hypothesis learning meaning

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StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing; 2024 Jan-.

StatPearls [Internet].

Learning theories.

Mustafa H. Gandhi ; Pinaki Mukherji .

Affiliations

Last Update: July 17, 2023 .

Definition/Introduction

Learning is the change in the behavior of an organism that is a result of prior experience. [1] Learning theory seeks to explain how individuals acquire, process, retain, and recall knowledge during the process of learning. Environmental, cognitive, and emotional influences, along with prior experiences, play a vital role in comprehending, acquiring, and retaining skills or knowledge. Motivation plays an important role in enabling the process of learning and is said to be the driving force where activity is started and sustained to achieve a target. [2]

It was Plato, the ancient Greek philosopher who first pondered about how an individual learns new information when the subject is brand new to him. According to Plato, learning is a passive process where knowledge is already innately in an individual at birth, and any information acquired is merely a recollection of knowledge the soul already holds. John Locke later offered a contrasting ‘blank slate’ theory where humans are born without any innate knowledge and which is gained from the environment. Since then, there have been numerous different theories proposed about the process of learning.

Issues of Concern

Currently, there are five widely accepted theories of learning.

Behaviorism: According to the theory of behaviorism, learning occurs by linking stimuli and responses. Knowledge is independent, and it becomes cemented by way of punishments and rewards. These ideas of positive and negative reinforcement, which may be natural consequences or implemented by another, are effective tools for learning and behavior modification. Behaviorism focuses on observed actions, the conditions under which they are performed, and the reinforcement of desired behaviors. A change in performance is evident after the learning process, and the outcome is measured in terms of being able to demonstrate a specific new behavior. [3]

Cognitivism: This theory of learning is grounded in the work of Jean Piaget, which states that learning occurs through the processing of information internally rather than merely responding to an external stimulus. Learning is a result of processing and reorganizing information within a matrix of previously acquired information. Cognitivism places the focus on the individual's thought processes and has the teacher emphasize reflecting on experiences with metacognition, thinking about their thinking. The behavioral change seen here is a result of learning which occurs after the inner workings of thinking based on the new information or knowledge received. The learning process encompasses both acquisition and reorganization of cognitive entities. [4]

Constructivism: It is based on the premise that individuals learn by constructing new ideas, and an understanding of the world is based on prior knowledge and experiences. Knowledge is built by adapting new information through the lens of previous experience. Constructivism focuses on the internal thinking of an individual, like cognitivism, but makes no assumptions on how concepts will be manipulated or what links will be made. Since the basis of learning is placed on making connections and creating ideas from prior knowledge, these mental representations are very subjective, and each individual will have a unique construction of knowledge.

Connectivism: This newer educational learning theory is grounded in the notion that learning is through the formation of connections between each other as well as their roles, hobbies, and other aspects of life. Therefore learning is the ability to traverse and construct these networks. Connectivism builds on the ideas of cognitivism, but in this theory, learning does not reside only within an individual, but rather also within and across a network of individuals. A "community of practice" has connectivism as its theoretical underpinning. Knowledge can reside outside the individual, but learning focuses on organizing and locating specialized information that may be decentralized from an individual. [5]

Humanism: This theory is closely related to constructivism and adult learning theory, and states that learning is a natural desire with the ultimate goal of achieving self-actualization. [6] Individuals function under needs that begin from those basic physiological needs of survival and culminate at self-actualization, which rests at the pinnacle of this hierarchy. All humans strive for self-actualization, which refers to a state wherein one feels that all their emotional, physical, and cognitive needs have been fulfilled. Humanistic learning theory emphasizes the freedom and autonomy of learners. It connects the ability to learn with the fulfillment of other needs (building on Maslow's hierarchy) and the perceived utility of the knowledge by the learner.

A learning style, on the other hand, refers to the way an individual prefers to absorb, process, comprehend and retain a new piece of information. While a learning theory explains how learning takes place, a learning style describes the preferred method of learning. Learning styles fall into seven basic categories, namely, physical, logical, social, solitary, visual, aural, and verbal. While descriptions of learning styles exist, catering to a preferred "learning style" leads to no improved outcomes in learning and may guide learners to avoid material presented in a manner that they feel is more uncomfortable. [7]

Clinical Significance

The advances in cognitive and learning sciences theories inform educators about best learning and teaching practices and their impact on the process of evaluation under differing circumstances. An understanding of these theories provides a sound rationale for choosing specific instructional and assessment strategies that measure that the curricular objectives. [8] In recent times, educators have started using social media as a means of instruction, and the sound application of social media in education is traceable to the learning theories. [9]

Implications for Teachers

In behaviorism, the teacher needs to be active and have a good knowledge base to set up the appropriate learning environment and elicit the correct responses from the learners. On the other hand, in cognitivism, the role of the teacher is to structure the content of the learning material. Under the structure of constructivism, the role of a facilitator is played by the teacher, who acts as a guide to the students, each of whom brings a unique set of previous experiences to approach the knowledge they are acquiring. Connectivism requires teachers to guide learners to related areas of knowledge outside their focus. Humanism focuses on learner autonomy and potential, having where teachers encourage learners to be self-directed. Thus we see how behaviorism is teacher-centered, whereas constructivism, connectivism, humanism, and cognitivism are learner-centered approaches.

Curriculum Design and Delivery

Behaviorism: It can be very useful in the sphere of clinical and communication skills because as students are provided feedback over a while, they learn the correct responses while performing skills. Their learning can occur in small chunks with repetition that help learn the intended behavior over some time. Behaviourism also enforces the mastery of prerequisite steps before moving onto other further modules, which ensures reinforcement of the correct skills. While teaching certain skills, the teacher can first demonstrate the technique or manner in which a particular skill is to be performed, after which the students try to imitate the same technique. They would then be assessed based on the perfectly they were able to perform the skill-based on what was demonstrated and receive positive or negative reinforcement. [10]

Cognitivism: Conventional basic science courses that occur in isolation to the clinical course make can use of cognitivism, as new information and knowledge are given and then processed internally to come to new ideas and improve the schemata of knowledge.

Constructivism: For basic science courses that occur integrated with clinical science courses, the theory of constructivism would be more appropriate as the student needs to grasp the concepts of the basic sciences and then be able to construct connections to the clinical aspect of it. Any area that requires knowledge to be acquired and then applied to a different sphere would benefit significantly from constructivism.

Connectivism: The learning process in connectivism is similar to that seen with constructivism. Since learning is through the process of forming connections between previous knowledge and an individual’s innate qualities, this approach is appropriate for areas that require the application of knowledge between different disciplines. It has a particular application for learning and teaching in this digital age. [5]

Humanistic: In the humanistic approach, a teacher would allow students to learn by their own free will and desire for knowledge. Since humanists believe that the desire to learn is innate and aimed towards the ultimate goal of self-actualization, the motivation must come from the learner. Although there is often a clear minimal structure for the teaching, the responsibility is on the students to learn as they wish to. [11]

Nursing, Allied Health, and Interprofessional Team Interventions

The most salient or easily applied strategums from the aforementioned learning theories can be administered when educating patients. Understanding the nuances of learning can help improve patient compliance, leading to an improved prognosis. Thus, it is imperative for interprofessional teams to understand which teaching modalities may engender the best compliance.

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Disclosure: Mustafa Gandhi declares no relevant financial relationships with ineligible companies.

Disclosure: Pinaki Mukherji declares no relevant financial relationships with ineligible companies.

This book is distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) ( http://creativecommons.org/licenses/by-nc-nd/4.0/ ), which permits others to distribute the work, provided that the article is not altered or used commercially. You are not required to obtain permission to distribute this article, provided that you credit the author and journal.

Cite this Page Gandhi MH, Mukherji P. Learning Theories. [Updated 2023 Jul 17]. In: StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing; 2024 Jan-.

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How to Write a Great Hypothesis

Hypothesis Definition, Format, Examples, and Tips

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Amy Morin, LCSW, is a psychotherapist and international bestselling author. Her books, including "13 Things Mentally Strong People Don't Do," have been translated into more than 40 languages. Her TEDx talk, "The Secret of Becoming Mentally Strong," is one of the most viewed talks of all time.

Verywell / Alex Dos Diaz

The Scientific Method

Hypothesis Format

Falsifiability of a hypothesis.

Operationalization

Hypothesis Types

Hypotheses examples.

Collecting Data

A hypothesis is a tentative statement about the relationship between two or more variables. It is a specific, testable prediction about what you expect to happen in a study. It is a preliminary answer to your question that helps guide the research process.

Consider a study designed to examine the relationship between sleep deprivation and test performance. The hypothesis might be: "This study is designed to assess the hypothesis that sleep-deprived people will perform worse on a test than individuals who are not sleep-deprived."

At a Glance

A hypothesis is crucial to scientific research because it offers a clear direction for what the researchers are looking to find. This allows them to design experiments to test their predictions and add to our scientific knowledge about the world. This article explores how a hypothesis is used in psychology research, how to write a good hypothesis, and the different types of hypotheses you might use.

The Hypothesis in the Scientific Method

In the scientific method , whether it involves research in psychology, biology, or some other area, a hypothesis represents what the researchers think will happen in an experiment. The scientific method involves the following steps:

Forming a question
Performing background research
Creating a hypothesis
Designing an experiment
Collecting data
Analyzing the results
Drawing conclusions
Communicating the results

The hypothesis is a prediction, but it involves more than a guess. Most of the time, the hypothesis begins with a question which is then explored through background research. At this point, researchers then begin to develop a testable hypothesis.

Unless you are creating an exploratory study, your hypothesis should always explain what you expect to happen.

In a study exploring the effects of a particular drug, the hypothesis might be that researchers expect the drug to have some type of effect on the symptoms of a specific illness. In psychology, the hypothesis might focus on how a certain aspect of the environment might influence a particular behavior.

Remember, a hypothesis does not have to be correct. While the hypothesis predicts what the researchers expect to see, the goal of the research is to determine whether this guess is right or wrong. When conducting an experiment, researchers might explore numerous factors to determine which ones might contribute to the ultimate outcome.

In many cases, researchers may find that the results of an experiment do not support the original hypothesis. When writing up these results, the researchers might suggest other options that should be explored in future studies.

In many cases, researchers might draw a hypothesis from a specific theory or build on previous research. For example, prior research has shown that stress can impact the immune system. So a researcher might hypothesize: "People with high-stress levels will be more likely to contract a common cold after being exposed to the virus than people who have low-stress levels."

In other instances, researchers might look at commonly held beliefs or folk wisdom. "Birds of a feather flock together" is one example of folk adage that a psychologist might try to investigate. The researcher might pose a specific hypothesis that "People tend to select romantic partners who are similar to them in interests and educational level."

Elements of a Good Hypothesis

So how do you write a good hypothesis? When trying to come up with a hypothesis for your research or experiments, ask yourself the following questions:

Is your hypothesis based on your research on a topic?
Can your hypothesis be tested?
Does your hypothesis include independent and dependent variables?

Before you come up with a specific hypothesis, spend some time doing background research. Once you have completed a literature review, start thinking about potential questions you still have. Pay attention to the discussion section in the journal articles you read . Many authors will suggest questions that still need to be explored.

How to Formulate a Good Hypothesis

To form a hypothesis, you should take these steps:

Collect as many observations about a topic or problem as you can.
Evaluate these observations and look for possible causes of the problem.
Create a list of possible explanations that you might want to explore.
After you have developed some possible hypotheses, think of ways that you could confirm or disprove each hypothesis through experimentation. This is known as falsifiability.

In the scientific method , falsifiability is an important part of any valid hypothesis. In order to test a claim scientifically, it must be possible that the claim could be proven false.

Students sometimes confuse the idea of falsifiability with the idea that it means that something is false, which is not the case. What falsifiability means is that if something was false, then it is possible to demonstrate that it is false.

One of the hallmarks of pseudoscience is that it makes claims that cannot be refuted or proven false.

The Importance of Operational Definitions

A variable is a factor or element that can be changed and manipulated in ways that are observable and measurable. However, the researcher must also define how the variable will be manipulated and measured in the study.

Operational definitions are specific definitions for all relevant factors in a study. This process helps make vague or ambiguous concepts detailed and measurable.

For example, a researcher might operationally define the variable " test anxiety " as the results of a self-report measure of anxiety experienced during an exam. A "study habits" variable might be defined by the amount of studying that actually occurs as measured by time.

These precise descriptions are important because many things can be measured in various ways. Clearly defining these variables and how they are measured helps ensure that other researchers can replicate your results.

Replicability

One of the basic principles of any type of scientific research is that the results must be replicable.

Replication means repeating an experiment in the same way to produce the same results. By clearly detailing the specifics of how the variables were measured and manipulated, other researchers can better understand the results and repeat the study if needed.

Some variables are more difficult than others to define. For example, how would you operationally define a variable such as aggression ? For obvious ethical reasons, researchers cannot create a situation in which a person behaves aggressively toward others.

To measure this variable, the researcher must devise a measurement that assesses aggressive behavior without harming others. The researcher might utilize a simulated task to measure aggressiveness in this situation.

Hypothesis Checklist

Does your hypothesis focus on something that you can actually test?
Does your hypothesis include both an independent and dependent variable?
Can you manipulate the variables?
Can your hypothesis be tested without violating ethical standards?

The hypothesis you use will depend on what you are investigating and hoping to find. Some of the main types of hypotheses that you might use include:

Simple hypothesis : This type of hypothesis suggests there is a relationship between one independent variable and one dependent variable.
Complex hypothesis : This type suggests a relationship between three or more variables, such as two independent and dependent variables.
Null hypothesis : This hypothesis suggests no relationship exists between two or more variables.
Alternative hypothesis : This hypothesis states the opposite of the null hypothesis.
Statistical hypothesis : This hypothesis uses statistical analysis to evaluate a representative population sample and then generalizes the findings to the larger group.
Logical hypothesis : This hypothesis assumes a relationship between variables without collecting data or evidence.

A hypothesis often follows a basic format of "If {this happens} then {this will happen}." One way to structure your hypothesis is to describe what will happen to the dependent variable if you change the independent variable .

The basic format might be: "If {these changes are made to a certain independent variable}, then we will observe {a change in a specific dependent variable}."

