospital in China (Southeast Hospital Affiliated to Xiamen University, China), and informed consent was obtained from the study subjects. From June 2022 to December 2022, 99 volunteers of different age groups (20–29 years, 30–39 years, 40–49 years, 50–59 years, 60–69 years, and 70–79 years) were recruited. There were a total of 48 males (average age 45.9 ± 13.7 years) and 51 females (average age 48.8 ± 9.8 years), with a body mass index (BMI) of 23.1 ± 2.7 kg/m \({^2}\) (range 16.71 \(-\) 30.86 kg/m \({^2}\) ).

The inclusion criteria were as follows: (1) normal socialization with the general population, normal language communication, and ability to cooperate with MRI; (2) healthy with no major illnesses and voluntary participation; (3) age 20–80 years; and (4) no differences in sex.

The exclusion criteria were as follows: (1) contraindications for MRI examination, including claustrophobia or magnetic metal implants in important organs, such as cardiovascular and cerebrovascular stents; (2) normal structure and metabolism of the lumbar spine altered by other factors, such as deformities, lumbar fractures, surgical history, infections, connective tissue diseases, endocrine diseases, tumours, and long-term medication; (3) behaviours that may affect lumbar metabolism within one day prior to MRI examination, including medication (such as medications promoting blood circulation and resolving stasis, vasodilators, and stimulants), alcoholism, physical therapy (such as lumbar microwave, radio-frequency, or massage), etc.; and (4) implants that affect the quality of MRI imaging, including giant metal grafts, such as artificial hip joints and pelvic internal fixation.

A total of 32 volunteers met the criteria and were included in the data analysis. The participants were aged 25–71 years, including 14 males, with an average age of 48.7 ± 12.6 years, and 18 females, with an average age of 47.6 ± 11.1 years, as detailed in Tables 1 and 2 .

Testing equipment: A 3.0T MR scanner (Philips Ingenia 3.0T, Netherlands) with a 32-channel coil on the spinal surface was used to measure metabolic indicators.

Research site: The lower lumbar spine bears more human weight than the upper lumbar spine, and the LBs and LDs are relatively more affected by endogenous heavy stress disturbances. Therefore, we chose the L \(_3\) , L \(_4\) , and L \(_5\) LBs and the L \(_{3/4}\) , L \(_{3/4}\) , and L \(_5/\) S \(_1\) LDs as the observation targets.

Region of interest (ROI): The midsagittal plane of the lumbar spine was selected as the observation plane to better observe the structure of the LBs and LDs. The LB medullary region and LD nucleus pulposus region were selected as the ROIs for measurement. The delineation area along the inner edge of the target LB bone cortex was manually drawn as the medullary ROI (avoiding the upper and lower endplates and bone cortex areas), and the delineation area along the inner edge of the target LD fibre ring was manually drawn as the ROI for the NP.

Detection technology

Magnetic resonance spectroscopy (MRS) was used for quantitative analysis of the biochemical metabolites of the LBs and LDs and extraction of information such as the area under the curve of relevant evaluation indicators.

MRI m-DIXON Quant imaging was used to measure the FF value of tissue within the ROI, reflecting the proportion of fat tissue volume within the ROI. The measurement process was repeated three times to reduce errors, and the average value was taken as the final evaluation value.

MRI T2* imaging was used to measure the T2* value of the tissue within the ROI, reflecting the hydration state of the tissue. The measurement process was repeated three times to reduce errors, and the average value was taken as the final evaluation value.

The detection indicators included MRI morphological and structural indicators and quantitative indicators of biological metabolism. MRI quantitative indicators were obtained using MRI technology, usually manifested as specific quantitative values or parameters, and are often widely used in clinical medical fields such as imaging disease diagnosis and treatment monitoring.

Morphological structure indicators represent the anatomical structure and pathological changes in tissues and organs. In this study, a Pfirrmann grading system, which is a method for evaluating the degree of LD degeneration based on the strength, structure, height, and endplate shape of LD signals, was used. The scoring system is divided into five levels, with Level I indicating normal LDs and Level V indicating severe degenerative changes. The Pfirrmann scoring criteria for LD are shown in Table 3 .

Biometabolic indicators reflect the relative content of biochemical metabolites in the body’s tissues. In this study, the indicators included MRS detection of N-acetyl, lipids, H2O, choline, and lactic acid (Lac) in the LBs. The values are usually measured using the area under the peak of the substance spectrum curve, such as A \(_{H_2O}\) , as well as MRI m-DIXON Quant measurements of the fat fraction (FF) and T2* imaging measurements of the LD T2* value (Figs.  1 , 2 , 3 ). A \(_{H_2O}\) : The A \(_{H_2O}\) spectrum at a chemical shift of 4.8 ppm in MRS can be used to evaluate the changes in water content in vertebral tissue by measuring the area under the peak of the curve spectrum. A \(_{N-acetyl}\) : The spectrum of N-acetyl, one of the metabolites of PGs, at a chemical shift of 2.23 ppm in MRS reflects the changes in intervertebral disc decomposition. \(\text{A}_{Lip}\) : The sum of the lip peak areas at 1.24 ppm, 1.12 ppm, and 0.8 ppm for MRS chemical shifts mainly reflects the methyl-(-CH3) and vinyl(-CH2-)-containing substances in adipose tissue in the ROI, which can help assess the relative content of adipose tissue in the vertebral body. A \(_{Lac}\) : The lac spectrum at a chemical shift of 1.3 ppm in MRS can be used to evaluate changes in oxygen metabolism in vertebral tissue by measuring its area below the peak. FF: Analysing the proportion of fat volume in the ROI, reflecting the distribution of LB fat, can provide important information for determining LDD grade. The FF of the adjacent upper and lower vertebrae of the intervertebral disc is represented by FF \(_U\) and FF \(_L\) , respectively. T2* value: Reflects the macroscopic content of \(H_2O\) in LDs, expressed as the T2* value, which is closely related to the structural integrity of the fibre ring.

Image processing: After inputting the original images and data into the Intelligent Portal Workstation (Philips), two radiologists who have 10 years and 8 years of experience in MR diagnosis and who specialize in bone and joint disease research performed double-blind postprocessing analysis and judgement on the images, including measurements of MRS postprocessing, the FF value of the LBs, and the T2* value of the LDs.

Measurement of N-acetyl, Lip, H \(_2\) O, Lac, and Cho metabolites in the ROI

Measurement of the lumbar FF value of the vertebral body

T2* measurement of LDs

MRS postprocessing was performed using postprocessing software provided by the Philips magnetic resonance scanner workstation to perform spectral analysis on the images. Manual and automatic debugging of filtering, noise reduction, zero filling, and baseline phase correction steps were used to fit the data into standard spectral lines. The peak shape, peak value, area under the peak, and signal-to-noise ratio (SNR) of the wave were recorded. If the baseline in the spectrum was unstable, the full width at half height was too large, and the SNR \(\le\) 2, the spectrum was considered unqualified. This study mainly measured A \(_{N-acetyl}\) , A \(_{Lip}\) , A \(_{H_2O}\) , and A \(_{Lac}\) in the LB of interest. Due to the lack of vertebral display of A \(_{N-acetyl}\) and, these two metabolic indicators were not analysed.

Data analysis method: The factor analysis method was used to evaluate lumbar disc degeneration based on quantitative MRI metabolic indicators.

MRI biochemical metabolic measurement indicators

A total of 96 samples were obtained and graded according to the LDD severity. The FF, A \(_{Lip}\) , A \(_{Lac}\) , and A \(_{H_2O}\) of 96 LBs were measured in 32 patients, and the T2* values of 96 LDs were measured as quantitative MRI indicators in the same sample, as shown in Table 4 .

Data preprocessing results

Factor analysis was used to reduce the dimensionality of the data. To eliminate the adverse effects caused by different dimensions, the original data were standardized, and KMO and Bartlett spherical tests were performed to verify whether the data were suitable for principal component analysis.

The measure of sampling adequacy for KMO sampling was 0.718, greater than 0.7, and the significance of Bartlett’s sphericity test was less than 0.01, indicating that the data were suitable for factor analysis (Table 5 ).

Factor load matrix estimation and factor rotation

Table 6 shows the correlation coefficient matrix of various MRI quantitative indicators, with values closer to 1 indicating a stronger positive correlation and values closer to -1 indicating a stronger negative correlation. As shown in the table, there was a strong correlation between the FF values of adjacent vertebral bodies in the LDs. The T2* of LDs had a positive correlation with the A \(_{H_2O}\) of adjacent vertebral bodies and a negative correlation with other quantitative MRI indicators. In addition, there was a positive correlation between the A \(_{Lip}\) and A \(_{Lac}\) of the LB. The determination of these correlations has guiding significance for further exploring the factors that affect the development of LDD.

Table 7 shows that the feature values in order of size are 3.588, 1.185, 1.012, 0.766, 0.554, 0.485, 0.395, and 0.026. Based on the degree to which each principal component explained the variability of the data, we drew a scree plot (Fig.  4 ), which shows that the first three eigenvalues are greater than 1. Therefore, the first three common factors were selected for further study to better explain the contributions of the original variables. When more than three common factors were selected, the change in feature root values was relatively small, and the contribution to the original variable was also relatively small. Therefore, in subsequent analyses, we considered only the impact of the first three common factors on the original variable. The cumulative variance contribution rate of the first three common factors was 72.151% of the variance of the original variable. This result suggests that the selection of the first three common factors can maximize the information in the original variables and play a greater role in explaining the variance of the variables.

The rotated component matrix of the maximum variance method (Table 9 ) showed that the first common factor had a significant load on the FF values of the LBs adjacent to the LDs and was named the lumbar FF value factor. The second common factor had a significant load on the A \(_{Lip}\) and A \(_{Lac}\) values of the LBs and was named the lipid and lactate factor. The third common factor had a significant load on the A \(_{H_2O}\) of the LBs and the T2* of the LDs and was named the water factor. Compared to the component matrix before rotation (Table 8 ), the meanings of the factors in the rotated component matrix were clearer and more reasonable, which was more conducive to the interpretation and application of subsequent data.

Through factor analysis and factor rotation, we obtained three main factors. The first common factor was the FF values of the LBs adjacent to the LDs, which represents changes in the distribution of LB fat in LDD patients. The second common factor was composed of the A \(_{Lip}\) and A \(_{Lac}\) of the LBs, which represents energy metabolism. The third common factor was composed of the A \(_{H_2O}\) value of LB and the T2* value of LD, which represents water balance.

Factor score

As shown in the component score coefficient matrix (Table 10 ), the expressions for the FF value factor, lipid and lactate factor, and water factor of LB can be obtained by the following equation:

Using the total variance explanation in Table 7 , we can obtain the comprehensive score with the following equation:

This equation can be used to calculate the comprehensive score in factor analysis, where the common factor coefficient is divided by the rotated variance contribution rate and the total variance contribution rate. Because the influence of the water factor on LDD grade is opposite to that of the other two common factors, a negative sign is added before it. The comprehensive scores were grouped, and the number of samples with LDD grades I to V in each group was summarized, resulting in the distribution table of comprehensive scores for LDD grades (Table 11 ).

The comprehensive score table of the LDD grade divides the comprehensive scores S of each sample into five categories: S< \(-\) 0.5, \(-\) 0.5 \(\le\) S<0, 0 \(\le\) S<0.5, 0.5 \(\le\) S<1, and S \(\ge\) 1. As shown in Table 11 , the LDD grades of samples with a comprehensive score greater than 1 were mainly Grade V, while the LDD grades of samples with a comprehensive score less than \(-\) 0.5 were mainly Grades I, II, and III. As the overall score decreased, the number of samples with low LDD grades (grades I and II) showed an increasing trend. Taking samples with LDD grade I as an example, the comprehensive scores of these samples were all less than 0. There were 2 samples with comprehensive scores within the range of [ \(-\) 0.5, 0) and 6 samples with comprehensive scores less than \(-\) 0.5. As the comprehensive score decreased, the number of samples with LDD grade I gradually increased. Therefore, calculating the comprehensive LD score provides a new method for diagnostic doctors to discover early LDD patients.

Research has shown that the degeneration of IDs is related to factors such as human ageing, mechanical stress, genetics, and nutritional disorders [ 12 ]. Among these factors, the continuous reduction in nutrition and long-term loss of nutrients are the key factors causing changes in ID cells [ 3 , 13 ]. There are two main nutritional pathways for IDs, namely, the CEP pathway and the NF pathway. The CEP is closely related to the longitudinal growth of the vertebral body. Nutrients from the blood vessels in the vertebral body can diffuse to the ID through the interfaces among the bone marrow cavity, blood sinuses, and cartilage endplate, providing nutrients for the ID. This process of nutrient diffusion is crucial for the growth, repair, and maintenance of the spinal structure. Therefore, the CEP nutrient pathway is the main pathway for ID nutrient supply and plays a crucial role in maintaining the normal physiological function of the spine [ 14 ]. The histological origin of the CEP is consistent with that of vertebral body histology. When the metabolism of nutrients in the vertebral body is disrupted or the supply is reduced, the nutritional supply function of the CEP will inevitably be damaged, ultimately leading to ID degeneration. Due to the direct impact of the vertebral body on the lifespan and characteristics of LDs, using specific vertebral MRI quantitative indicators for targeted and specific detection and analysis is an effective method. By observing the changes in quantitative indicators of vertebral MR images under pathological conditions and correlating them with the degree of LDD, as evaluated using the Pfirrmann grading method, it is possible to better understand the upstream mechanism of LDD.

In recent years, MRI quantitative technology has provided a powerful tool for the complete quantitative evaluation of LDD by utilizing digital calculations and MRI image analysis. This technology covers multiple biological metabolic indicators. [ 15 ] found significant differences in N-acetyl/carbohydrate, N-acetyl/lipid, and lactate regions among different Pfirrmann grades of LDD in cadavers through the Tukey-Kramer test, as well as significant differences in N-acetyl/choline, N-acetyl/lipid, and lactate regions before and after bovine LD denaturation. [ 16 ] used gas chromatography-mass spectrometry (GC-MS) to analyse changes in plasma metabolic levels in LD patients. Multivariate statistical analysis and metabolic network analysis revealed that the main upregulated metabolites were glutamate, aspartic acid, and glycine, while the downregulated metabolite was glucose 1-phosphate. [ 17 ] used H-HR-MAS NMR to determine the metabolite concentration in LDs and evaluated the correlation between metabolite concentration and LD with different Pfirrmann grades. The spectral analysis of LDs with Pfirrmann grades IV and V revealed that the concentrations of creatine, glycine, hydroxyproline, alanine, leucine, valine, acetate, isoleucine \(\alpha /\beta\) , glucose and inositol were significantly greater, while the intensity of the N-acetyl peak of chondroitin sulfate was decreased.

In contrast to previous studies, this study analysed metabolites, including Lip, Lac, N-acetyl, Cho, and H 2 O, of the vertebral body, which, as the upstream nutrient source, may be related to LDD. In previous studies, biochemical metabolites in the intervertebral disc were often analysed to determine the outcomes of LDD changes. This study innovatively analysed the upstream nutrient supply side of the disc, so the results more closely reflect the interrelation between the nutritional status of the LB and LD performance. Due to the limited vertebral display of N-acetyl and Cho, which may be limited by the MRS resolution of the MRI instrument, these two metabolic indicators were not analysed. During the LDD process, these MRI quantitative indicators typically exhibit specific changes [ 18 ], but their usefulness in evaluating the LDD process is not clear and has not been reported in the literature.