A few examples of simple hypotheses:

"Students who eat breakfast will perform better on a math exam than students who do not eat breakfast."
"Students who experience test anxiety before an English exam will get lower scores than students who do not experience test anxiety."
"Motorists who talk on the phone while driving will be more likely to make errors on a driving course than those who do not talk on the phone."
"Children who receive a new reading intervention will have higher reading scores than students who do not receive the intervention."

Examples of a complex hypothesis include:

"People with high-sugar diets and sedentary activity levels are more likely to develop depression."
"Younger people who are regularly exposed to green, outdoor areas have better subjective well-being than older adults who have limited exposure to green spaces."

Examples of a null hypothesis include:

"There is no difference in anxiety levels between people who take St. John's wort supplements and those who do not."
"There is no difference in scores on a memory recall task between children and adults."
"There is no difference in aggression levels between children who play first-person shooter games and those who do not."

Examples of an alternative hypothesis:

"People who take St. John's wort supplements will have less anxiety than those who do not."
"Adults will perform better on a memory task than children."
"Children who play first-person shooter games will show higher levels of aggression than children who do not."

Collecting Data on Your Hypothesis

Once a researcher has formed a testable hypothesis, the next step is to select a research design and start collecting data. The research method depends largely on exactly what they are studying. There are two basic types of research methods: descriptive research and experimental research.

Descriptive Research Methods

Descriptive research such as case studies , naturalistic observations , and surveys are often used when conducting an experiment is difficult or impossible. These methods are best used to describe different aspects of a behavior or psychological phenomenon.

Once a researcher has collected data using descriptive methods, a correlational study can examine how the variables are related. This research method might be used to investigate a hypothesis that is difficult to test experimentally.

Experimental Research Methods

Experimental methods are used to demonstrate causal relationships between variables. In an experiment, the researcher systematically manipulates a variable of interest (known as the independent variable) and measures the effect on another variable (known as the dependent variable).

Unlike correlational studies, which can only be used to determine if there is a relationship between two variables, experimental methods can be used to determine the actual nature of the relationship—whether changes in one variable actually cause another to change.

The hypothesis is a critical part of any scientific exploration. It represents what researchers expect to find in a study or experiment. In situations where the hypothesis is unsupported by the research, the research still has value. Such research helps us better understand how different aspects of the natural world relate to one another. It also helps us develop new hypotheses that can then be tested in the future.

Thompson WH, Skau S. On the scope of scientific hypotheses . R Soc Open Sci . 2023;10(8):230607. doi:10.1098/rsos.230607

Taran S, Adhikari NKJ, Fan E. Falsifiability in medicine: what clinicians can learn from Karl Popper [published correction appears in Intensive Care Med. 2021 Jun 17;:]. Intensive Care Med . 2021;47(9):1054-1056. doi:10.1007/s00134-021-06432-z

Eyler AA. Research Methods for Public Health . 1st ed. Springer Publishing Company; 2020. doi:10.1891/9780826182067.0004

Nosek BA, Errington TM. What is replication ? PLoS Biol . 2020;18(3):e3000691. doi:10.1371/journal.pbio.3000691

Aggarwal R, Ranganathan P. Study designs: Part 2 - Descriptive studies . Perspect Clin Res . 2019;10(1):34-36. doi:10.4103/picr.PICR_154_18

Nevid J. Psychology: Concepts and Applications. Wadworth, 2013.

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

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What is hypothesis in Machine Learning?

The hypothesis is a word that is frequently used in Machine Learning and data science initiatives. As we all know, machine learning is one of the most powerful technologies in the world, allowing us to anticipate outcomes based on previous experiences. Moreover, data scientists and ML specialists undertake experiments with the goal of solving an issue. These ML experts and data scientists make an initial guess on how to solve the challenge.

What is a Hypothesis?

A hypothesis is a conjecture or proposed explanation that is based on insufficient facts or assumptions. It is only a conjecture based on certain known facts that have yet to be confirmed. A good hypothesis is tested and yields either true or erroneous outcomes.

Let's look at an example to better grasp the hypothesis. According to some scientists, ultraviolet (UV) light can harm the eyes and induce blindness.

In this case, a scientist just states that UV rays are hazardous to the eyes, but people presume they can lead to blindness. Yet, it is conceivable that it will not be achievable. As a result, these kinds of assumptions are referred to as hypotheses.

Defining Hypothesis in Machine Learning

In machine learning, a hypothesis is a mathematical function or model that converts input data into output predictions. The model's first belief or explanation is based on the facts supplied. The hypothesis is typically expressed as a collection of parameters characterizing the behavior of the model.

If we're building a model to predict the price of a property based on its size and location. The hypothesis function may look something like this −

$$\mathrm{h(x)\:=\:θ0\:+\:θ1\:*\:x1\:+\:θ2\:*\:x2}$$

The hypothesis function is h(x), its input data is x, the model's parameters are 0, 1, and 2, and the features are x1 and x2.

The machine learning model's purpose is to discover the optimal values for parameters 0 through 2 that minimize the difference between projected and actual output labels.

To put it another way, we're looking for the hypothesis function that best represents the underlying link between the input and output data.

Types of Hypotheses in Machine Learning

The next step is to build a hypothesis after identifying the problem and obtaining evidence. A hypothesis is an explanation or solution to a problem based on insufficient data. It acts as a springboard for further investigation and experimentation. A hypothesis is a machine learning function that converts inputs to outputs based on some assumptions. A good hypothesis contributes to the creation of an accurate and efficient machine-learning model. Several machine learning theories are as follows −

1. Null Hypothesis

A null hypothesis is a basic hypothesis that states that no link exists between the independent and dependent variables. In other words, it assumes the independent variable has no influence on the dependent variable. It is symbolized by the symbol H0. If the p-value falls outside the significance level, the null hypothesis is typically rejected (). If the null hypothesis is correct, the coefficient of determination is the probability of rejecting it. A null hypothesis is involved in test findings such as t-tests and ANOVA.

2. Alternative Hypothesis

An alternative hypothesis is a hypothesis that contradicts the null hypothesis. It assumes that there is a relationship between the independent and dependent variables. In other words, it assumes that there is an effect of the independent variable on the dependent variable. It is denoted by Ha. An alternative hypothesis is generally accepted if the p-value is less than the significance level (α). An alternative hypothesis is also known as a research hypothesis.

3. One-tailed Hypothesis

A one-tailed test is a type of significance test in which the region of rejection is located at one end of the sample distribution. It denotes that the estimated test parameter is more or less than the crucial value, implying that the alternative hypothesis rather than the null hypothesis should be accepted. It is most commonly used in the chi-square distribution, where all of the crucial areas, related to, are put in either of the two tails. Left-tailed or right-tailed one-tailed tests are both possible.

4. Two-tailed Hypothesis

The two-tailed test is a hypothesis test in which the region of rejection or critical area is on both ends of the normal distribution. It determines whether the sample tested falls within or outside a certain range of values, and an alternative hypothesis is accepted if the calculated value falls in either of the two tails of the probability distribution. α is bifurcated into two equal parts, and the estimated parameter is either above or below the assumed parameter, so extreme values work as evidence against the null hypothesis.

Overall, the hypothesis plays a critical role in the machine learning model. It provides a starting point for the model to make predictions and helps to guide the learning process. The accuracy of the hypothesis is evaluated using various metrics like mean squared error or accuracy.

The hypothesis is a mathematical function or model that converts input data into output predictions, typically expressed as a collection of parameters characterizing the behavior of the model. It is an explanation or solution to a problem based on insufficient data. A good hypothesis contributes to the creation of an accurate and efficient machine-learning model. A two-tailed hypothesis is used when there is no prior knowledge or theoretical basis to infer a certain direction of the link.

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Hypothesis Testing – A Deep Dive into Hypothesis Testing, The Backbone of Statistical Inference

September 21, 2023

Explore the intricacies of hypothesis testing, a cornerstone of statistical analysis. Dive into methods, interpretations, and applications for making data-driven decisions.

In this Blog post we will learn:

What is Hypothesis Testing?
Steps in Hypothesis Testing 2.1. Set up Hypotheses: Null and Alternative 2.2. Choose a Significance Level (α) 2.3. Calculate a test statistic and P-Value 2.4. Make a Decision
Example : Testing a new drug.
Example in python

1. What is Hypothesis Testing?

In simple terms, hypothesis testing is a method used to make decisions or inferences about population parameters based on sample data. Imagine being handed a dice and asked if it’s biased. By rolling it a few times and analyzing the outcomes, you’d be engaging in the essence of hypothesis testing.

Think of hypothesis testing as the scientific method of the statistics world. Suppose you hear claims like “This new drug works wonders!” or “Our new website design boosts sales.” How do you know if these statements hold water? Enter hypothesis testing.

2. Steps in Hypothesis Testing

Set up Hypotheses : Begin with a null hypothesis (H0) and an alternative hypothesis (Ha).
Choose a Significance Level (α) : Typically 0.05, this is the probability of rejecting the null hypothesis when it’s actually true. Think of it as the chance of accusing an innocent person.
Calculate Test statistic and P-Value : Gather evidence (data) and calculate a test statistic.
p-value : This is the probability of observing the data, given that the null hypothesis is true. A small p-value (typically ≤ 0.05) suggests the data is inconsistent with the null hypothesis.
Decision Rule : If the p-value is less than or equal to α, you reject the null hypothesis in favor of the alternative.

2.1. Set up Hypotheses: Null and Alternative

Before diving into testing, we must formulate hypotheses. The null hypothesis (H0) represents the default assumption, while the alternative hypothesis (H1) challenges it.

For instance, in drug testing, H0 : “The new drug is no better than the existing one,” H1 : “The new drug is superior .”

2.2. Choose a Significance Level (α)

When You collect and analyze data to test H0 and H1 hypotheses. Based on your analysis, you decide whether to reject the null hypothesis in favor of the alternative, or fail to reject / Accept the null hypothesis.

The significance level, often denoted by $α$, represents the probability of rejecting the null hypothesis when it is actually true.

In other words, it’s the risk you’re willing to take of making a Type I error (false positive).

Type I Error (False Positive) :

Symbolized by the Greek letter alpha (α).
Occurs when you incorrectly reject a true null hypothesis . In other words, you conclude that there is an effect or difference when, in reality, there isn’t.
The probability of making a Type I error is denoted by the significance level of a test. Commonly, tests are conducted at the 0.05 significance level , which means there’s a 5% chance of making a Type I error .
Commonly used significance levels are 0.01, 0.05, and 0.10, but the choice depends on the context of the study and the level of risk one is willing to accept.

Example : If a drug is not effective (truth), but a clinical trial incorrectly concludes that it is effective (based on the sample data), then a Type I error has occurred.

Type II Error (False Negative) :

Symbolized by the Greek letter beta (β).
Occurs when you accept a false null hypothesis . This means you conclude there is no effect or difference when, in reality, there is.
The probability of making a Type II error is denoted by β. The power of a test (1 – β) represents the probability of correctly rejecting a false null hypothesis.

Example : If a drug is effective (truth), but a clinical trial incorrectly concludes that it is not effective (based on the sample data), then a Type II error has occurred.

Balancing the Errors :

In practice, there’s a trade-off between Type I and Type II errors. Reducing the risk of one typically increases the risk of the other. For example, if you want to decrease the probability of a Type I error (by setting a lower significance level), you might increase the probability of a Type II error unless you compensate by collecting more data or making other adjustments.

It’s essential to understand the consequences of both types of errors in any given context. In some situations, a Type I error might be more severe, while in others, a Type II error might be of greater concern. This understanding guides researchers in designing their experiments and choosing appropriate significance levels.

2.3. Calculate a test statistic and P-Value

Test statistic : A test statistic is a single number that helps us understand how far our sample data is from what we’d expect under a null hypothesis (a basic assumption we’re trying to test against). Generally, the larger the test statistic, the more evidence we have against our null hypothesis. It helps us decide whether the differences we observe in our data are due to random chance or if there’s an actual effect.

P-value : The P-value tells us how likely we would get our observed results (or something more extreme) if the null hypothesis were true. It’s a value between 0 and 1. – A smaller P-value (typically below 0.05) means that the observation is rare under the null hypothesis, so we might reject the null hypothesis. – A larger P-value suggests that what we observed could easily happen by random chance, so we might not reject the null hypothesis.

2.4. Make a Decision

Relationship between $α$ and P-Value

When conducting a hypothesis test:

We then calculate the p-value from our sample data and the test statistic.

Finally, we compare the p-value to our chosen $α$:

If $p−value≤α$: We reject the null hypothesis in favor of the alternative hypothesis. The result is said to be statistically significant.
If $p−value>α$: We fail to reject the null hypothesis. There isn’t enough statistical evidence to support the alternative hypothesis.

3. Example : Testing a new drug.

Imagine we are investigating whether a new drug is effective at treating headaches faster than drug B.

Setting Up the Experiment : You gather 100 people who suffer from headaches. Half of them (50 people) are given the new drug (let’s call this the ‘Drug Group’), and the other half are given a sugar pill, which doesn’t contain any medication.

Set up Hypotheses : Before starting, you make a prediction:
Null Hypothesis (H0): The new drug has no effect. Any difference in healing time between the two groups is just due to random chance.
Alternative Hypothesis (H1): The new drug does have an effect. The difference in healing time between the two groups is significant and not just by chance.

Calculate Test statistic and P-Value : After the experiment, you analyze the data. The “test statistic” is a number that helps you understand the difference between the two groups in terms of standard units.

For instance, let’s say:

The average healing time in the Drug Group is 2 hours.
The average healing time in the Placebo Group is 3 hours.

The test statistic helps you understand how significant this 1-hour difference is. If the groups are large and the spread of healing times in each group is small, then this difference might be significant. But if there’s a huge variation in healing times, the 1-hour difference might not be so special.

Imagine the P-value as answering this question: “If the new drug had NO real effect, what’s the probability that I’d see a difference as extreme (or more extreme) as the one I found, just by random chance?”

For instance:

P-value of 0.01 means there’s a 1% chance that the observed difference (or a more extreme difference) would occur if the drug had no effect. That’s pretty rare, so we might consider the drug effective.
P-value of 0.5 means there’s a 50% chance you’d see this difference just by chance. That’s pretty high, so we might not be convinced the drug is doing much.
If the P-value is less than ($α$) 0.05: the results are “statistically significant,” and they might reject the null hypothesis , believing the new drug has an effect.
If the P-value is greater than ($α$) 0.05: the results are not statistically significant, and they don’t reject the null hypothesis , remaining unsure if the drug has a genuine effect.

4. Example in python

For simplicity, let’s say we’re using a t-test (common for comparing means). Let’s dive into Python:

Making a Decision : “The results are statistically significant! p-value < 0.05 , The drug seems to have an effect!” If not, we’d say, “Looks like the drug isn’t as miraculous as we thought.”

5. Conclusion

Hypothesis testing is an indispensable tool in data science, allowing us to make data-driven decisions with confidence. By understanding its principles, conducting tests properly, and considering real-world applications, you can harness the power of hypothesis testing to unlock valuable insights from your data.

Correlation – connecting the dots, the role of correlation in data analysis, sampling and sampling distributions – a comprehensive guide on sampling and sampling distributions, law of large numbers – a deep dive into the world of statistics, central limit theorem – a deep dive into central limit theorem and its significance in statistics, skewness and kurtosis – peaks and tails, understanding data through skewness and kurtosis”, similar articles, complete introduction to linear regression in r, how to implement common statistical significance tests and find the p value, logistic regression – a complete tutorial with examples in r.

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Home » What is a Hypothesis – Types, Examples and Writing Guide

What is a Hypothesis – Types, Examples and Writing Guide

Table of Contents

Definition:

Hypothesis is an educated guess or proposed explanation for a phenomenon, based on some initial observations or data. It is a tentative statement that can be tested and potentially proven or disproven through further investigation and experimentation.

Hypothesis is often used in scientific research to guide the design of experiments and the collection and analysis of data. It is an essential element of the scientific method, as it allows researchers to make predictions about the outcome of their experiments and to test those predictions to determine their accuracy.

Types of Hypothesis

Types of Hypothesis are as follows:

Research Hypothesis

A research hypothesis is a statement that predicts a relationship between variables. It is usually formulated as a specific statement that can be tested through research, and it is often used in scientific research to guide the design of experiments.

Null Hypothesis

The null hypothesis is a statement that assumes there is no significant difference or relationship between variables. It is often used as a starting point for testing the research hypothesis, and if the results of the study reject the null hypothesis, it suggests that there is a significant difference or relationship between variables.

Alternative Hypothesis

An alternative hypothesis is a statement that assumes there is a significant difference or relationship between variables. It is often used as an alternative to the null hypothesis and is tested against the null hypothesis to determine which statement is more accurate.

Directional Hypothesis

A directional hypothesis is a statement that predicts the direction of the relationship between variables. For example, a researcher might predict that increasing the amount of exercise will result in a decrease in body weight.

Non-directional Hypothesis

A non-directional hypothesis is a statement that predicts the relationship between variables but does not specify the direction. For example, a researcher might predict that there is a relationship between the amount of exercise and body weight, but they do not specify whether increasing or decreasing exercise will affect body weight.

Statistical Hypothesis

A statistical hypothesis is a statement that assumes a particular statistical model or distribution for the data. It is often used in statistical analysis to test the significance of a particular result.

Composite Hypothesis

A composite hypothesis is a statement that assumes more than one condition or outcome. It can be divided into several sub-hypotheses, each of which represents a different possible outcome.

Empirical Hypothesis

An empirical hypothesis is a statement that is based on observed phenomena or data. It is often used in scientific research to develop theories or models that explain the observed phenomena.

Simple Hypothesis

A simple hypothesis is a statement that assumes only one outcome or condition. It is often used in scientific research to test a single variable or factor.

Complex Hypothesis

A complex hypothesis is a statement that assumes multiple outcomes or conditions. It is often used in scientific research to test the effects of multiple variables or factors on a particular outcome.

Applications of Hypothesis

Hypotheses are used in various fields to guide research and make predictions about the outcomes of experiments or observations. Here are some examples of how hypotheses are applied in different fields:

Science : In scientific research, hypotheses are used to test the validity of theories and models that explain natural phenomena. For example, a hypothesis might be formulated to test the effects of a particular variable on a natural system, such as the effects of climate change on an ecosystem.
Medicine : In medical research, hypotheses are used to test the effectiveness of treatments and therapies for specific conditions. For example, a hypothesis might be formulated to test the effects of a new drug on a particular disease.
Psychology : In psychology, hypotheses are used to test theories and models of human behavior and cognition. For example, a hypothesis might be formulated to test the effects of a particular stimulus on the brain or behavior.
Sociology : In sociology, hypotheses are used to test theories and models of social phenomena, such as the effects of social structures or institutions on human behavior. For example, a hypothesis might be formulated to test the effects of income inequality on crime rates.
Business : In business research, hypotheses are used to test the validity of theories and models that explain business phenomena, such as consumer behavior or market trends. For example, a hypothesis might be formulated to test the effects of a new marketing campaign on consumer buying behavior.
Engineering : In engineering, hypotheses are used to test the effectiveness of new technologies or designs. For example, a hypothesis might be formulated to test the efficiency of a new solar panel design.

How to write a Hypothesis

Here are the steps to follow when writing a hypothesis:

Identify the Research Question

The first step is to identify the research question that you want to answer through your study. This question should be clear, specific, and focused. It should be something that can be investigated empirically and that has some relevance or significance in the field.

Conduct a Literature Review

Before writing your hypothesis, it’s essential to conduct a thorough literature review to understand what is already known about the topic. This will help you to identify the research gap and formulate a hypothesis that builds on existing knowledge.

Determine the Variables

The next step is to identify the variables involved in the research question. A variable is any characteristic or factor that can vary or change. There are two types of variables: independent and dependent. The independent variable is the one that is manipulated or changed by the researcher, while the dependent variable is the one that is measured or observed as a result of the independent variable.

Formulate the Hypothesis

Based on the research question and the variables involved, you can now formulate your hypothesis. A hypothesis should be a clear and concise statement that predicts the relationship between the variables. It should be testable through empirical research and based on existing theory or evidence.

Write the Null Hypothesis

The null hypothesis is the opposite of the alternative hypothesis, which is the hypothesis that you are testing. The null hypothesis states that there is no significant difference or relationship between the variables. It is important to write the null hypothesis because it allows you to compare your results with what would be expected by chance.

Refine the Hypothesis

After formulating the hypothesis, it’s important to refine it and make it more precise. This may involve clarifying the variables, specifying the direction of the relationship, or making the hypothesis more testable.

Examples of Hypothesis

Here are a few examples of hypotheses in different fields:

Psychology : “Increased exposure to violent video games leads to increased aggressive behavior in adolescents.”
Biology : “Higher levels of carbon dioxide in the atmosphere will lead to increased plant growth.”
Sociology : “Individuals who grow up in households with higher socioeconomic status will have higher levels of education and income as adults.”
Education : “Implementing a new teaching method will result in higher student achievement scores.”
Marketing : “Customers who receive a personalized email will be more likely to make a purchase than those who receive a generic email.”
Physics : “An increase in temperature will cause an increase in the volume of a gas, assuming all other variables remain constant.”
Medicine : “Consuming a diet high in saturated fats will increase the risk of developing heart disease.”

Purpose of Hypothesis

The purpose of a hypothesis is to provide a testable explanation for an observed phenomenon or a prediction of a future outcome based on existing knowledge or theories. A hypothesis is an essential part of the scientific method and helps to guide the research process by providing a clear focus for investigation. It enables scientists to design experiments or studies to gather evidence and data that can support or refute the proposed explanation or prediction.

The formulation of a hypothesis is based on existing knowledge, observations, and theories, and it should be specific, testable, and falsifiable. A specific hypothesis helps to define the research question, which is important in the research process as it guides the selection of an appropriate research design and methodology. Testability of the hypothesis means that it can be proven or disproven through empirical data collection and analysis. Falsifiability means that the hypothesis should be formulated in such a way that it can be proven wrong if it is incorrect.

In addition to guiding the research process, the testing of hypotheses can lead to new discoveries and advancements in scientific knowledge. When a hypothesis is supported by the data, it can be used to develop new theories or models to explain the observed phenomenon. When a hypothesis is not supported by the data, it can help to refine existing theories or prompt the development of new hypotheses to explain the phenomenon.

When to use Hypothesis

Here are some common situations in which hypotheses are used:

In scientific research , hypotheses are used to guide the design of experiments and to help researchers make predictions about the outcomes of those experiments.
In social science research , hypotheses are used to test theories about human behavior, social relationships, and other phenomena.
I n business , hypotheses can be used to guide decisions about marketing, product development, and other areas. For example, a hypothesis might be that a new product will sell well in a particular market, and this hypothesis can be tested through market research.

Characteristics of Hypothesis

Here are some common characteristics of a hypothesis:

Testable : A hypothesis must be able to be tested through observation or experimentation. This means that it must be possible to collect data that will either support or refute the hypothesis.
Falsifiable : A hypothesis must be able to be proven false if it is not supported by the data. If a hypothesis cannot be falsified, then it is not a scientific hypothesis.
Clear and concise : A hypothesis should be stated in a clear and concise manner so that it can be easily understood and tested.
Based on existing knowledge : A hypothesis should be based on existing knowledge and research in the field. It should not be based on personal beliefs or opinions.
Specific : A hypothesis should be specific in terms of the variables being tested and the predicted outcome. This will help to ensure that the research is focused and well-designed.
Tentative: A hypothesis is a tentative statement or assumption that requires further testing and evidence to be confirmed or refuted. It is not a final conclusion or assertion.
Relevant : A hypothesis should be relevant to the research question or problem being studied. It should address a gap in knowledge or provide a new perspective on the issue.

Advantages of Hypothesis

Hypotheses have several advantages in scientific research and experimentation:

Guides research: A hypothesis provides a clear and specific direction for research. It helps to focus the research question, select appropriate methods and variables, and interpret the results.
Predictive powe r: A hypothesis makes predictions about the outcome of research, which can be tested through experimentation. This allows researchers to evaluate the validity of the hypothesis and make new discoveries.
Facilitates communication: A hypothesis provides a common language and framework for scientists to communicate with one another about their research. This helps to facilitate the exchange of ideas and promotes collaboration.
Efficient use of resources: A hypothesis helps researchers to use their time, resources, and funding efficiently by directing them towards specific research questions and methods that are most likely to yield results.
Provides a basis for further research: A hypothesis that is supported by data provides a basis for further research and exploration. It can lead to new hypotheses, theories, and discoveries.
Increases objectivity: A hypothesis can help to increase objectivity in research by providing a clear and specific framework for testing and interpreting results. This can reduce bias and increase the reliability of research findings.

Limitations of Hypothesis

Some Limitations of the Hypothesis are as follows:

Limited to observable phenomena: Hypotheses are limited to observable phenomena and cannot account for unobservable or intangible factors. This means that some research questions may not be amenable to hypothesis testing.
May be inaccurate or incomplete: Hypotheses are based on existing knowledge and research, which may be incomplete or inaccurate. This can lead to flawed hypotheses and erroneous conclusions.
May be biased: Hypotheses may be biased by the researcher’s own beliefs, values, or assumptions. This can lead to selective interpretation of data and a lack of objectivity in research.
Cannot prove causation: A hypothesis can only show a correlation between variables, but it cannot prove causation. This requires further experimentation and analysis.
Limited to specific contexts: Hypotheses are limited to specific contexts and may not be generalizable to other situations or populations. This means that results may not be applicable in other contexts or may require further testing.
May be affected by chance : Hypotheses may be affected by chance or random variation, which can obscure or distort the true relationship between variables.

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3 Learning Theories: Understanding How People Learn

Introduction.

Learning theories describe the conditions and processes through which learning occurs, providing teachers with models to develop instruction sessions that lead to better learning. These theories explain the processes that people engage in as they make sense of information, and how they integrate that information into their mental models so that it becomes new knowledge. Learning theories also examine what motivates people to learn, and what circumstances enable or hinder learning.

Sometimes people are skeptical of having to learn theory, believing those theories will not be relevant in the real world, but learning theories are widely applicable. The models and processes that they describe tend to apply across different populations and settings, and provide us with guidelines to develop exercises, assignments, and lesson plans that align with how our students learn best. Learning theories can also be engaging. People who enjoy teaching often find the theories interesting and will be excited when they start to see connections between the theory and the learning they see happening in their own classrooms.

General Learning Theories

With a basic understanding of learning theories, we can create lessons that enhance the learning process. This understanding helps us explain our instructional choices, or the “why” behind what and how we teach. As certain learning theories resonate with us and we consciously construct lessons based on those theories, we begin to develop a personal philosophy of teaching that will guide our instructional design going forward. This chapter provides a bridge from theory to practice by providing specific examples of how the theories can be applied in the library classroom. These theories provide a foundation to guide the instructional design and reflective practices presented in the rest of this textbook.

As you read, you might consider keeping track of the key points of each theory and thinking about how these theories could be applied to your practice. Figure 3.1 provides you with an example of a graphic organizer, one of the instructional materials that will be discussed in Chapter 11, that you could use to take notes as you read this chapter. In addition to the examples in practice that are provided in this chapter, you might add some of your own.

Figure 3.1: Graphic Organizer for Major Learning Theories

A table with four columns. The columns are labeled theory, major theorists, key concepts, and examples in practice. There are three blank rows where students can take notes.

Behaviorism

Behaviorism is based largely on the work of John B. Watson and B. F. Skinner. Behaviorists were concerned with establishing psychology as a science and focused their studies on behaviors that could be empirically observed, such as actions that could be measured and tested, rather than on internal states such as emotions (McLeod, 2015). According to behaviorists, learning is dependent on a person’s interactions with their external environment. As people experience consequences from their interactions with the environment, they modify their behaviors in reaction to those consequences. For instance, if a person hurts their hand when touching a hot stove, they will learn not to touch the stove again, and if they are praised for studying for a test, they will be likely to study in the future

According to behavioral theorists, we can change people’s behavior by manipulating the environment in order to encourage certain behaviors and discourage others, a process called conditioning (Popp, 1996). Perhaps the most famous example of conditioning is Pavlov’s dog. In his classic experiment, Pavlov demonstrated that a dog could be conditioned to associate the sound of a bell with food, so that eventually the dog would salivate whenever it heard the bell, regardless of whether it received food. Watson adapted stimulus conditioning to humans (Jensen, 2018). He gave an 11-month-old baby a rat, and the baby seemed to enjoy playing with it. Over time, Watson caused a loud, unpleasant sound each time he brought out the rat. Eventually, the baby associated the rat with the noise and cried when he saw the rat. Although Watson’s experiment is now considered ethically questionable, it did establish that people’s behavior could be modified through control of environmental stimuli.