In this study, we used a factor analysis method to identify MRI quantitative indicators with strong correlations by observing the interrelationships between the measured MRI quantitative indicators in the LBs and LDs, i.e., the A \(_{Lip}\) , A \(_{H_2O}\) , A \(_{Lac}\) , and FF values of the LB and the T2* values of the LD, and extracting a small number of important interpretable common factors. Factor analysis is a mature and classic statistical method that can identify potential correlations between multiple variables, providing clues for further research. This method can compress multiple related variables into fewer potential factors through dimensionality reduction methods, thereby reducing the complexity of data analysis. These common factors can serve as covariates for the BP neural network LDD grade diagnostic model, helping to reduce model complexity and make the model more intuitive and easier to interpret. In addition, the comprehensive scores of each LD can be calculated through common factors, and the LDD grade can also be analysed based on the comprehensive scores.

The results of this study show that the first common factor is composed of the lumbar FF values measured in the upper and lower vertebral bodies of the LDs. Because FF values can be used to reflect the distribution of fat in tissues, this factor may represent changes in the content of fat in the LBs in LDD patients. Reflecting the health status of intervertebral discs is closely related to quantifying the vertebral fat content.

The second common factor is composed of the A \(_{Lip}\) and A \(_{Lac}\) in the LBs, which may represent the energy metabolism status of LDD patients. The lipid peak represents the abundance of lipids, while the lactate peak reflects the accumulation of lactic acid in the body, which may be caused by disorders in energy metabolism. Therefore, this factor may reflect the dual changes in lipid metabolism and energy metabolism in LDD patients.

The third common factor is composed of the A \(_{H_2O}\) value of the LB and the T2* value of the LD, which are closely related to the water content, so this factor reflects the water balance status of LDD patients. Water balance plays an important role in maintaining the normal structure and function of intervertebral discs, thus providing valuable information for studying the mechanism and treatment of LDD.

These three common factors provide valuable information for LDD research and reveal some key indicators. By analysing these factors in depth, we can better understand the causes of LDD and provide a basis for diagnosis and treatment. Therefore, these three common factors can serve as covariates for evaluating LDD diagnostic models, optimizing the accuracy and reliability of these models, and play a crucial role in the early diagnosis and treatment of LDD.

In summary, this study provides new approaches and methods for the diagnosis and treatment of LDD, as well as a new perspective for the application of MRI technology, which has important implications and reference value for clinical practice. In response to the problems encountered during the data collection process, areas for improvement can be considered in subsequent studies, such as the following: 1) Ensuring the accuracy and consistency of data collection. We plan to develop a more detailed and specific data collection plan, focussing on the reliability of data sources and protecting personal privacy and data security during the collection process, and set up data monitoring points to check data error rates and inconsistencies. 2) Reducing the data loss rate. When collecting quantitative MRI data from patients, attention should be given to the issue of data loss. Measures should be taken to reduce the data loss rate, such as imaginative navigation, fat suppression, and Laplace filtering, to increase the dimensionality and accuracy of the data and ensure the authenticity and reliability of the results.

Future work can also be carried out in the following areas: 1) Expanding the sample size of the dataset. The collection of more patient data can increase the detection of LDD indicators, increase the understanding of influencing factors, and reduce data bias. 2) The exploration of advanced machine learning and omics analysis techniques, such as deep learning, one-dimensional convolutional neural networks (1D-CNNs), and support vector machines (SVMs), can assist in establishing more accurate, comprehensive, and fast LDD diagnostic models, enhancing clinical application value. 3) Exploring other research methods, such as magnetic resonance elastography (MRE) and magnetic resonance spectroscopy (MRS), can deepen the understanding of LDD levels when used in conjunction with MRI technology.

Availability of data and materials

All data generated during the project will be made freely available via 909th Hospital (Affiliated Southeast Hospital, Xiamen University). DOIs to these data will be provided (as part of the DataCite program) and cited in any published articles using these data and any other data generated in the project. There are no security, licensing, or ethical issues related to these data.

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This work was supported by the Other Provincial and Ministerial Level Projects in China (CLB21J017), Fujian Province Region Development Project (2019Y3007) and Natural Science Foundation of Fujian Province (2020J01794, 2021J01981, 2021J01982, 2023J01910).

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Boxin Zheng and Lin Ouyang: Co-first author.

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Radiology Department, 909th Hospital (Affiliated Southeast Hospital, Xiamen University), Zhangzhou, China

Boxin Zheng, Lin Ouyang, Xiaochan Shen & Hanbin Lei

School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, China

Boxin Zheng, Jianhua Shi, Xiaochan Shen & Hanbin Lei

Institute of Medical Imaging Medical College, Xiamen University, Xiamen, China

Fujian Key Laboratory of Granular Computing and Applications, Zhangzhou, China

Jianhua Shi

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Conceptualization, Ouyang, Lin; Data curation, Ouyang, Lin; Data collection and manuscript revision，Xiaochan, Shen，Hanbin, Lei；Formal analysis, Boxin, Zheng, Ouyang, Lin; Investigation, Boxin, Zheng, Ouyang, Lin, Jianhua ,Shi; Methodology, Boxin, Zheng and Jianhua ,Shi. All authors have read and agreed to the published version of the manuscript.

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Zheng, B., Ouyang, L., Shi, J. et al. Evaluating lumbar disc degeneration by MRI quantitative metabolic indicators: the perspective of factor analysis. J Orthop Surg Res 19 , 281 (2024). https://doi.org/10.1186/s13018-024-04726-8

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Establishment of a real-time fluorescent quantitative PCR detection method and phylogenetic analysis of BoAHV-1

• Lihui Xu 2   na1 ,
• Guiyang Ge 2   na1 ,
• Dongli Li 2 ,
• Jianming Li 1 ,
• Qinglong Gong 2 ,
• Kun Shi 1 ,
• Fei Liu 2 ,
• Naichao Diao 1 ,
• Zhenzhen Cui 1 ,
• Yingyu Liu 2 ,
• Xue Leng 1 &

BMC Veterinary Research volume  20 , Article number:  180 ( 2024 ) Cite this article

Metrics details

Infectious bovine rhinotracheitis  (IBR), caused by Bovine alphaherpesvirus-1 (BoAHV-1), is an acute, highly contagious disease primarily characterized by respiratory tract lesions in infected cattle. Due to its severe pathological damage and extensive transmission, it results in significant economic losses in the cattle industry. Accurate detection of BoAHV-1 is of paramount importance. In this study, we developed a real-time fluorescent quantitative PCR detection method for detecting BoAHV-1 infections. Utilizing this method, we tested clinical samples and successfully identified and isolated a strain of BoAHV-1.1 from positive samples. Subsequently, we conducted a genetic evolution analysis on the isolate strain’s gC, TK, gG, gD, and gE genes.

The study developed a real-time quantitative PCR detection method using SYBR Green II, achieving a detection limit of 7.8 × 10 1 DNA copies/μL. Specificity and repeatability analyses demonstrated no cross-reactivity with other related pathogens, highlighting excellent repeatability. Using this method, 15 out of 86 clinical nasal swab samples from cattle were found to be positive (17.44%), which was higher than the results obtained from conventional PCR detection (13.95%, 12/86). The homology analysis and phylogenetic tree analysis of the gC, TK, gG, gD, and gE genes of the isolated strain indicate that the JL5 strain shares high homology with the BoAHV-1.1 reference strains. Amino acid sequence analysis revealed that gC, gE, and gG each had two amino acid mutations, while the TK gene had one synonymous mutation and one H to Y mutation, with no amino acid mutations observed in the gD gene. Phylogenetic tree analysis indicated that the JL5 strain belongs to the BoAHV-1.1 genotype and is closely related to American strains such as C33, C14, and C28.