Skinner (1938) examined how conditioning could shape behavior in longer-term and more complex ways by introducing the concept of reinforcement. According to Skinner, when people receive positive reinforcement, such as praise and rewards for certain behaviors, those behaviors are strengthened, while negative reinforcement will deter behaviors. According to Skinner, by carefully controlling the environment and establishing a system of reinforcements, teachers, parents, and others can encourage and develop desired behaviors (Jensen, 2018). A simple example of behaviorism in the classroom is a point system in which students are awarded points for good behavior and deducted points for unwanted behavior. Eventually, accumulated points might be traded in for rewards like small gifts or homework passes. This approach assumes that motivation is external, in that students will engage in certain behaviors in order to gain the rewards.

Because it emphasizes the external environment, behaviorism largely ignores or discounts the role of internal influences such as prior knowledge and emotion (Popp, 1996). To an extent, behaviorists view learners as blank slates and emphasize the role of the teacher in the classroom. In this teacher-centered approach, instructors hold the knowledge, decide what will be learned, and establish the rewards for learning. Since their experience and prior knowledge are not considered relevant, learners are passive participants simply expected to absorb the knowledge transmitted by the teacher. While the idea of learners as blank slates has fallen out of favor, many of the conditioning aspects of behaviorism remain popular. As almost any student can attest, behavioral methods of reinforcement, such as the point system described above, are still common, especially in younger grades. Recent trends toward gaming in the classroom, where certain behaviors are rewarded with points and leveling up, are based in a behaviorist approach to learning. See Activity 3.1 for a brief activity on behaviorism.

Activity 3.1: Reflecting on Behaviorism

Think of some of your own learning experiences, whether they were in a traditional classroom, through professional development training, or related to personal interests, such as dance or photography lessons. Try to identify a few examples of behaviorism from those experiences and reflect on the following questions:

How did your instructors use behavioral practice in their classrooms?
Did you find those practices motivating? Why or why not?
If you can think of examples of behaviorism from several different learning experiences, were they more appropriate in some situations than others? How so?
Have you ever used, or can you imagine using, behaviorism in your own teaching practice? How so?

Humanism recognizes the basic dignity and worth of each individual and believes people should be able to exercise some control over their environment. Although humanism as an educational philosophy has its roots in the Italian Renaissance, the more modern theorists associated with this approach include John Dewey, Carl Rogers, Maria Montessori, Paolo Freire, and Abraham Maslow. Humanist learning theory is a whole-person approach to education that centers on the individual learners and their needs, and that considers affective as well as cognitive aspects of learning. At its essence, “humanism in education traditionally has referred to a broad, diffuse outlook emphasizing human freedom, dignity, autonomy, and individualism” (Lucas, 1996). Within this broader context, humanism is also characterized by the following tenets (Madsen & Wilson, 2012; Sharp, 2012):

Students are whole people, and learning must attend to their emotional as well as their cognitive state.
Teachers should be empathetic.
Learners are self-directed and internally motivated.
The outcome of learning is self-actualization.

Humanism centers the individual person as the subject and recognizes learners as whole beings with emotional and affective states that accompany their cognitive development. Recognizing the role of students’ emotions means understanding how those emotions impact learning. Student anxiety, say around a test or a research paper, can interfere with the cognitive processes necessary to be successful. Empathetic teachers recognize and try to understand students’ emotional states, taking steps to alleviate negative emotions that might detract from learning by creating a supportive learning environment.

In a library context, Mellon (1986) identified the phenomenon of library anxiety, or the negative emotions that some people experience when doing research or interacting with library tools and services. This anxiety can distract learners and make it difficult to engage in the processes necessary to search for, evaluate, and synthesize the information they need to complete their task. Similarly, in her Information Search Process, Kuhlthau (1990) describes the affective states as well as the cognitive processes students engage in when doing research, acknowledging that their emotions fluctuate among anxiety, optimism, and, ultimately, satisfaction or disappointment.

A humanist approach to education recognizes these affective states and seeks to limit their negative impact. For instance, we can acknowledge that feelings of anxiety are common so learners recognize that they are not alone. We can also explain how the skills students learn are relevant to their lives in and outside of the classroom.

Because humanists see people as autonomous beings, they believe that learning should be self-directed, meaning students should have some choice in what and how they learn. Humanistic education is often connected with student-centered pedagogical approaches such as differentiated curricula, self-paced learning, and discovery learning (Lucas, 1996). Self-directed learning can take many forms, but it generally means that the instructor acts as a guide, and learners are given the freedom to take responsibility for their own learning. Teachers will provide the materials and opportunities for learning, but students will engage with the learning on their own terms. In a library classroom, we can give students choices about the topics they will research or offer learners different types of activities to practice skills and demonstrate what they have learned.

Humanists also believe that learning is part of a process of self-actualization. They maintain that learning should be internally motivated and driven by students’ interests and goals, rather than externally motivated and focused on a material end goal such as achievement on tests, or employment (Sharp, 2012). The expectation is that when students are allowed to follow their interests and be creative, and when learning takes place within a supportive environment, students will engage in learning for its own sake. This emphasis on self-actualization is largely based on Maslow’s (1943) hierarchy of needs. Maslow identified five levels of needs: basic physiological needs such as food, water, and shelter; safety and security needs; belongingness and love needs, including friends and intimate relationships; esteem needs, including feelings of accomplishment; and self-actualization, when people achieve their full potential. Importantly, these needs are hierarchical, meaning a person cannot achieve the higher needs such as esteem and self-actualization until more basic needs such as food and safety are met. The role of the humanist teacher is to facilitate the student’s self-actualization by helping to ensure needs such as safety and esteem are met through empathetic teaching and a supportive classroom.

In his book, Pedagogy of the Oppressed , Freire (2000) brings together many of the student-centered elements of humanistic education, with a strong emphasis on social justice aspects of learning and teaching. In contrast to behaviorist approaches, Freire emphasizes the importance of students’ life experience to their learning. He criticizes what he describes as the “banking model” of education, in which students are viewed as passive and empty vessels into which teachers simply deposit bits of knowledge that students are expected to regurgitate on exams or papers without any meaningful interaction. Freire insists that learning must be relevant to the student’s life and the student should be an active participant in order for learning to be meaningful. Freire also emphasized the emancipatory role of education, arguing that the purpose of education was for learners to gain agency to challenge oppressive systems and improve their lives, and praxis, in which learners put abstract and theoretical knowledge into practice in the real world.

While a student-centered approach and choice can be introduced in any classroom, observers note that in an age of curriculum frameworks and standardized tests, where teachers are often constrained by the material, the ability to provide students with choice and allow for exploration is limited (Sharp, 2012; Zucca-Scott, 2010). Librarians often face similar constraints. School librarians also must meet state and district curriculum standards. Academic librarians generally depend on faculty invitations to conduct instruction and need to adapt their sessions to fit the content, time frame, and learning objectives of the faculty member. Nevertheless, we can always find ways to integrate some self-direction. For instance, rather than using planned examples to demonstrate searches, we might have students suggest topics to search. If we plan hands-on practice activities, we could allow learners to explore their own interests as they engage in the activity, rather than limiting them to preselected topics.

Cognitivism

Cognitivism, or cognitive psychology, was pioneered in the mid-twentieth century by scientists including George Miller, Ulric Neisser, and Noam Chomsky. Whereas behaviorists focus on the external environment and observable behavior, cognitive psychologists are interested in mental processes (Codington-Lacerte, 2018). They assert that behavior and learning entail more than just response to environmental stimuli and require rational thought and active participation in the learning process (Clark, 2018). To cognitivists, learning can be described as “acquiring knowledge and skills and having them readily available from memory so you can make sense of future problems and opportunities” (Brown et al., 2014, p. 2).

Cognitivists view the brain as an information processor somewhat like a computer that functions on algorithms that it develops in order to process information and make decisions. According to cognitive psychology, people acquire and store knowledge, referred to as schema, in their long-term memory. In addition to storing knowledge, people organize their knowledge into categories, and create connections across categories or schema that help them retrieve relevant pieces of information when needed (Clark, 2018). When individuals encounter new information, they process it against their existing knowledge or schema in order to make new connections. Cognitivists are interested in the specific functions that allow the brain to store, recall, and use information, as well as in mental processes such as pattern recognition and categorization, and the circumstances that influence people’s attention (Codington-Lacerte, 2018).

Because cognitivists view memory and recall as the key to learning, they are interested in the processes and conditions that enhance memory and recall. According to cognitive psychology research, traditional methods of study, including rereading texts and drilling practice, or the repetition of terms and concepts, are not effective for committing information to memory (Brown et al., 2014). Rather, cognitivists assert that activities that require learners to recall information from memory, sometimes referred to as “retrieval practice,” lead to better memory and ultimately better learning. For example, they suggest that language learners use flash cards to practice vocabulary words, rather than writing the words out over and over or reading and rereading a list of words, because the flash cards force the learner to recall information from memory.

While testing has fallen out of favor with many educators and education theorists, cognitivists find tests can be beneficial as both a retrieval practice and a diagnostic tool. They view tests not only as a way to measure what has been learned but as a way to practice retrieval of important concepts, and as a way to identify gaps or weaknesses in knowledge so that learners know where to concentrate their efforts (Brown et al., 2014). Cognitivists encourage “spaced practice,” or recalling previously learned information at regular intervals, and “interleaving,” or learning related concepts together to establish connections among them. Their research has found that retrieval is more effective when the brain is forced to recall information after some time has passed, and when the recall involves two or more related subjects or concepts. Finally, cognitivists also promote problem-based learning, maintaining that “trying to solve a problem before being taught the solution leads to better learning, even when errors are made in the attempt” (Brown et al., 2014, p.4).

These processes that enhance memory and recall, and thus learning, have some implications for instructors in creating an optimal environment for learning. Gagné (1985) proposed nine conditions for learning, referred to as the external conditions of learning, or the nine events of instruction:

Gain attention. Engage students’ attention by tying learning to relevant events in their lives and asking stimulating questions.
Inform the learner of the objective. Begin by sharing the learning goals with the students, thus setting expectations and providing a map of the learning.
Stimulate recall of prior learning. Encourage students to remember previously learned relevant skills and knowledge before introducing new information.
Present the stimulus. Share new information. This step depends on the content of the lesson. For instance, a lesson on Boolean operators might begin with a Venn diagram and examples of the uses of and , or , and not .
Provide learner guidance. Facilitate learning by demonstration and explanation.
Elicit performance. Allow time for students to practice skills and demonstrate their abilities. Ideally, students would be given low-stakes opportunities for practice, so they feel comfortable if they do not succeed immediately.
Provide feedback. Offer students input on what they are doing well and where they can improve.
Assess performance. Employ measures such as assignments, activities, and projects to gauge whether learning has occurred.
Enhance retention and transfer. Give students opportunities to practice skills in new contexts, which improves retention and helps students see how the skills are applied to different areas.

Cognitivism remains a popular approach to learning. However, one criticism of cognitive psychology is that, unlike humanism, it does not account for the role of emotions in learning (Codington-Lacerte, 2018). Further, some critics believe that cognitivism overemphasizes memorization and recall of facts to the detriment of higher-order skills such as creativity and problem solving. However, cognitivists argue that the ability to recall facts and concepts is essential to higher-order thinking, and therefore the two are not mutually exclusive but actually interdependent (Brown et al., 2014). Finally, cognitivism is considered teacher-centered, rather than learner-centered, since it emphasizes the role of the instructor in organizing learning activities and establishing the conditions of learning (Clark, 2018). Activity 3.2 is a brief exercise on cognitivism.

Activity 3.2: Reflecting on Cognitivism

Cognitive scientists recommend retrieval practice, including spaced practice and interleaving, over drilling.

Questions for Reflection and Discussion:

What kind of study practices do you tend to use? Do your practices vary depending on the content or material you are studying? How so?
Can you think of ways to integrate retrieval practices into your work for this class?
Spaced practice involves returning to previously learned concepts at later times, but information professionals often teach one-shot sessions. Can you think of ways to integrate spaced practice into a one-shot session?

Constructivism

Constructivism posits that individuals create knowledge and meaning through their interactions with the world. Like cognitivism, and as opposed to behaviorism, constructivism acknowledges the role of prior knowledge in learning, believing that individuals interpret what they experience within the framework of what they already know (Kretchmar, 2019a). Social constructs, such as commonly held beliefs, and shared expectations around behavior and values provide a framework for knowledge, but people “do not just receive this knowledge as if they were empty vessels waiting to be filled. Individuals and groups interact with each other, contributing to the common trove of information and beliefs, reaching consensus with others on what they consider is the true nature of identity, knowledge, and reality” (Mercadal, 2018). Cognitivism and constructivism overlap in a number of ways. Both approaches build on the theories of Jean Piaget, who is sometimes referred to as a cognitive constructivist. However, while cognitivism is considered teacher-centered, constructivism centers the learner by recognizing their role in engaging with content and constructing meaning. Constructivist teachers act as guides or coaches, facilitating learning by developing supportive activities and environments, and building on what students already know (Kretchmar, 2019b).

Piaget discusses the concepts of assimilation, accommodation, and disequilibrium to describe how people create knowledge. In his early work as a biologist, Piaget noticed how organisms would adapt to their environment in order to survive. Through such adaptation, the organism achieved equilibrium. Extending these observations to cognitive science, he posited that human beings also seek equilibrium (Kretchmar, 2019a).

When they encounter new situations, or new information, human beings must find a way to deal with the new information. Similar to the processes described in the section on cognitivism, people will examine their existing knowledge, or schema, to see if the new information fits into what they already know. If it does, they are able to assimilate the information relatively easily. However, if the new information does not fit into what people already know, they experience disequilibrium or cognitive conflict, and must adapt by accommodating the new information. For example, once children learn what a dog is, they might call any four-legged creature they see a dog. This is assimilation, as the children are fitting new information into their existing knowledge. However, as children learn the differences between, say, a dog and cat, they can adjust their schema to accommodate this new knowledge (Heick, 2019).

Disequilibrium and accommodation can be uncomfortable. People might be confused or anxious when they encounter information that does not fit their existing schema, and they might struggle to accommodate that new information, but disequilibrium is crucial to learning (Kretchmar, 2019a). During assimilation, people might be adding new bits of information to their knowledge store, but they are not changing their understanding of the world. During accommodation, as people change their schema, construct new knowledge, and draw new connections among existing areas of knowledge, actual learning occurs, and accommodation requires disequilibrium.

Acknowledging the role of disequilibrium is important for both instructors and students. People naturally want to avoid discomfort, but that can also mean avoiding real learning. As instructors, we can facilitate accommodation by acknowledging that the process might be challenging, and by creating conditions that allow students to feel safe exploring new information. We can reassure learners that feelings of discomfort or anxiety are normal and provide them with low-stakes opportunities to engage with new information.

Social Constructivism

Social constructivism builds on the traditions of constructivism and cognitivism; whereas those theories focus on how individuals process information and construct meaning, social constructivists also consider how people’s interactions with others impact their understanding of the world. Social constructivists recognize that different people can have different reactions and develop different understandings from the same events and circumstances, and are interested in how factors such as identity, family, community, and culture help shape those understandings (Mercadal, 2018).While cognitivists and constructivists view other people as mostly incidental to an individual’s learning, social constructivists see community as central. Social constructivism can be defined as “the belief that the meanings attached to experience are socially assembled, depending on the culture in which the child is reared and on the child’s caretakers” (Schaffer, 2006). Like constructivism, social constructivism centers on the learners’ experiences and engagement, and sees the role of the instructor as a facilitator or guide. Two of the major theorists associated with social constructivism are Pierre Bourdieu and Lev Vygotsky.

Vygotsky built on the work of Piaget and believed knowledge is constructed, but felt that prior theories overemphasized the role of the individual in that construction of knowledge. Instead, he “was most interested in the role of other people in the development and learning processes of children,” including how children learn in cooperation with adults and older or more experienced peers who can guide them with more complex concepts (Kretchmar, 2019b). Vygotsky was also interested in how language and learning are related. He postulated that the ways in which people communicate their thoughts and understandings, even when talking themselves through a concept or problem, are a crucial element of learning (Kretchmar, 2019b). For Vygotsky, interaction and dialogue among students, teachers, and peers are key to how learners develop an understanding of the world and of the socially constructed meanings of their communities.

Bourdieu examined the way in which social structures influence people’s values, knowledge, and beliefs, and how these structures often become so ingrained as to be invisible. People within a society become so enculturated into the systems and beliefs of that society that they often accept them as “normal” and do not see them as imposed structures (Roth, 2018). As a result, individuals might not question or challenge those structures, even when they are unfair or oppressive. In addition to examining how community and culture help shape knowledge, Bourdieu was interested in how issues of class impact learning. He observed that over time, schools developed to reflect the cultures of wealthier families, which enabled their children to succeed because they inherently understood the culture of the classroom and the system of education. We continue to see such issues today, and as discussed more in Chapter 5 and Chapter 6, part of our critical practice is to ensure that our classrooms and instructional strategies are inclusive of and responsive to all students.

Activity 3.3 explores how we can use theory to guide our practice.

Activity 3.3: Using Learning Theory to Plan Lessons

While learning theories can be interesting on their own, our goal as instructors is to apply them to classroom practice. Imagine that you are a high school librarian working with a class that has just been assigned a research paper. Your goal for this session is for students to brainstorm keywords and synonyms for their topics, and to learn how to string those words together using the Boolean operators and , or , and not . You want to be sure the students understand the function of the Boolean operators and can remember how to use them for future searches.

Choose one of the learning theories outlined in this chapter and design a brief lesson to teach Boolean operators from the perspective of that theory. Concentrate less on what you would teach but rather on how you would teach it in keeping with the chosen theory:

How would you introduce the topic?
What sort of learning activities would you use?
What would you be doing during the lesson? What would you expect students to do?
How might any of your answers to these questions change if you were to use a different theory as your guide?

Developmental Stages

The learning theories outlined above discuss various cognitive processes involved in learning, as well as some of the motivators and conditions that facilitate learning. While these theories attempt to describe how people learn, it is important to note that individuals are not born ready to engage in all of these processes at once, nor do they necessarily all engage in the same processes at the same time. Rather, more complex processes develop over time as people experience the world and as their brain matures. In addition to studying how people learn, some theorists have also proposed theories or frameworks to describe developmental stages, or the various points in human development when different cognitive processes are enabled, and different kinds of learning can occur.

Piaget outlined four hierarchical stages of cognitive development: sensorimotor, preoperational, concrete operational, and formal operational (Clouse, 2019), illustrated in Table 3.1. In the sensorimotor stage, from birth to about two years, infants react to their environment with inherent reflexes such as sucking, swallowing, and crying. By about age two, they begin problem solving using trial and error. The preoperational stage, also sometimes called the intuitive intelligence stage, lasts from about ages two to seven. During this time, children develop language and mental imagery. They are able to use their imagination, but they view the world only from their own perspective and have trouble understanding other perspectives. Their understanding of the world during this stage is tied to their perceptions. Children are in the operational stage from about ages seven to 12, during which time they begin to think more logically about the world, can understand that objects are not always as they appear, and begin to understand other people’s perspectives. The final stage, formal operationalism, begins around age 12. At this point, individuals can think abstractly and engage in ideas that move beyond the concrete world around them, and they can use deductive reasoning and think through consequences (Clark, 2018; Clouse, 2019).

Table 3.1: Piaget’s Four Stages of Cognitive Development

Perry’s (1970) Scheme of Intellectual and Moral Development offers another useful framework for understanding the developmental stages of learning. Perry proposed four stages of learning. In the first stage, dualism, children generally believe that all problems can be solved, and that there are right and wrong answers to each question. At this stage, children generally look to instructors to provide them with correct answers. The second stage is multiplicity, where learners realize that there are conflicting views and controversies on topics. Learners in the multiplicity stage often have trouble assessing the authority and credibility of arguments. They tend to believe that all perspectives are equally valid and rely on their own experiences to form opinions and decide what information to trust. In the next stage, referred to as relativism, learners begin to understand that there are different lenses for understanding and evaluating information. They learn that different disciplines have their own methods of research and analysis, and they can begin to apply these perspectives as they evaluate sources and evidence. At this point, learners can understand that not all answers or perspectives are equal, but that some answers or arguments might be more valid than others. In the final stage, commitment, students integrate selected information into their knowledge base. You might notice connections between Perry and the cognitivists and constructivists described above in the way they each describe people making sense of information by comparing new information to existing knowledge. However, Perry organizes the processes into developmental stages that outline a progression of learning.

Understanding the stages laid out by Piaget and Perry, we can develop lessons that are appropriate to learners at each stage. For example, in presenting a lesson on climate change to preoperational students using Piaget’s framework, an instructor could gather pictures of different animal habitats, or take children on a nature walk to observe the surrounding environment. Instructors could ask these children to describe what they see and reflect on their personal experiences with weather, while older children could be asked to imagine how the changes are impacting other people and organisms, anticipate consequences of the impact of climate change, and perhaps use problem solving to propose steps to improve their environment. Considering Perry’s Scheme, instructors might guide students from multiplicity to relativism by explaining scientific methods for measuring climate, and challenging learners to evaluate and compare different sources of information to determine which presents the strongest evidence.

Piaget and Perry offer developmental models that outline stages broadly aligned with a person’s age. Both models assume a relatively linear chronological development, with children and young adults passing through different stages at roughly the same time. Vygotsky, on the other hand, describes a model that focuses more on the content being mastered rather than the age of the student. According to Vygotsky’s theory, known as Zone of Proximal Development (ZPD), as learners acquire new knowledge or develop new skills, they pass through three stages, often illustrated as concentric circles, as in Figure 3.2. The center circle, or first zone, represents tasks that the learner can do on their own. The second zone, or the Zone of Proximal Development, represents an area of knowledge or set of tasks that the learner can accomplish with assistance. The tasks and knowledge in this zone require students to stretch their abilities somewhat beyond their current skill level but are not so challenging as to be completely frustrating. The outermost circle, or third zone, represents tasks that the learner cannot yet do. Vygotsky posits that by working within the ZPD, learners can continue to grow their skills and abilities and increase their knowledge (Flair, 2019).

Figure 3.2: The Zone of Proximal Development

Whereas Piaget and Perry’s theories suggest that learners pass through the same stages at roughly the same time, Vygotsky maintains that the ZPD, or the zone of learning that will appropriately challenge the learner, is different for each student, depending on their background knowledge, experience, and ability (Flair, 2019). The same individual can experience different ZPDs in different subject areas; they might be advanced in math and able to take on material above their grade level but might find languages more challenging. Like with social constructivism, interaction with others is central to ZPD. According to Vygotsky, learning takes place when students interact with others who are more knowledgeable, including peers and instructors, who can provide guidance in the ZPD (Schaffer, 2006).

Math can provide a good example of working within the ZPD. Once students are comfortable with addition, they can probably learn subtraction with some help from a teacher or other peers but are probably not ready to learn long division. Our challenge as instructors is to identify the ZPD for each student so that we are neither boring learners with material that is too easy nor overwhelming them with material that is too hard. Chapter 7 discusses methods for assessing learners’ background knowledge to help determine the appropriate level of learning.

Most of the educational theories and frameworks outlined in this chapter were developed with a focus on children and young adults. While many of the principles can apply to an adult audience, they do not necessarily account for the specific issues, challenges, and motivations of adult learners. Yet, many information professionals will work mostly or even exclusively with adults. Academic librarians and archivists largely work with students who are at least 17 years old and, as the numbers of nontraditional students continue to increase, will find themselves increasingly working with older learners. Likewise, information professionals in corporations and medical and legal settings work almost exclusively with adults. Public librarians see a range of patrons, and many public libraries are increasing educational programming for their adult patrons. This section presents the educational concept of andragogy, which addresses teaching and learning for adults.

Knowles proposed andragogy as “the art and science of helping adults learn” (1988, p. 43). Andragogy is based on a set of assumptions about the ways in which adult learners’ experience, motivations, and needs differ from those of younger students, and suggests that traditional classroom approaches developed with younger students in mind will not necessarily be successful with adult learners. Perhaps one of the biggest differences between child and adult learners, according to Knowles (1988), is that adults are interested in the immediate applicability of what they are learning and are often motivated by their social roles as employees, parents, and so on. As Knowles notes, in traditional classrooms, children are usually taught discrete subjects like math, reading, and history, and their learning is focused on building up knowledge for the future. Young students might not use geometry in their everyday lives, but it forms a foundation for more complex math and for future job or life tasks like measuring materials for home repairs.

Adults, on the other hand, are already immersed in the social roles for which younger students are only preparing, and they want to see how their learning applies to those roles. Thus, Knowles suggests that adults will be interested in a competency-based, rather than a subject-based, approach to learning. Further, as autonomous individuals, adults are likely to be more self-directed in their learning. That is, they will want to, and should be encouraged to, take an active part in the design and planning of lessons, providing input on content and goals. Finally, Knowles also argues that adults’ wider experience and larger store of knowledge should be a resource for learning.

Knowles (1988, p. 45) organized his approach around four assumptions of adult learners:

Their self-concept moves from one of being a dependent personality toward a self-directed human being.
They accumulate a growing reservoir of experience that becomes an increasingly rich resource for learning.
Their readiness to learn becomes oriented increasingly to the developmental tasks of their social roles.
Their time perspective changes from one of postponed application of knowledge to immediacy of application, and, accordingly, their orientation toward learning shifts from one of subject-centeredness to one of performance-centeredness.

Later, he elaborated with two additional assumptions, summed up by Merriam et al. (2007):

The most potent motivations are internal rather than external.
Adults need to know why they need to learn something.

Certain understandings follow from Knowles’ assumptions that we can use to guide our practice with adult learners. To begin with, we should recognize and respect adults’ tendency to be self-motivated and self-directed learners. After all, in most states, school attendance is compulsory up to a certain age, and relatively strict curriculum standards are set by each state, meaning that children have little choice about attending school in some form or about what content they learn. At least in theory, adults have a choice about whether to attend college or engage in other kinds of learning opportunities such as workshops and professional development and continuing education courses. Presumably, adults are motivated to pursue these opportunities for a specific reason, whether out of personal curiosity, to advance in their careers, or to gain a new skill. These adult learners will likely have opinions and ideas about what they want to learn and perhaps even how they want to engage with the content, so Knowles suggests we provide adult learners with choices and opportunities for input to help shape the curriculum.

Adult learners also have a larger store of knowledge and experience than their younger counterparts. From a cognitivist or constructivist point of view, adults have a larger schema against which to compare new information and make new connections. As instructors, we should recognize this store of knowledge and find ways to integrate it into the classroom, by providing ample opportunity for reflection and using guiding questions to encourage learners to draw on that knowledge. We can approach adult learners as peers or co-learners, acting more as coaches or facilitators in the learning process than as the more directive teacher associated with a traditional school classroom. This focus on learner-centered approaches and a democratic environment overlaps with humanistic and constructivist approaches to teaching.

Points three, four, and six in Knowles’ list of assumptions underscore the importance of relevance and transparency for adult learners. Knowles suggests that adults have different priorities in learning, perhaps in part because they are learning by choice and are in a better position to direct their own learning. Adult learners also tend to have more demands on their time than younger students; they may have families and jobs that impact the time they have to devote to their studies. Thus, adult learners want to see the applicability of what they are learning and might be resistant to work or information that seems incidental. We should be transparent with our adult students, both about what they will learn and how that learning is important and relevant. Sharing learning goals is an important step toward transparency, as it can help set expectations so that students understand the purpose of the lesson and activities. To illustrate relevance, we can provide concrete examples of how the learning can be applied in practice. One could argue that all students, not just adults, deserve transparency and to see the relevance of lesson goals and learning. Knowles’ point is that adults are more likely to expect, and perhaps appreciate, such transparency.