Conclusions

The established real-time fluorescent quantitative PCR detection method exhibits good repeatability, specificity, and sensitivity. Furthermore, genetic evolution analysis of the isolated BoAHV-1 JL-5 strain indicates that it belongs to the BoAHV-1.1 subtype. These findings provide a foundation and data for the detection, prevention, and control Infectious Bovine Rhinotracheitis.

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Introduction

BoAHV-1 is a significant pathogen in the global livestock industry that is capable of causing upper respiratory tract diseases in cattle, such as rhinitis and bronchitis. Additionally, BoAHV-1 can lead to other reproductive complications, including abortions, fetal deformities, and reproductive tract infections in cows [ 1 ]. Infected cattle initially exhibit clinical infections and parallelly establish latent infections, which later transform into persistent infections, with intermittent shedding of the virus into the environment. In a livestock farm, if one dairy cow becomes infected with BoAHV-1, the virus can spread rapidly throughout the entire cattle herd within a relatively short period, establishing a lifelong latent period [ 2 ]. During periods of immunosuppression, BoAHV-1 can undergo reactivation. This reactivation can be induced by corticosteroids or stress, leading to the activation of latent viruses. Subsequently, the virus can spread through respiratory secretions, ocular secretions, reproductive tract secretions, and even through infected bull semen transmission [ 3 , 4 ]. BoAHV-1 infection can also suppress the host's immune system, resulting in secondary bacterial infections that further worsen the condition [ 5 ]. In addition, BoAHV-1, along with other respiratory viruses, such as bovine viral diarrhea virus (BVDV), bovine respiratory syncytial virus (BRSV), bovine parainfluenza virus type 3 (BPIV-3), and bacterial coinfections, can cause bovine respiratory disease complex (BRDC), inflicting significant damage to the global cattle industry [ 6 ].

The disease first appeared in the 1950s in Colorado, USA, and subsequently spread to Europe through trade and commerce [ 7 ]. In recent years, there have been reports of BoAHV-1 infections reemerging in some countries where it was not previously reported, as well as in countries that had previously declared BoAHV-1 eradicated [ 8 ]. A meta-analysis revealed that the overall infection rate of BoAHV-1 in Chinese cattle is 40%, with the Inner Mongolia region showing a particularly high rate of 66%. These findings suggest that BoAHV-1 is widely prevalent in cattle populations in China and has shown an increasing trend in recent years [ 9 ]. As of the end of 2022, the total cattle inventory in China reached 102.16 million head, showing an increase of 3.99 million head compared to the previous year-end, representing a growth rate of 4.1%. The large population of cattle and their rapid growth rate have led to the accelerated spread of BoAHV-1, which has hindered the development of China's cattle industry. Currently, cell culture, polymerase chain reaction (PCR), real-time fluorescence quantitative PCR, enzyme-linked immunosorbent assay (ELISA), and virus neutralization assay have been developed to detect BoAHV-1. Among them, Real-Time Fluorescent Quantitative PCR is widely used because of its high sensitivity, accuracy and specificity compared with other methods [ 10 ]. Therefore, in this study, a Real-Time Fluorescent Quantitative PCR method was developed to support the early prevention and transmission of BoAHV-1.

The evolutionary dynamics of numerous viruses within the Alphaherpesvirinae subfamily have been partially attributed to the process of recombination [ 11 ]. Recombination plays a particularly significant role in the evolution and diversity of Alphaherpesviruses. However, there is currently limited research regarding genetic variation in BoAHV-1 [ 12 ]. To promptly understand the genetic evolution characteristics and epidemiological trends of BoHV-1 and formulate more effective prevention and control strategies, it is imperative to investigate this aspect further. Therefore, in this study, a Real-Time Fluorescent Quantitative PCR method based on SYBR Green II was developed to support the detection of BoAHV-1.The genetic relationships between BoAHV-1 strain JL5 and other isolates were analyzed to provide insights for the development of regional prevalent strain vaccines against BoHV-1. This endeavor aims to contribute scientific evidence and support for the prevention and control of BoAHV-1.

Establishment of the standard curve for qPCR

The results showed that the amplification curves of the TK gene had good reproducibility, and the fluorescence intensity varied regularly with the plasmid concentration (Fig.  1 A). The linear regression equation of the standard curve for the TK gene was y = -3.40X + 35.11. The correlation coefficient R 2 was 0.996, and the amplification efficiency (E) was 96.83% (Fig.  1 B). The melting curve analysis showed that all positive samples exhibited a single peak with a melting temperature of 89.08 ± 0.5 °C (Fig.  1 C). Meanwhile, no melting curves or dimer curves were observed in the negative control.

An amplification plot, melting curve analysis, and a standard curve. A  A plot of amplification: the Y-axis represents the fluorescence intensity, and 1–6 show plasmid concentrations, ranging from 7.80 × 10 3  ~ 7.80 × 10 8 copies/μl. B  Standard Curve: The X-axis represents the copy number, which ranges from 7.80 × 10 3  ~ 7.80 × 10 8 copies/μl. The corresponding Ct values are represented on the Y-axis. C  The melting curve with a melting peak at 89.08 °C ± 0.5 °C. The peak is single and of good quality

Specificity, sensitivity and reproducibility of RT‒qPCR detection

The BoAHV-1 strain exhibited strong fluorescence signals through specificity analysis, while no signals were detected in BVDV, BRSV and BPIV-3, indicating excellent specificity of the established detection method (Fig.  2 A). And the twenty BoAHV-1 negative sampls were all negative by this method. Based on the analysis of the amplification curves and standard curves, the LoDs of TK were detected by real-time qPCR to be 7.80 × 10 1 copies/µL (Fig.  2 A, B). Conventional PCR results showed that the detection limit of the recombinant positive plasmid pMD18-T-TK was 7.80 × 10 3 copies/µL (Fig.  2 C). Therefore, real-time qPCR was 100 times more sensitive than conventional PCR. The twenty BoAHV-1 positive sampls were all positive by this method. The results of the reproducibility test showed that the intrabatch coefficients of variation ranged from 0.10% to 0.71%, and the interbatch coefficients of variation ranged from 0.03% to 3.39%. These results indicate that the real-time fluorescence quantitative PCR assay is highly reproducible.

Specificity and sensitivity test curve of real-time PCR of TK. A  Specificity analysis; 1–5: BoAHV-1, BVDV, BRSV, BPIV-3 and ddH2O; B  TK 1–9: 7.80 × 10 8 , 7.80 × 10 7 , 7.80 × 10 6 , 7.80 × 10 5 , 7.80 × 10 4 , 7.80 × 10 3 , 7.80 × 10 2 , 7.80 × 10 1 , 7.80 × 10 0 copies/µL; 10: Negative control; C  Sensitivity test of conventional PCR of TK; Lane M: DL500 DNA Marker; Lane M1-9: 7.80 × 10 8 , 7.80 × 10 7 , 7.80 × 10 6 , 7.80 × 10 5 , 7.80 × 10 4 , 7.80 × 10 3 , 7.80 × 10 2 , 7.80 × 10 1 , 7.80 × 10 0 copies/µL; 10: Negative

Detection of the clinical samples

The detection of 86 clinical samples of nasal swabs showed a positive rate of 13.95% (12/86) by conventional PCR. The positive detection rate of the TK gene using SYBR Green II real-time PCR was 17.44% (15/86), and the concordance rate with the positive detection rate of conventional PCR was 80% (12/15) (Table 1 ). The results indicate that the SYBR Green II real-time PCR assays established in this study are more sensitive than conventional PCR.

Virus isolation and identification

The nasal swab fluid identified as positive by qPCR was inoculated onto MDBK cells. Cellular pathology was observed in the first passage post-inoculation, manifested by phenomena such as round shrinkage, network formation, and aggregation resembling grape-like clusters. Approximately 80% of the cells exhibited pathological changes by 40 h post-inoculation, with cells gradually detaching and undergoing apoptosis over prolonged incubation periods. Similar observations were noted in the positive control group, while cells in the blank control group maintained normal morphology. Subsequently, after purification and cultivation, a viral isolate with a titer of 1 × 10^ 7.5 TCID 50 /mL was obtained. The application of the previously established real-time PCR for detection showed amplification signals for the isolated virus (Fig.  3 A), while no target bands were obtained for the BVDV, BRSV and BPIV-3 genes (Fig.  3 B). In conventional PCR testing, positive bands were observed in the positive control group and the isolated virus strain group, while no bands were detected in the other groups.

Identification of the JL5 strain of the virus. A Fluorescent quantitative PCR identification results: 1–3: BoAHV-1 positive control, isolated BoAHV-1 strain detection, negative control. B Conventional PCR identification results: Lane M: DL2000 DNA marker; Lane 1: BoAHV-1 standard positive strain; Lane 2: Isolated BoAHV-1 strain; Lane 3: Negative control of BoAHV-1 (MDBK cells); Lane 4: BVDV; Lane 5: BRSV; Lane 6: BPIV-3

Phylogenetic analysis

The fragment lengths of gE, TK, gG, gD and gC were 1728 bp, 1080 bp, 1335 bp, 1254 bp and 1527 bp, respectively, by sequencing. In the gC gene, nucleotide homology with BoAHV-1 type reference strains ranges from 98.2% to 99.9%. The amino acid sequence analysis revealed a nonsynonymous mutation at position 228 (A to T) and a mutation at position 504 (A to D). In the gD gene, nucleotide homology with BoAHV-1 type reference strains ranges from 98.5% to 100.0%. Amino acid sequence analysis showed no amino acid mutations, indicating that the gD gene is relatively conserved in genetic evolution. Concerning the gE gene, nucleotide homology with BoAHV-1 type reference strains is between 99.4% and 100.0%. Amino acid sequence analysis identified nonsynonymous mutations at positions 62 (D to G) and 86 (L to H). In the gG gene, nucleotide homology with BoAHV-1 type reference strains is in the range of 98.9% to 99.9%. Amino acid sequence analysis revealed nonsynonymous mutations at positions 4 (A to T) and 341 (N to I). In the TK gene, nucleotide homology with BoAHV-1 type reference strains is between 99.4% and 99.8%. Amino acid sequence analysis found synonymous mutations at position 239 and a nonsynonymous mutation at position 85 (H to Y) (Table 2 ).

In summary, our analysis revealed a high homology between the JL5 strain and BoAHV-1.1 subtype strains, especially with U.S. strains such as C33, C14, C43, C28, and vaccine strains. The homology with strains from other countries, including China's NM06 strain, was relatively low. Therefore, we speculate that the BoAHV-1 JL5 strain may originate from the U.S. strains C33 and C14, possibly introduced through international trade. U.S. vaccine strains MH724206.1 and MH724209.1 showed high homology with U.S. strains C14, C18, C29, and C33, suggesting that U.S. BoAHV-1 vaccines might be effective in preventing and controlling the JL5 strain. In conclusion, genetic evolutionary tree analysis based on five genes indicates that the JL5 strain belongs to the BoAHV-1.1 subtype rather than the BoAHV-1.2 subtype (Fig.  4 ).

A-E Phylogenetic tree analysis of gC, gD, gE, gG and TK genes

Each strain is listed by GenBank accession number, geographic origin, and collection date. Bootstrap values are shown as percentages at each tree node. Scale bar indicates substitutions per site.

Bovine herpesvirus 1 (BoAHV-1) is recognized as a significant pathogen causing bovine respiratory disease complex, contributing to substantial economic losses in the global cattle farming industry. The rapid development of China's beef and dairy products sector in recent years has resulted in an increase in cattle transportation frequency. Concurrently, the importation of dairy cows and expansion of cattle herds have contributed to the rising prevalence of BoAHV-1. Although BoAHV-1 vaccines are available to mitigate clinical symptoms, their effectiveness in controlling latent infections remains suboptimal [ 13 , 14 ]. Research has shown that sheep and goats can be infected with BoAHV-1 and develop diseases. BoAHV-1 antibodies have been detected in captive Asian elephants [ 15 ], and the virus can also be isolated from healthy individuals of antelope, zebras, ferrets, and minks [ 16 ]. Recently, it was discovered that BoAHV-1 is also present in dromedary camels [ 17 ]. This indicates that the range of BoAHV-1 infection is continuously expanding and may have an impact on different animal populations. Consequently, the complete eradication of BoAHV-1 has become exceedingly challenging, emphasizing the urgency for the development of a rapid and reliable detection method.

Currently, there are various methods available for detecting infectious bovine rhinotracheitis virus (BoAHV-1), and among them, the most widely used and technically mature approaches include virus isolation, virus neutralization tests, enzyme-linked immunosorbent assay (ELISA), and polymerase chain reaction (PCR) [ 18 , 19 , 20 , 21 ]. Among these methods, fluorescence quantitative PCR (qPCR) is the most widely applied technique for laboratory detection. It is also the BoAHV-1 detection method recommended by the World Organization for Animal Health (WOAH). It does not require gel electrophoresis to obtain results, thus compensating for the time-consuming aspect of conventional PCR and making it suitable for testing a large number of clinical samples. Compared to TaqMan probe-based real-time qPCR, SYBR Green II-based real-time qPCR does not require the design of specific probes. This simplifies the experimental procedure and reduces the overall cost, making it advantageous for widespread promotion and application [ 22 ]. Certainly, real-time qPCR also has certain limitations. For instance, it may require higher personnel and equipment demands compared to some other methods. It cannot detect infections caused by vaccines with deleted TK genes, as the results of this method would be negative. Additionally, there would be better applications in the future if the detection costs and requirements could be reduced.

The selection of target genes for fluorescence quantitative PCR (qPCR) is of paramount importance in BoAHV-1 detection. The genome of BoAHV-1 is extensive and encompasses numerous essential genes, including gB, gC, gD, gE and TK [ 23 , 24 , 25 , 26 , 27 ]. In this study, we chose the TK gene as target genes because the TK gene is a key and conserved gene responsible for maintaining continuous BoAHV-1 infection, and it is also one of the major virulence genes, making it a good candidate target for BoAHV-1 detection. Moreover, as the TK gene is a nonessential gene, it is also one of the main target genes for developing BoAHV gene-deleted vaccines [ 28 ]. This also implies that our developed detection method can distinguish between natural BoAHV-1 infection in cattle and infection caused by BoAHV-1 gene-deleted vaccines targeting the TK gene. The utilization of these key genes as targets in our research contributes to the advancement of BoAHV-1 detection methods and aids in the effective control and management of BoAHV-1-related outbreaks. BoAHV-1 is a double-stranded DNA virus belonging to the Varicellovirus genus in the Alphaherpesvirinae subfamily. It has a genome size of approximately 140 kb [ 24 ]. In BoAHV-1, the TK gene is a nonessential gene located in the UL region of BoAHV-1. This gene primarily encodes BoAHV-1 thymidine kinase, which is an essential enzyme in the thymidine synthesis pathway. TK serves as one of the major virulence genes in herpesviruses and is also a nonessential gene in herpesvirus replication, playing a significant role in nucleic acid metabolism [ 29 ]. When the TK gene is deleted, it significantly reduces the virulence and replicative capacity of BoAHV-1. Therefore, in the development of BoAHV-1 gene-deletion vaccines, the TK gene is often targeted for knockout [ 28 ]. Furthermore, the gene sequence of BoAHV-1 TK is relatively conserved, making it a promising candidate target for BoAHV-1 detection.