While some controversy exists over whether andragogy really constitutes a theory per se or is more a set of guiding principles or best practices, the assumptions provide helpful guidance to instructors not just in how they organize content but also in how they frame the lesson and its purposes. Based on these assumptions, we can take certain steps to set an appropriate environment for adult education (Bartle, 2019):

Set a cooperative learning climate.
Create mechanisms for input.
Arrange for a diagnosis of learner needs and interests.
Enable the formulation of learning objectives based on the diagnosed needs and interests.
Design sequential activities for achieving the objectives.
Execute the design by selecting methods, materials, and resources.
Evaluate the quality of the learning experience while rediagnosing needs for further learning.

As noted above, andragogy overlaps with other theories such as humanism and constructivism, and some of the principles of andragogy, like transparency, would benefit all learners. Still, this framework is useful in reminding instructors that adult learners likely have different priorities and motivations, and thus some differences in classroom approach might be warranted.

In addition to how people learn, we should also know something about why people learn. What motivates a student to put the time and effort into learning a skill or topic, and what can we do to cultivate that motivation? Svinicki (2004) offers an intriguing model that amalgamates some of the prevailing theories of motivation in learning. She suggests that motivation is a factor of the perceived value of the learning, along with students’ belief in their own self-efficacy, or their belief in their ability to achieve the goal. As Svinicki explains, “motivation involves a constant balancing of these two factors of value and expectations for success” (2004, p. 146). Most of the learning theories outlined above address motivation implicitly or explicitly. For instance, behaviorists talk in terms of reinforcement, or external motivators, as students strive to avoid negative consequences and achieve the rewards of good work. Humanists, on the other hand, focus on the internal motivation of self-actualization. As instructors, we can create environments to increase our learners’ motivation or their perception of the value of the goal and their self-efficacy:

Emphasize the relevance of the material. As outlined in the section on andragogy, learners are motivated when they see the benefits of learning and understand why the material is important. Instructors should explain how the effort individuals put into learning can help them achieve personal goals, such as getting a good grade on a paper or finding a job.
Make the material appropriately challenging. Reminiscent of the Zone of Proximal Development, material that is too easy will be boring for learners, while material that is too challenging will be overwhelming and frustrating.
Give learners a sense of choice and control. Choice allows learners to have a stake in the class, while control helps them determine the level of risk they will take and thus increase their confidence. We can foster choice and control by allowing learners options in the types of activities and assignments they engage in, or in the topics they research.
Set learners up for success. Clear expectations for the class or the assignment help learners understand what a successful performance or project looks like. By providing meaningful feedback, we can guide learners toward success.
Guide self-assessment. When learners accurately assess their current level of knowledge and skill, they can make reasonable predictions of the likelihood of their success with the current material.

Activity 3.4 offers an opportunity to reflect on motivation in learning.

Activity 3.4: What Motivates You?

Think back on learning experiences such as courses or workshops where you felt more or less motivated as a learner. These experiences could be related to academics, hobbies, sports, or other interests.

In the experiences in which you felt motivated, what steps did the instructor take that helped you feel motivated?
In the experiences where you felt less motivated, what could the instructor have done differently?
In each case, what role did self-efficacy, or your confidence in your own abilities, play?

Growth Mindset

Dweck’s (2016) mindset theory has gained much attention in the field of education over the last few decades and has some implications for student motivation. Although this theory is somewhat different in its conceptualizations than those described in the rest of this chapter, it is included here both because of its popularity and because it provides interesting insight into how instructors can coach learners to understand and build on their potential. Dweck’s theory is less about how people learn and more about how their attitude toward learning and their self-concept can impact their ability and willingness to learn. According to Dweck, people tend to approach learning with a fixed mindset or a growth mindset. Those with more of a fixed mindset tend to believe that ability is innate; either people are born with a certain talent and ability, or they are not. If individuals are not born with natural ability in a certain area, they would waste time working on that area because they will never truly be successful. People with more of a growth mindset, on the other hand, tend to believe that ability is the outcome of hard work and effort. These people see value in working at areas in which they are not immediately successful because they believe they can improve. Even when they are good at something, they are willing to continue to work at it because they believe they can continue to get better (Dweck, 2016).

These mindsets can have a profound impact on how a person approaches learning (Dweck, 2016). People with a fixed mindset will view low grades or poor test performance as a sign of their lack of natural ability and are likely to become discouraged. They might try to avoid that subject altogether or resign themselves to failure because they do not believe that practice or study will help them improve. Instead, they will tend to stick to subjects in which they already perform well. People with a growth mindset take an opposite view. They tend to view low grades or poor performance as a diagnostic tool that helps them see where they need to concentrate their efforts in order to get better. They are willing to put in extra effort because they believe that their hard work will lead to improved performance. They are also willing to take risks because they understand that failure is just part of the process of learning. We can see connections between Dweck’s theory and Piaget’s argument that the discomfort of disequilibrium is necessary to learning.

Understandably, people with a growth mindset are usually more successful learners because they believe in their own ability to learn and grow. Luckily, Dweck maintains that these mindsets themselves are not necessarily immutable. That is, a person with a fixed mindset can be coached to adopt a growth mindset. Learners can begin by recognizing when they are engaging in fixed mindset thinking, for instance when getting anxious about mistakes or telling themselves that they are “no good” at something. Once learners understand that this thinking is counterproductive, they can change their thinking to adopt a more encouraging voice.

Importantly, Dweck notes that encouraging a growth mindset in the classroom does not mean lowering standards for learning. She maintains that instructors should have high standards but also create a supportive and nurturing atmosphere. To begin with, instructors themselves must believe that learning and growth are possible, and not give up on students who are struggling. Instructors can model this belief for students by replacing fixed mindset feedback with growth mindset feedback. For example, Dweck suggests that if learners are struggling, instructors can respond by telling them they have not succeeded yet. The word “yet” implies that they will achieve the necessary learning; they just need to keep working at it. In that way, instructors can reframe mistakes and struggles as opportunities to learn rather than as failures. Instructors should encourage and appreciate effort as well as learning. In other words, rather than focusing only on a student’s achievement, instructors can praise the effort and hard work that led to that achievement. At the same time, Dweck (2015) notes that a growth mindset is not just about effort. In addition to putting in the work, learners must also be willing to try different strategies and be open to feedback on their performance. The goal is to help students view challenges as part of the learning process and to work with them rather than to fear or avoid them.

Learning theories are meant to help instructors understand the processes and circumstances that enable learning and, by extension, offer guidance in developing activities and environments that best support learning. But what to make of the fact that there are so many different theories and that some contradict each other? The truth is that the human brain and its cognitive processes are incredibly complex and not yet fully understood. Learning theorists do their best to describe how people learn based on careful observation and experimentation, but no learning theory is perfect. Indeed, each theory has its critics, and the various theories go in and out of favor over time. Even so, the theories provide us with an empirically based understanding of how learning occurs.

Further, these theories are not mutually exclusive. We do not have to strictly adhere to one theory but can combine elements across theories in ways that resonate with our teaching styles and reflect our best understanding of our students. For instance, a teacher might draw on elements of cognitivism to enhance students’ retention and recall but also develop group activities that promote social constructivism through peer-to-peer communication. Especially with younger children, instructors might draw on behaviorism by using rewards and positive reinforcement to motivate student engagement with the content, but also integrate humanism by empathizing with students and use constructive feedback to encourage a growth mindset. We can use our understanding of developmental stages to create lessons and activities that provide an appropriate level of challenge to help students grow in their understanding. Ultimately, we should view learning theories as guidelines, not rules, and draw on them in ways that reflect our own values and understandings.

Keeping this idea of learning across theories in mind, we can sum up the key takeaways from this chapter:

Learning is the change in knowledge, behavior, or understanding that occurs when people make connections between new information and their existing knowledge. Various theories attempt to describe the factors that enable the learning process.
Learning does not happen in the same way or at the same time for all students. Understanding developmental stages can help instructors align instruction with student readiness. Adult learners may have needs and constraints that differ from younger learners.
The learning process is influenced by internal factors such as the student’s level of motivation and feelings of self-efficacy, and external factors such as the classroom environment and the adults and peers with whom the learner interacts.
Creating a democratic, empathetic, and supportive learning environment
Assisting students in becoming self-directed learners and enhancing their motivation by offering a sense of control and choice in their learning
Acknowledging that learning can be challenging, and helping students develop the mindset and self-efficacy that will support their persistence
Offering regular and meaningful feedback

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What Is a Hypothesis? (Science)

If...,Then...

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Ph.D., Biomedical Sciences, University of Tennessee at Knoxville
B.A., Physics and Mathematics, Hastings College

A hypothesis (plural hypotheses) is a proposed explanation for an observation. The definition depends on the subject.

In science, a hypothesis is part of the scientific method. It is a prediction or explanation that is tested by an experiment. Observations and experiments may disprove a scientific hypothesis, but can never entirely prove one.

In the study of logic, a hypothesis is an if-then proposition, typically written in the form, "If X , then Y ."

In common usage, a hypothesis is simply a proposed explanation or prediction, which may or may not be tested.

Writing a Hypothesis

Most scientific hypotheses are proposed in the if-then format because it's easy to design an experiment to see whether or not a cause and effect relationship exists between the independent variable and the dependent variable . The hypothesis is written as a prediction of the outcome of the experiment.

Null Hypothesis and Alternative Hypothesis

Statistically, it's easier to show there is no relationship between two variables than to support their connection. So, scientists often propose the null hypothesis . The null hypothesis assumes changing the independent variable will have no effect on the dependent variable.

In contrast, the alternative hypothesis suggests changing the independent variable will have an effect on the dependent variable. Designing an experiment to test this hypothesis can be trickier because there are many ways to state an alternative hypothesis.

For example, consider a possible relationship between getting a good night's sleep and getting good grades. The null hypothesis might be stated: "The number of hours of sleep students get is unrelated to their grades" or "There is no correlation between hours of sleep and grades."

An experiment to test this hypothesis might involve collecting data, recording average hours of sleep for each student and grades. If a student who gets eight hours of sleep generally does better than students who get four hours of sleep or 10 hours of sleep, the hypothesis might be rejected.

But the alternative hypothesis is harder to propose and test. The most general statement would be: "The amount of sleep students get affects their grades." The hypothesis might also be stated as "If you get more sleep, your grades will improve" or "Students who get nine hours of sleep have better grades than those who get more or less sleep."

In an experiment, you can collect the same data, but the statistical analysis is less likely to give you a high confidence limit.

Usually, a scientist starts out with the null hypothesis. From there, it may be possible to propose and test an alternative hypothesis, to narrow down the relationship between the variables.

Example of a Hypothesis

Examples of a hypothesis include:

If you drop a rock and a feather, (then) they will fall at the same rate.
Plants need sunlight in order to live. (if sunlight, then life)
Eating sugar gives you energy. (if sugar, then energy)
White, Jay D. Research in Public Administration . Conn., 1998.
Schick, Theodore, and Lewis Vaughn. How to Think about Weird Things: Critical Thinking for a New Age . McGraw-Hill Higher Education, 2002.
Null Hypothesis Definition and Examples
Definition of a Hypothesis
What Are the Elements of a Good Hypothesis?
Six Steps of the Scientific Method
Independent Variable Definition and Examples
What Are Examples of a Hypothesis?
Understanding Simple vs Controlled Experiments
Scientific Method Flow Chart
Scientific Method Vocabulary Terms
What Is a Testable Hypothesis?
Null Hypothesis Examples
What 'Fail to Reject' Means in a Hypothesis Test
How To Design a Science Fair Experiment
What Is an Experiment? Definition and Design
Hypothesis Test for the Difference of Two Population Proportions

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Definition of hypothesis

Did you know.

The Difference Between Hypothesis and Theory

A hypothesis is an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.

In the scientific method, the hypothesis is constructed before any applicable research has been done, apart from a basic background review. You ask a question, read up on what has been studied before, and then form a hypothesis.

A hypothesis is usually tentative; it's an assumption or suggestion made strictly for the objective of being tested.

A theory , in contrast, is a principle that has been formed as an attempt to explain things that have already been substantiated by data. It is used in the names of a number of principles accepted in the scientific community, such as the Big Bang Theory . Because of the rigors of experimentation and control, it is understood to be more likely to be true than a hypothesis is.

In non-scientific use, however, hypothesis and theory are often used interchangeably to mean simply an idea, speculation, or hunch, with theory being the more common choice.

Since this casual use does away with the distinctions upheld by the scientific community, hypothesis and theory are prone to being wrongly interpreted even when they are encountered in scientific contexts—or at least, contexts that allude to scientific study without making the critical distinction that scientists employ when weighing hypotheses and theories.

The most common occurrence is when theory is interpreted—and sometimes even gleefully seized upon—to mean something having less truth value than other scientific principles. (The word law applies to principles so firmly established that they are almost never questioned, such as the law of gravity.)

This mistake is one of projection: since we use theory in general to mean something lightly speculated, then it's implied that scientists must be talking about the same level of uncertainty when they use theory to refer to their well-tested and reasoned principles.

The distinction has come to the forefront particularly on occasions when the content of science curricula in schools has been challenged—notably, when a school board in Georgia put stickers on textbooks stating that evolution was "a theory, not a fact, regarding the origin of living things." As Kenneth R. Miller, a cell biologist at Brown University, has said , a theory "doesn’t mean a hunch or a guess. A theory is a system of explanations that ties together a whole bunch of facts. It not only explains those facts, but predicts what you ought to find from other observations and experiments.”

While theories are never completely infallible, they form the basis of scientific reasoning because, as Miller said "to the best of our ability, we’ve tested them, and they’ve held up."

proposition
supposition

hypothesis , theory , law mean a formula derived by inference from scientific data that explains a principle operating in nature.

hypothesis implies insufficient evidence to provide more than a tentative explanation.

theory implies a greater range of evidence and greater likelihood of truth.

law implies a statement of order and relation in nature that has been found to be invariable under the same conditions.

Examples of hypothesis in a Sentence

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'hypothesis.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History

Greek, from hypotithenai to put under, suppose, from hypo- + tithenai to put — more at do

1641, in the meaning defined at sense 1a

Phrases Containing hypothesis

counter - hypothesis
nebular hypothesis
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Whorfian hypothesis

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Hypothesis testing involves formulating assumptions about population parameters based on sample statistics and rigorously evaluating these assumptions against empirical evidence. This article sheds light on the significance of hypothesis testing and the critical steps involved in the process.