Therefore, this study successfully established the SYBR Green II RT‒qPCR detection method for BoAHV-1 targeting the TK gene. The method exhibited a good linear relationship of the standard curves, meeting the needed criteria, with correlation coefficients (R 2 ) and amplification efficiencies (E) within acceptable ranges. When using the established detection method on clinical samples, we observed a positivity rate of 17.44% (15/86). This indicates a relatively high prevalence of BoAHV-1 clinical infections. The detection method we have developed has a detection limit of 7.8 × 10^ 1 copies/μL. Compared to the fluorescence quantitative PCR method established by Wang et al. [ 30 ] (5.747 × 10^ 2 copies/μL), it demonstrates higher sensitivity. In contrast to the conventional duplex PCR methods established by Xu et al. [ 31 ] with detection limits of 2.3 × 10^ 3 copies/μL and 2.4 × 10^ 3 copies/μL respectively, our method not only offers higher sensitivity but also significantly saves experimental time, thereby enhancing the efficiency of clinical sample detection. Moreover, compared to the LAMP method established by Gao et al. l [ 32 ] (with a detection limit of 1 × 10^ 3 copies/μL and a duration of 1 h), our method exhibits a similar experimental duration but with higher sensitivity.Since we were unable to obtain isolates of Bubaline alphaherpesvirus 1 (BuAHV-1) and Bovine alphaherpesvirus 5 (BoAHV-5), to ensure specificity in our results, we performed sequence alignment analysis of the TK gene sequences of BuAHV-1 (KU936049.1) and BoAHV-5 (NC_005261.3) during primer design. We synthesized specific primers to ensure the specificity of our detection method. Additionally, we utilized the specific primers for BuAHV-1 and BoAHV-5 as outlined in the study by Peletto et al. [ 33 ] to detect clinical samples. The results indicated that both BuAHV-1 and BoAHV-5 were negative.Additionally, we tested for cross-reactivity with Bovine Viral Diarrhea Virus (BVDV), Bovine Respiratory Syncytial Virus (BRSV), and Bovine Parainfluenza Virus-3 (BPIV-3), and the results showed no cross-reactivity. This indicates that our detection method is specific and suitable for detecting BoAHV-1 in complex clinical samples from cattle (Fig.  2 A). The detection method provide an effective means for the early detection of BoAHV-1, reducing the risk of virus shedding from infected cattle and offering crucial technical support for the control and prevention of bovine infectious rhinotracheitis.

In this study, during the isolation of suspected viral samples, characteristic cytopathic effects (CPE) were observed after inoculating MDBK cells. The CPE showed a distinctive appearance, with cells forming grape-like clusters and becoming rounded, and as the culture time increased, the cells detached and appeared as individual cells. The established fluorescent quantitative detection method was utilized to confirm that the isolated strain was BoAHV-1. This strain was subsequently named BoAHV-1 JL5. The TCID 50 of the virus strain was 1 × 10 7.5 TCID 50 /mL, which is similar to the TCID 50 of the Inner Mongolia BoAHV virus strain isolated by Zhang Pengfei [ 34 ]. Our further analysis of JL5, including homology and genetic evolution analysis, indicates that the BoAHV-1 JL5 strain belongs to the BoAHV-1.1 type (Fig.  4 ), consistent with the clinical observations we made during sample collection. The BoAHV-1.1 type primarily affects the respiratory tract, and infected cattle may exhibit symptoms such as coughing, tearing, and the discharge of purulent secretions from the nasal cavity and eyes [ 35 ]. The multiple sequence alignment results indicate that the gC, TK, gG, and gE genes of the BoAHV-1 JL5 strain have relatively few variations, and the gD gene shows no amino acid mutations. Additionally, the TK genes exhibit synonymous mutations (Table 2 ), which suggests that the JL5 strain shows good conservation. This is consistent with the results of the sequence analysis of the gC, gI and VP22 genes of the NM06 strain isolated in Inner Mongolia by Bai [ 36 ] and Hu et al. [ 37 ]. Combining the genetic variation analysis of the JL5 strain isolated in Jilin Province in this experiment, it can be concluded that BoAHV-1 strains isolated from the Jilin Province region are relatively conserved. Currently, there is limited information on the isolation, biological characteristics, and genetic evolution of BoAHV-1 epidemic strains in China. Therefore, the isolation of epidemic strains, analysis of key genes in isolated strains, and exploration of their biological characteristics are of significant importance in enriching our understanding of BoAHV-1 outbreak strains.

In conclusion, our analysis reveals a high homology between the JL5 strain and BoAHV-1.1 subtype strains, especially when compared to strains such as C33, C14, C43, and C28 and vaccine strains from the United States. In contrast, its homology is lower when compared to the Chinese NM06 strain and strains from other countries. Therefore, we hypothesize that the BoAHV-1 JL5 strain may have been introduced through international trade activities, possibly originating from the U.S. strains such as C33 and C14. Moreover, U.S. vaccine strains MH724206.1 and MH724209.1 exhibit significant homology with strains such as C14, C18, C29 and C33. Consequently, we speculate that U.S. BoAHV-1 vaccines may also be applicable in preventing and controlling the JL5 strain. In summary, the genetic evolutionary tree analysis of five genes clearly indicates that the JL5 strain belongs to the BoAHV -1.1 subtype rather than the BoAHV-1.2 subtype.

This study successfully established a SYBR Green II real-time quantitative PCR detection method for BoAHV-1. The developed method demonstrates high sensitivity, good specificity, and rapid results, making it suitable for clinical diagnosis. Furthermore, this method was successfully applied to identify a new BoAHV-1 JL5 strain. Systematic phylogenetic analysis revealed that the gC, TK, gG, gD and gE genes of the BoAHV-1 JL5 strain clustered together with the reference strain of the BoAHV-1.1 type, indicating their close evolutionary relationship. This study provides new data for the epidemiological study of BoAHV-1 in China and lays the foundation for the development of novel BoAHV-1 detection technology and vaccines.

Materials and methods

Virus strains, clinical samples and primer design.

BVDV, BRSV, and BPIV-3 were preserved at the Economic Animal Infectious Disease Laboratory of Jilin Agricultural University and were tested by the RT‒qPCR method [ 38 ]. Eighty-six cow nasal swabs were collected randomly from farms in Jilin province, some of the cows exhibit symptoms of increased secretion from the eyes and nose.

From the National Center for Biotechnology Information (NCBI) database ( https://www.ncbi.nlm.nih.gov ), the TK, gC, TK, gG, gD and gE genes of BoAHV-1 (GenBank accession number: AJ004801) were downloaded as reference sequences. The software Primer 5.0 was used to design one pair of primers suitable for fluorescence quantitative PCR in the conserved region of TK that were suitable for real-time fluorescent quantitative PCR. Additionally, primers for the identification of the full-length sequences of the gC, TK, gG, gD and gE (including gE1 and gE2) genes were also designed. The primer sequences are listed in Table  3 . These primers were synthesized by Shanghai Sangon Biotech Co., Ltd. (Shanghai, China).