What is Hypothesis Testing?

Hypothesis testing is a statistical method that is used to make a statistical decision using experimental data. Hypothesis testing is basically an assumption that we make about a population parameter. It evaluates two mutually exclusive statements about a population to determine which statement is best supported by the sample data.

Example: You say an average height in the class is 30 or a boy is taller than a girl. All of these is an assumption that we are assuming, and we need some statistical way to prove these. We need some mathematical conclusion whatever we are assuming is true.

Defining Hypotheses

$\mu$

Key Terms of Hypothesis Testing

$\alpha$

P-value: The P value , or calculated probability, is the probability of finding the observed/extreme results when the null hypothesis(H0) of a study-given problem is true. If your P-value is less than the chosen significance level then you reject the null hypothesis i.e. accept that your sample claims to support the alternative hypothesis.
Test Statistic: The test statistic is a numerical value calculated from sample data during a hypothesis test, used to determine whether to reject the null hypothesis. It is compared to a critical value or p-value to make decisions about the statistical significance of the observed results.
Critical value : The critical value in statistics is a threshold or cutoff point used to determine whether to reject the null hypothesis in a hypothesis test.
Degrees of freedom: Degrees of freedom are associated with the variability or freedom one has in estimating a parameter. The degrees of freedom are related to the sample size and determine the shape.

Why do we use Hypothesis Testing?

Hypothesis testing is an important procedure in statistics. Hypothesis testing evaluates two mutually exclusive population statements to determine which statement is most supported by sample data. When we say that the findings are statistically significant, thanks to hypothesis testing.

One-Tailed and Two-Tailed Test

One tailed test focuses on one direction, either greater than or less than a specified value. We use a one-tailed test when there is a clear directional expectation based on prior knowledge or theory. The critical region is located on only one side of the distribution curve. If the sample falls into this critical region, the null hypothesis is rejected in favor of the alternative hypothesis.

One-Tailed Test

There are two types of one-tailed test:

$\mu \geq 50$

Two-Tailed Test

A two-tailed test considers both directions, greater than and less than a specified value.We use a two-tailed test when there is no specific directional expectation, and want to detect any significant difference.

$\mu =$

What are Type 1 and Type 2 errors in Hypothesis Testing?

In hypothesis testing, Type I and Type II errors are two possible errors that researchers can make when drawing conclusions about a population based on a sample of data. These errors are associated with the decisions made regarding the null hypothesis and the alternative hypothesis.

$\alpha$

How does Hypothesis Testing work?

Step 1: define null and alternative hypothesis.

We first identify the problem about which we want to make an assumption keeping in mind that our assumption should be contradictory to one another, assuming Normally distributed data.

Step 2 – Choose significance level

$\alpha$

Step 3 – Collect and Analyze data.

Gather relevant data through observation or experimentation. Analyze the data using appropriate statistical methods to obtain a test statistic.

Step 4-Calculate Test Statistic

The data for the tests are evaluated in this step we look for various scores based on the characteristics of data. The choice of the test statistic depends on the type of hypothesis test being conducted.

There are various hypothesis tests, each appropriate for various goal to calculate our test. This could be a Z-test , Chi-square , T-test , and so on.

Z-test : If population means and standard deviations are known. Z-statistic is commonly used.
t-test : If population standard deviations are unknown. and sample size is small than t-test statistic is more appropriate.
Chi-square test : Chi-square test is used for categorical data or for testing independence in contingency tables
F-test : F-test is often used in analysis of variance (ANOVA) to compare variances or test the equality of means across multiple groups.

We have a smaller dataset, So, T-test is more appropriate to test our hypothesis.

T-statistic is a measure of the difference between the means of two groups relative to the variability within each group. It is calculated as the difference between the sample means divided by the standard error of the difference. It is also known as the t-value or t-score.

Step 5 – Comparing Test Statistic:

In this stage, we decide where we should accept the null hypothesis or reject the null hypothesis. There are two ways to decide where we should accept or reject the null hypothesis.

Method A: Using Crtical values

Comparing the test statistic and tabulated critical value we have,

If Test Statistic>Critical Value: Reject the null hypothesis.
If Test Statistic≤Critical Value: Fail to reject the null hypothesis.

Note: Critical values are predetermined threshold values that are used to make a decision in hypothesis testing. To determine critical values for hypothesis testing, we typically refer to a statistical distribution table , such as the normal distribution or t-distribution tables based on.

Method B: Using P-values

We can also come to an conclusion using the p-value,

$p\leq\alpha$

Note : The p-value is the probability of obtaining a test statistic as extreme as, or more extreme than, the one observed in the sample, assuming the null hypothesis is true. To determine p-value for hypothesis testing, we typically refer to a statistical distribution table , such as the normal distribution or t-distribution tables based on.

Step 7- Interpret the Results

At last, we can conclude our experiment using method A or B.

Calculating test statistic

To validate our hypothesis about a population parameter we use statistical functions . We use the z-score, p-value, and level of significance(alpha) to make evidence for our hypothesis for normally distributed data .

1. Z-statistics:

When population means and standard deviations are known.

$z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

μ represents the population mean,
σ is the standard deviation
and n is the size of the sample.

2. T-Statistics

T test is used when n<30,

t-statistic calculation is given by:

$t=\frac{x̄-μ}{s/\sqrt{n}}$

t = t-score,
x̄ = sample mean
μ = population mean,
s = standard deviation of the sample,
n = sample size

3. Chi-Square Test

Chi-Square Test for Independence categorical Data (Non-normally distributed) using:

$\chi^2 = \sum \frac{(O_{ij} - E_{ij})^2}{E_{ij}}$

i,j are the rows and columns index respectively.

$E_{ij}$

Real life Hypothesis Testing example

Let’s examine hypothesis testing using two real life situations,

Case A: D oes a New Drug Affect Blood Pressure?

Imagine a pharmaceutical company has developed a new drug that they believe can effectively lower blood pressure in patients with hypertension. Before bringing the drug to market, they need to conduct a study to assess its impact on blood pressure.

Before Treatment: 120, 122, 118, 130, 125, 128, 115, 121, 123, 119
After Treatment: 115, 120, 112, 128, 122, 125, 110, 117, 119, 114

Step 1 : Define the Hypothesis

Null Hypothesis : (H 0 )The new drug has no effect on blood pressure.
Alternate Hypothesis : (H 1 )The new drug has an effect on blood pressure.

Step 2: Define the Significance level

Let’s consider the Significance level at 0.05, indicating rejection of the null hypothesis.

If the evidence suggests less than a 5% chance of observing the results due to random variation.

Step 3 : Compute the test statistic

Using paired T-test analyze the data to obtain a test statistic and a p-value.

The test statistic (e.g., T-statistic) is calculated based on the differences between blood pressure measurements before and after treatment.

t = m/(s/√n)

m = mean of the difference i.e X after, X before
s = standard deviation of the difference (d) i.e d i = X after, i − X before,
n = sample size,

then, m= -3.9, s= 1.8 and n= 10

we, calculate the , T-statistic = -9 based on the formula for paired t test

Step 4: Find the p-value

The calculated t-statistic is -9 and degrees of freedom df = 9, you can find the p-value using statistical software or a t-distribution table.

thus, p-value = 8.538051223166285e-06

Step 5: Result

If the p-value is less than or equal to 0.05, the researchers reject the null hypothesis.
If the p-value is greater than 0.05, they fail to reject the null hypothesis.

Conclusion: Since the p-value (8.538051223166285e-06) is less than the significance level (0.05), the researchers reject the null hypothesis. There is statistically significant evidence that the average blood pressure before and after treatment with the new drug is different.

Python Implementation of Hypothesis Testing

Let’s create hypothesis testing with python, where we are testing whether a new drug affects blood pressure. For this example, we will use a paired T-test. We’ll use the scipy.stats library for the T-test.

Scipy is a mathematical library in Python that is mostly used for mathematical equations and computations.

We will implement our first real life problem via python,

In the above example, given the T-statistic of approximately -9 and an extremely small p-value, the results indicate a strong case to reject the null hypothesis at a significance level of 0.05.

The results suggest that the new drug, treatment, or intervention has a significant effect on lowering blood pressure.
The negative T-statistic indicates that the mean blood pressure after treatment is significantly lower than the assumed population mean before treatment.

Case B : Cholesterol level in a population

Data: A sample of 25 individuals is taken, and their cholesterol levels are measured.

Cholesterol Levels (mg/dL): 205, 198, 210, 190, 215, 205, 200, 192, 198, 205, 198, 202, 208, 200, 205, 198, 205, 210, 192, 205, 198, 205, 210, 192, 205.

Populations Mean = 200

Population Standard Deviation (σ): 5 mg/dL(given for this problem)

Step 1: Define the Hypothesis

Null Hypothesis (H 0 ): The average cholesterol level in a population is 200 mg/dL.
Alternate Hypothesis (H 1 ): The average cholesterol level in a population is different from 200 mg/dL.

As the direction of deviation is not given , we assume a two-tailed test, and based on a normal distribution table, the critical values for a significance level of 0.05 (two-tailed) can be calculated through the z-table and are approximately -1.96 and 1.96.

$(203.8 - 200) / (5 \div \sqrt{25})$

Step 4: Result

Since the absolute value of the test statistic (2.04) is greater than the critical value (1.96), we reject the null hypothesis. And conclude that, there is statistically significant evidence that the average cholesterol level in the population is different from 200 mg/dL

Limitations of Hypothesis Testing

Although a useful technique, hypothesis testing does not offer a comprehensive grasp of the topic being studied. Without fully reflecting the intricacy or whole context of the phenomena, it concentrates on certain hypotheses and statistical significance.
The accuracy of hypothesis testing results is contingent on the quality of available data and the appropriateness of statistical methods used. Inaccurate data or poorly formulated hypotheses can lead to incorrect conclusions.
Relying solely on hypothesis testing may cause analysts to overlook significant patterns or relationships in the data that are not captured by the specific hypotheses being tested. This limitation underscores the importance of complimenting hypothesis testing with other analytical approaches.

Hypothesis testing stands as a cornerstone in statistical analysis, enabling data scientists to navigate uncertainties and draw credible inferences from sample data. By systematically defining null and alternative hypotheses, choosing significance levels, and leveraging statistical tests, researchers can assess the validity of their assumptions. The article also elucidates the critical distinction between Type I and Type II errors, providing a comprehensive understanding of the nuanced decision-making process inherent in hypothesis testing. The real-life example of testing a new drug’s effect on blood pressure using a paired T-test showcases the practical application of these principles, underscoring the importance of statistical rigor in data-driven decision-making.

Frequently Asked Questions (FAQs)

1. what are the 3 types of hypothesis test.

There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed. Right-tailed tests assess if a parameter is greater, left-tailed if lesser. Two-tailed tests check for non-directional differences, greater or lesser.

2.What are the 4 components of hypothesis testing?

Null Hypothesis ( ): No effect or difference exists. Alternative Hypothesis ( ): An effect or difference exists. Significance Level ( ): Risk of rejecting null hypothesis when it’s true (Type I error). Test Statistic: Numerical value representing observed evidence against null hypothesis.

3.What is hypothesis testing in ML?

Statistical method to evaluate the performance and validity of machine learning models. Tests specific hypotheses about model behavior, like whether features influence predictions or if a model generalizes well to unseen data.

4.What is the difference between Pytest and hypothesis in Python?

Pytest purposes general testing framework for Python code while Hypothesis is a Property-based testing framework for Python, focusing on generating test cases based on specified properties of the code.

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Hypothetical Learning Trajectories in Mathematics Education

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CCSSO/NGA (2010) Common core state standards for mathematics. Council of Chief State School Officers and the National Governors Association Center for Best Practices, Washington, DC. http://corestandards.org

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Simon, M. (2014). Hypothetical Learning Trajectories in Mathematics Education. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4978-8_72

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The Acquisition-Learning Hypothesis: Definition and Criticism

January 19, 2018, 8:00 am

Linguist and educator Stephen Krashen proposed the Monitor Model, his theory of second language acquisition, in Principles and practice in second language acquisition published in 1982. Influenced by the theory of first language acquisition proposed by Noam Chomsky, the Monitor Model posits five hypotheses about second language acquisition and learning:

Acquisition-learning hypothesis
Natural order hypothesis
Monitor hypothesis
Input hypothesis
Affective filter hypothesis

The following sections offer a description of the first hypothesis of the Monitor Model, the acquisition-learning hypothesis, as well as the major criticism surrounding the hypothesis.

Definition of the Acquisition-Learning Hypothesis

The first hypothesis of Krashen’s Monitor Model, the acquisition-learning hypothesis, distinguishes between the processes of language acquisition and language learning. Krashen contrasts acquisition and learning as two distinct and separate language processes. Acquisition occurs passively and unconsciously through implicit, informal, or natural learning, resulting in implicit knowledge and acquired competence of a language; in other words, to acquire a language is to “pick up” a language by relying on “feelings” of correctness rather than conscious knowledge of language rules.

In contrast to acquisition, learning occurs actively and consciously through explicit or formal learning and instruction, resulting in explicit knowledge about a language; learning results in metalinguistic knowledge and awareness. Furthermore, the acquisition-learning hypothesis states that both children and adults acquire language via access to an innate language acquisition device (LAD) regardless of age as well as that learning cannot become acquisition. The most important pedagogical implication of the first hypothesis of the Monitor Model is that explicit teaching and learning is unnecessary, indeed inadequate, for second language acquisition.

Criticism of the Acquisition-Learning Hypothesis

The first critique of Krashen’s Monitor Model is that the hypothesized distinction between acquisition and learning as posited by the acquisition-learning hypothesis, or, more specifically, determining whether the process involved in language production resulted from implicit acquisition or explicit learning, is impossible to prove. As Barry McLaughlin offers as anecdotal evidence, he feels that the German * Ich habe nicht das Kind gesehen “I have not seen the children” is incorrect based on intuition but also knows that the utterance is incorrect based on his knowledge of the rules of German grammar.