Standard plasmid construction

DNA of BoAHV-1 was extracted (OMEGA USA) and amplified by PCR with qTK-F and qTK-R, and the target fragments of the amplified fragments were ligated to the pMD18-T vector.

These recombinant plasmids were sent to Shanghai Sangon Biotech Co., Ltd. (Changchun, China) for synthesis and sequencing. The correctly sequenced plasmids were quantified using a nucleic acid analyser from Shimadzu Corporation (China). The sample copy number calculation formula was used to convert the copy number of the positive standard into appropriate units.

Formula: Sample copy number = [concentration (ng/µL) × Avogadro's constant (NA) × 10 –9 ]/(660 × length of recombinant plasmid DNA in base pairs).

Establishment of a standard curve for qPCR

Fluorescence quantitative PCR (qPCR) was performed using 6 different concentrations of recombinant positive plasmids, pMD18-T-TK (ranging from 10 3 to 10 8 copies/µL), as templates. A 25 µl amplification system was established with the following components: 12.5 µl of TB Green Premix Ex Taq II (Japan Takara), 9.5 µl of ddH 2 O, 1 µl of BoAHV-1-F (10 mM), 1 µl of BoAHV-1-R (10 mM), and 1 µl of the template. The qPCR was carried out in eight tubes by fluorescence quantitative PCR in a qTOWER3 G instrument (Analytik Jena AG, Jena, Germany). The PCR conditions consisted of an initial denaturation step at 95 °C for 30 s, followed by 40 cycles of denaturation at 95 °C for 5 s and annealing at 55 °C for 30 s. A negative water control was included. The amplification reactions generated cycle threshold (Ct) values, and the results were analysed to construct the standard curve. The standard curve was generated by monitoring the fluorescence signals of SYBR Green II during qPCR amplification.

Specificity, sensitivity and reproducibility testing

To exclude any cross-reactivity between BoAHV-1 and other bovine viral pathogens, cDNA samples from BoAHV-1, BVDV, BRSV and BPIV-3 were used as templates in SYBR Green II real-time quantitative PCR. This approach allows for specific detection and quantification of each viral pathogen, ensuring the accuracy and reliability of the results. water was used as a blank control. Simultaneously, we employed the PCR method established in the laboratory to confirm 20 negative clinical samples for BoAHV-1 to test the specificity of this method. The primer sequences are listed in Table  3 .

The sensitivity of BoAHV-1 Real-Time Fluorescent Quantitative PCR was determined by using a tenfold serial dilution of recombinant positive plasmid pMD18-T-TK (7.80 × 10 8 、7.80 × 10 7 、7.80 × 10 6 、7.80 × 10 5 、7.80 × 10 4 、7.80 × 10 3 、7.80 × 10 2 、7.80 × 10 1 、7.80 × 10 0 copies/µL).The minimum concentration of target DNA detected by qPCR using this dilution series as a template. Simultaneously, we compared the sensitivity of SYBR Green II real-time quantitative PCR with that of conventional PCR. This comparison provided valuable insights into the sensitivity of the real-time PCR approach and its performance in comparison to conventional PCR. Simultaneously, we employed the PCR method already established in the laboratory to confirm 20 positive clinical samples for BoAHV-1 to assess the specificity of this method. The primer sequences are listed in Table  3 .

Six groups of recombinant positive plasmids were prediluted at different concentrations (ranging from 10 3 to 10 8 copies/µL). Under the same conditions, 3 interbatch replicates and 3 intrabatch replicates were performed. By dividing the standard deviation (SD) of each test sample by the mean value, we calculated the coefficients of variation (CV) for intrabatch and interbatch variability.

Detection of BoAHV-1 in clinical samples

Using the SYBR Green II real-time quantitative PCR method established in this study, we performed BoAHV-1 detection on 86 nasal swab samples collected from cattle farms in Jilin Province. Simultaneously, the primers F and R were used to conduct detection using conventional PCR (Table  1 ) according to the reference [ 39 ], and the detection rates of the two methods were compared.

Virus isolation

The positive nasal swab samples by qPCR were subjected to repeated freeze‒thaw cycles, followed by centrifugation, and then filtered through a 0.22-micron membrane filter for sterilization. The processed nasal swab fluid was inoculated onto MDBK cells for virus isolation. If cytopathic changes appeared during this period, the virus was passaged 5 times continuously and the TCID 50 was tested [ 12 ]. At the same time, we utilized the laboratory-preserved BoAHV-1 viral fluid as the positive control, and supplemented DMEM with 2% horse serum as the negative control.

Virus identification

The extracted virus samples were subjected to genome analysis using the established SYBR Green II real-time quantitative PCR assay for bovine infectious rhinotracheitis virus (BoAHV-1) detection. Additionally, viral genome samples were separately tested using conventional PCR assays for BoAHV-1, bovine viral diarrhea virus (BVDV), bovine respiratory syncytial virus (BRSV), and bovine parainfluenza virus-3 (BPIV-3) detection. To verify the results, sequencing was performed on the isolated strains.

Using BoAHV-1 JL5 strain DNA as a template, PCR amplification was performed for the gC, TK, gG, gD and gE genes. After ligation into the pMD18-T vector, the samples were sent to Shanghai Sangon Biotech Co., Ltd. for synthesis (Changchun, China) and sequencing. In this study, we utilized DNAstar software (DNAstar, Inc., located in Madison, Wisconsin, USA) to analyse and compare the nucleotide and amino acid sequences of the bacterial strain. This analysis aimed to investigate the differences between this strain and isolates from China and other countries (Table  4 ). We employed version 7.0 of MEGA and conducted an assessment with 1000 bootstrap replicates using the maximum likelihood method to construct the phylogenetic relationships. Ultimately, a neighbor-joining phylogenetic tree was established. Translate the JL5 nucleotide sequence into an amino acid sequence using DNAStar software. Subsequently, perform multiple sequence alignment using the Clustal W program in the Megalign module of DNAStar software.

GenBank accession numbers

The sequences obtained here of a part of the BoAHV-1 gene were submitted to the Genbank under the accession number: gD:PP277988;gG:PP277989;gC:PP277990;gE:PP277991;TK:PP277992.

Availability of data and materials

No datasets were generated or analysed during the current study

Abbreviations

Infectious bovine rhinotracheitis

Bovine herpesvirus 1

Bovine viral diarrhea virus

Bovine respiratory syncytial virus

Bovine parainfluenza virus type 3

Bovine respiratory disease complex

Quantitative PCR

Cytopathic effects

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This research was supported by the Science and Technology Development Project of Jilin Province (20220101332JC, 20190301004NY, and YDZJ202301ZYTS334).

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Lihui Xu and Guiyang Ge contributed equally to this work.

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College of Chinese Medicine Materials, Jilin Agricultural University, Changchun, 130118, Jilin, China

Jianming Li, Kun Shi, Naichao Diao, Zhenzhen Cui, Xue Leng & Rui Du

College of Animal Science and Technology, Jilin Agricultural University, Changchun, 130118, Jilin, China

Lihui Xu, Guiyang Ge, Dongli Li, Qinglong Gong, Fei Liu & Yingyu Liu

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LHX: Methodology, Writing-review & editing Investigation; GYG: Writing-review & editing Data analysis, Writing-original draft. DLL: Methodology; JML: Formal analysis; QLG: Investigation; Resources; KS, FL and NCD: Validation; ZZC: Data curation; YYL: Data analysis; XL: Resources, Supervision; RD: Supervision, Project administration. All authors have read and agreed to the published version of the manuscript.

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The clinical samples used in this study were nasal swabs collected from a cattle farm.The sample collection process did not cause any harm to the cows. The animal study was reviewed and approved by Animal Welffare and Research Ethics Committee of Jinlin Agricultural University (JLAU08201409). And this study obtained informed consent from the animal owner.

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Xu, L., Ge, G., Li, D. et al. Establishment of a real-time fluorescent quantitative PCR detection method and phylogenetic analysis of BoAHV-1. BMC Vet Res 20 , 180 (2024). https://doi.org/10.1186/s12917-024-04025-8

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The stock market's sell-off is over and the Fed gave 5 bullish signs to investors at its latest meeting, Fundstrat's Tom Lee says

• The sell-off that battered stocks in April probably won't stretch into May, according to Fundstrat's Tom Lee.
• The uber-bullish forecaster pointed to five dovish signs the Fed gave after its policy meeting on Wednesday
• That suggests equities will end the month of May with a gain, Lee predicted.

The stock market's sell-off could be over, and five bullish signals the Fed gave at its latest policy meeting are setting the stage for gains in May, according to Fundstrat's head of research Tom Lee.

In a video sent to Fundstrat clients on Wednesday, Lee pointed to the May Federal Open Markets Committee meeting, which sparked a brief rally in stocks . Central bankers opted to keep interest rates level and suggested a rate hike was unlikely, fueling bullish sentiment among traders.

"That gets us to a situation where I'm still confidence that April is going to be the end of that selloff," Lee said. "I think May's going to end up being an up month.

He pointed to five dovish signals the central bank gave markets, which suggests that the path ahead for stocks looks a lot brighter:

1. The Fed is slowing its pace of quantitative tightening

Central bankers said they would slow their pace of balance sheet reductions , which is a positive for stocks. The Fed has shed over a trillion from its balance sheet in order to tighten financial conditions and help control inflation.

Balance sheet reductions will slow from $60 billion to $25 billion a month starting in June, the central bank said in a statement.

2. Inflation is pointing lower

Inflation came in hotter-than-expected all throughout the first quarter, and prices in the economy still remain above the Fed's 2% target. But inflation is on the decline overall, Lee said: Consumer prices grew 3.5% year-per-year in March , down from a peak of 9.1% growth posted in mid-2022.

In prepared remarks, Powell added that he was confident inflation would continue to fall toward the Fed's long-run target this year. Continued disinflation could give the Fed more leeway to cut rates later in 2024, Lee added.

3. Rate cuts can coexist with a strong labor market

Some investors have fretted over the robust labor market , as the Fed could raise interest rates to weaken too-strong hiring conditions.

But Powell has suggested that won't be the case, Lee said. The Fed chief noted that the labor market was "really tight" last year, yet the economy still saw inflation fall while growth remained strong.

"A healthy labor market doesn't preclude rate cuts," Lee said. 

4. The economy isn't facing stagflation

Market participants have also been eyeing the threat of stagflation , a phenomenon where prices keep rising while economic growth remains sluggish. Fears of that scenario began to pick up as investors took in above-expected inflation prints over the first quarter, while first-quarter GDP came in below-expected. 

But Powell seemed "puzzled" over that possibility, Lee said, with the central bank chief pointing to "solid" growth in the economy in his presser. Other economists have also dismissed stagflation risks for now, given that consumer spending and the job market remain in full-force.

5. A rate hike is unlikely

Powell added that the Fed's next move was unlikely to be a rate hike. That was comforting to investors, given that many have come to fear more tightening as the economy stays strong and inflation moves in the wrong direction this year. 

Investors are now pricing in a 69% chance the Fed could rate rates once or twice by the end of the year, according to the CME FedWatch tool .

Stock investors have already perked up on a brighter outlook for Fed rate cuts this year. Stocks reacted positively to the Wednesday Fed meeting. Meanwhile, nearly 40% of investors said they were bullish on stocks over the next six months, according to the latest AAII Investor Sentiment Survey , up from 32% of respondents who said they were bullish the prior week.

• Main content

Variables in Quantitative Research: A Beginner's Guide – PSL

Quantitative variables.

Because quantitative methodology requires measurement, the concepts being investigated need to be defined in a way that can be measured. Organizational change, reading comprehension, emergency response, or depression are concepts but they cannot be measured as such. Frequency of organizational change, reading comprehension scores, emergency response time, or types of depression can be measured. They are variables (concepts that can vary).

Quantitative research involves many kinds of variables. There are four main types:

• Independent variables (IV).
• Dependent variables (DV).
• Sample variables.
• Extraneous variables.

Each is discussed below.

Independent variables (IV)

Independent variables (IV) are those that are suspected of being the cause in a causal relationship. If you are asking a cause and effect question, your IV will be the variable (or variables if more than one) that you suspect causes the effect. If you do not understand this, go to your statistics texts and study up.

There are two main sorts of IV, active independent variables and attribute independent variables:

• Active IV are interventions or conditions that are being applied to the participants. A special tutorial for the 3rd graders, a new therapy for clients, or a new training program being tested on employees would be active IVs.
• Attribute IV are intrinsic characteristics of the participants that are suspected of causing a result. For example, if you are examining whether gender—which is intrinsic to the participants—results in higher or lower scores on some skill, gender is an attribute IV.
• In the example above, the active IV special tutorial , receiving the tutorial is one level, and tutorial withheld (control) is a second level.
• In the same example, being a third grader would be an attribute IV. It could be defined as only one level—being in 3rd grade—or you might wish to define it with more than one level, such as first half of 3rd grade and second half of 3rd grade. Indeed, that attribute IV could take many more, for example, if you wished to look at each month of third grade.

Independent variables are frequently called different things depending on the nature of the research question. In predictive questions where a variable is thought to predict another but it is not yet appropriate to ask whether it causes the other, the IV is usually called a predictor or criterion variable rather than an independent variable.

Dependent Variables (DV)

Dependent variables are those that are influenced by the independent variables. If you ask, Does A cause [or predict or influence or affect, and so on] B? then B is the dependent variable (DV).

• Dependent variables are variables that depend on and are influenced by the independent variables.
• They are outcomes or results of the influence of the independent variable.
• Dependent variables answer the question: What do I observe happening when I apply the intervention?
• The dependent variable receives the intervention.

In questions where full causation is not assumed, such as a predictive question or a question about differences between groups but no manipulation of an IV, the dependent variables are usually called outcome variables , and the independent variable are usually called the predictor or criterion variables.

Sample Variables

In some studies, some characteristic of the participants must be measured for some reason, but that characteristic is not the IV or the DV. In this case, these are called sample variables. For example, suppose you are investigating whether amount of sleep affects level of concentration in depressed people. In order to obtain a sample of depressed people, a standard test of depression will be given. So the presence or absence of depression will be a sample variable. That score is not used as an IV or a DV, but simply to get the appropriate people into the sample.

When there is no measure of a characteristic of the participants, the characteristic is called a "sample characteristic." When the characteristic must be measured, it is called a "sample variable."

Extraneous Variables

Extraneous variables are not of interest to the study but may influence the dependent variable. For this reason, most quantitative studies attempt to control extraneous variables. The literature should inform you what extraneous variables to account for. For example, in the study of third graders' reading scores, such variables as noise levels in the testing room, the size or lighting or temperature of the room, and whether the children had had a good breakfast, all might be extraneous variables.

There is a special class of extraneous variables called confounding variables. These are variables that can cause the effect we're looking for if they are not controlled for, resulting in a false finding that the IV is effective when it is not. In a study of changes in skill levels in a group of workers after a training program, if the follow-up measure is taken relatively late after the training, the simple effect of practicing the skills might explain improved scores, and the training might be mistakenly thought to be successful when it was not.

There are many details about variables not covered in this handout. Please consult any text on research methods for a more comprehensive review.

Doc. reference: phd_t2_coun_u02s2_h05_quantvar.html