Furthermore, critics consider the argument that learning cannot become acquisition questionable. Kevin R. Gregg offers anecdotal evidence of his personal experience learning a second language as counterevidence to the clear division between acquisition and learning: He initially consciously learned the conjugations of Japanese verbs through rote memorization, which ultimately led to unconscious acquisition. In his case, learning became acquisition. Both examples of personal experience with a second language illustrate the problem with stringently distinguishing the process of language acquisition from the process of language learning. Thus, the claim that acquisition is distinct from learning fails to withstand evidence-based criticism

Although influential within the field of second language acquisition over the past few decades, the Monitor Model is not without criticism as illustrated by the major critiques of the learning-acquisition hypothesis.

Gregg, Kevin R. 1984. Krashen’s monitor and Occam’s razor. Applied Linguistics 5(2). 79-100. Krashen, Stephen D. 1982. Principles and practice in second language acquisition . Oxford: Pergamon. Krashen, Stephen D. 2009. Principles and practice in second language acquisition , 1st internet edn. Oxford: Pergamon. http://www.sdkrashen.com/Principles_and_Practice/Principles_and_Practice.pdf. Lightbrown, Patsy M. & Nina Spada. 2006. How languages are learned , 3rd edn. Oxford: Oxford University Press. McLaughlin, Barry. 1978. The monitor model: Some methodological considerations. Language Learning 28(2). 309-332. Zafar, Manmay. 2009. Monitoring the ‘monitor’: A critique of Krashen’s five hypotheses. Dhaka University Journal of Linguistics 2(4). 139-146.

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8.1: The Elements of Hypothesis Testing

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Learning Objectives

To understand the logical framework of tests of hypotheses.
To learn basic terminology connected with hypothesis testing.
To learn fundamental facts about hypothesis testing.

Types of Hypotheses

A hypothesis about the value of a population parameter is an assertion about its value. As in the introductory example we will be concerned with testing the truth of two competing hypotheses, only one of which can be true.

Definition: null hypothesis and alternative hypothesis

The null hypothesis , denoted $H_0$, is the statement about the population parameter that is assumed to be true unless there is convincing evidence to the contrary.
The alternative hypothesis , denoted $H_a$, is a statement about the population parameter that is contradictory to the null hypothesis, and is accepted as true only if there is convincing evidence in favor of it.

Definition: statistical procedure

Hypothesis testing is a statistical procedure in which a choice is made between a null hypothesis and an alternative hypothesis based on information in a sample.

The end result of a hypotheses testing procedure is a choice of one of the following two possible conclusions:

Reject $H_0$ (and therefore accept $H_a$), or
Fail to reject $H_0$ (and therefore fail to accept $H_a$).

The null hypothesis typically represents the status quo, or what has historically been true. In the example of the respirators, we would believe the claim of the manufacturer unless there is reason not to do so, so the null hypotheses is $H_0:\mu =75$. The alternative hypothesis in the example is the contradictory statement $H_a:\mu <75$. The null hypothesis will always be an assertion containing an equals sign, but depending on the situation the alternative hypothesis can have any one of three forms: with the symbol $<$, as in the example just discussed, with the symbol $>$, or with the symbol $\neq$. The following two examples illustrate the latter two cases.

Example $\PageIndex{1}$

A publisher of college textbooks claims that the average price of all hardbound college textbooks is $\$127.50$. A student group believes that the actual mean is higher and wishes to test their belief. State the relevant null and alternative hypotheses.

The default option is to accept the publisher’s claim unless there is compelling evidence to the contrary. Thus the null hypothesis is $H_0:\mu =127.50$. Since the student group thinks that the average textbook price is greater than the publisher’s figure, the alternative hypothesis in this situation is $H_a:\mu >127.50$.

Example $\PageIndex{2}$

The recipe for a bakery item is designed to result in a product that contains $8$ grams of fat per serving. The quality control department samples the product periodically to insure that the production process is working as designed. State the relevant null and alternative hypotheses.

The default option is to assume that the product contains the amount of fat it was formulated to contain unless there is compelling evidence to the contrary. Thus the null hypothesis is $H_0:\mu =8.0$. Since to contain either more fat than desired or to contain less fat than desired are both an indication of a faulty production process, the alternative hypothesis in this situation is that the mean is different from $8.0$, so $H_a:\mu \neq 8.0$.

In Example $\PageIndex{1}$, the textbook example, it might seem more natural that the publisher’s claim be that the average price is at most $\$127.50$, not exactly $\$127.50$. If the claim were made this way, then the null hypothesis would be $H_0:\mu \leq 127.50$, and the value $\$127.50$ given in the example would be the one that is least favorable to the publisher’s claim, the null hypothesis. It is always true that if the null hypothesis is retained for its least favorable value, then it is retained for every other value.

Thus in order to make the null and alternative hypotheses easy for the student to distinguish, in every example and problem in this text we will always present one of the two competing claims about the value of a parameter with an equality. The claim expressed with an equality is the null hypothesis. This is the same as always stating the null hypothesis in the least favorable light. So in the introductory example about the respirators, we stated the manufacturer’s claim as “the average is $75$ minutes” instead of the perhaps more natural “the average is at least $75$ minutes,” essentially reducing the presentation of the null hypothesis to its worst case.

The first step in hypothesis testing is to identify the null and alternative hypotheses.

The Logic of Hypothesis Testing

Although we will study hypothesis testing in situations other than for a single population mean (for example, for a population proportion instead of a mean or in comparing the means of two different populations), in this section the discussion will always be given in terms of a single population mean $\mu$.

The null hypothesis always has the form $H_0:\mu =\mu _0$ for a specific number $\mu _0$ (in the respirator example $\mu _0=75$, in the textbook example $\mu _0=127.50$, and in the baked goods example $\mu _0=8.0$). Since the null hypothesis is accepted unless there is strong evidence to the contrary, the test procedure is based on the initial assumption that $H_0$ is true. This point is so important that we will repeat it in a display:

The test procedure is based on the initial assumption that $H_0$ is true.

The criterion for judging between $H_0$ and $H_a$ based on the sample data is: if the value of $\overline{X}$ would be highly unlikely to occur if $H_0$ were true, but favors the truth of $H_a$, then we reject $H_0$ in favor of $H_a$. Otherwise we do not reject $H_0$.

Supposing for now that $\overline{X}$ follows a normal distribution, when the null hypothesis is true the density function for the sample mean $\overline{X}$ must be as in Figure $\PageIndex{1}$: a bell curve centered at $\mu _0$. Thus if $H_0$ is true then $\overline{X}$ is likely to take a value near $\mu _0$ and is unlikely to take values far away. Our decision procedure therefore reduces simply to:

if $H_a$ has the form $H_a:\mu <\mu _0$ then reject $H_0$ if $\bar{x}$ is far to the left of $\mu _0$;
if $H_a$ has the form $H_a:\mu >\mu _0$ then reject $H_0$ if $\bar{x}$ is far to the right of $\mu _0$;
if $H_a$ has the form $H_a:\mu \neq \mu _0$ then reject $H_0$ if $\bar{x}$ is far away from $\mu _0$ in either direction.

Think of the respirator example, for which the null hypothesis is $H_0:\mu =75$, the claim that the average time air is delivered for all respirators is $75$ minutes. If the sample mean is $75$ or greater then we certainly would not reject $H_0$ (since there is no issue with an emergency respirator delivering air even longer than claimed).

If the sample mean is slightly less than $75$ then we would logically attribute the difference to sampling error and also not reject $H_0$ either.

Values of the sample mean that are smaller and smaller are less and less likely to come from a population for which the population mean is $75$. Thus if the sample mean is far less than $75$, say around $60$ minutes or less, then we would certainly reject $H_0$, because we know that it is highly unlikely that the average of a sample would be so low if the population mean were $75$. This is the rare event criterion for rejection: what we actually observed $(\overline{X}<60)$ would be so rare an event if $\mu =75$ were true that we regard it as much more likely that the alternative hypothesis $\mu <75$ holds.

In summary, to decide between $H_0$ and $H_a$ in this example we would select a “rejection region” of values sufficiently far to the left of $75$, based on the rare event criterion, and reject $H_0$ if the sample mean $\overline{X}$ lies in the rejection region, but not reject $H_0$ if it does not.

The Rejection Region

Each different form of the alternative hypothesis Ha has its own kind of rejection region:

if (as in the respirator example) $H_a$ has the form $H_a:\mu <\mu _0$, we reject $H_0$ if $\bar{x}$ is far to the left of $\mu _0$, that is, to the left of some number $C$, so the rejection region has the form of an interval $(-\infty ,C]$;
if (as in the textbook example) $H_a$ has the form $H_a:\mu >\mu _0$, we reject $H_0$ if $\bar{x}$ is far to the right of $\mu _0$, that is, to the right of some number $C$, so the rejection region has the form of an interval $[C,\infty )$;
if (as in the baked good example) $H_a$ has the form $H_a:\mu \neq \mu _0$, we reject $H_0$ if $\bar{x}$ is far away from $\mu _0$ in either direction, that is, either to the left of some number $C$ or to the right of some other number $C′$, so the rejection region has the form of the union of two intervals $(-\infty ,C]\cup [C',\infty )$.

The key issue in our line of reasoning is the question of how to determine the number $C$ or numbers $C$ and $C′$, called the critical value or critical values of the statistic, that determine the rejection region.

Definition: critical values

The critical value or critical values of a test of hypotheses are the number or numbers that determine the rejection region.

Suppose the rejection region is a single interval, so we need to select a single number $C$. Here is the procedure for doing so. We select a small probability, denoted $\alpha$, say $1\%$, which we take as our definition of “rare event:” an event is “rare” if its probability of occurrence is less than $\alpha$. (In all the examples and problems in this text the value of $\alpha$ will be given already.) The probability that $\overline{X}$ takes a value in an interval is the area under its density curve and above that interval, so as shown in Figure $\PageIndex{2}$ (drawn under the assumption that $H_0$ is true, so that the curve centers at $\mu _0$) the critical value $C$ is the value of $\overline{X}$ that cuts off a tail area $\alpha$ in the probability density curve of $\overline{X}$. When the rejection region is in two pieces, that is, composed of two intervals, the total area above both of them must be $\alpha$, so the area above each one is $\alpha /2$, as also shown in Figure $\PageIndex{2}$.

The number $\alpha$ is the total area of a tail or a pair of tails.

Example $\PageIndex{3}$

In the context of Example $\PageIndex{2}$, suppose that it is known that the population is normally distributed with standard deviation $\alpha =0.15$ gram, and suppose that the test of hypotheses $H_0:\mu =8.0$ versus $H_a:\mu \neq 8.0$ will be performed with a sample of size $5$. Construct the rejection region for the test for the choice $\alpha =0.10$. Explain the decision procedure and interpret it.

If $H_0$ is true then the sample mean $\overline{X}$ is normally distributed with mean and standard deviation

\[\begin{align} \mu _{\overline{X}} &=\mu \nonumber \\[5pt] &=8.0 \nonumber \end{align} \nonumber \]

\[\begin{align} \sigma _{\overline{X}}&=\dfrac{\sigma}{\sqrt{n}} \nonumber \\[5pt] &= \dfrac{0.15}{\sqrt{5}} \nonumber\\[5pt] &=0.067 \nonumber \end{align} \nonumber \]

Since $H_a$ contains the $\neq$ symbol the rejection region will be in two pieces, each one corresponding to a tail of area $\alpha /2=0.10/2=0.05$. From Figure 7.1.6, $z_{0.05}=1.645$, so $C$ and $C′$ are $1.645$ standard deviations of $\overline{X}$ to the right and left of its mean $8.0$:

\[C=8.0-(1.645)(0.067) = 7.89 \; \; \text{and}\; \; C'=8.0 + (1.645)(0.067) = 8.11 \nonumber \]

The result is shown in Figure $\PageIndex{3}$. α = 0.1

The decision procedure is: take a sample of size $5$ and compute the sample mean $\bar{x}$. If $\bar{x}$ is either $7.89$ grams or less or $8.11$ grams or more then reject the hypothesis that the average amount of fat in all servings of the product is $8.0$ grams in favor of the alternative that it is different from $8.0$ grams. Otherwise do not reject the hypothesis that the average amount is $8.0$ grams.

The reasoning is that if the true average amount of fat per serving were $8.0$ grams then there would be less than a $10\%$ chance that a sample of size $5$ would produce a mean of either $7.89$ grams or less or $8.11$ grams or more. Hence if that happened it would be more likely that the value $8.0$ is incorrect (always assuming that the population standard deviation is $0.15$ gram).

Because the rejection regions are computed based on areas in tails of distributions, as shown in Figure $\PageIndex{2}$, hypothesis tests are classified according to the form of the alternative hypothesis in the following way.

Definitions: Test classifications

If $H_a$ has the form $\mu \neq \mu _0$ the test is called a two-tailed test .
If $H_a$ has the form $\mu < \mu _0$ the test is called a left-tailed test .
If $H_a$ has the form $\mu > \mu _0$the test is called a right-tailed test .

Each of the last two forms is also called a one-tailed test .

Two Types of Errors

The format of the testing procedure in general terms is to take a sample and use the information it contains to come to a decision about the two hypotheses. As stated before our decision will always be either

reject the null hypothesis $H_0$ in favor of the alternative $H_a$ presented, or
do not reject the null hypothesis $H_0$ in favor of the alternative $H_0$ presented.

There are four possible outcomes of hypothesis testing procedure, as shown in the following table:

As the table shows, there are two ways to be right and two ways to be wrong. Typically to reject $H_0$ when it is actually true is a more serious error than to fail to reject it when it is false, so the former error is labeled “ Type I ” and the latter error “ Type II ”.

Definition: Type I and Type II errors

In a test of hypotheses:

A Type I error is the decision to reject $H_0$ when it is in fact true.
A Type II error is the decision not to reject $H_0$ when it is in fact not true.

Unless we perform a census we do not have certain knowledge, so we do not know whether our decision matches the true state of nature or if we have made an error. We reject $H_0$ if what we observe would be a “rare” event if $H_0$ were true. But rare events are not impossible: they occur with probability $\alpha$. Thus when $H_0$ is true, a rare event will be observed in the proportion $\alpha$ of repeated similar tests, and $H_0$ will be erroneously rejected in those tests. Thus $\alpha$ is the probability that in following the testing procedure to decide between $H_0$ and $H_a$ we will make a Type I error.

Definition: level of significance

The number $\alpha$ that is used to determine the rejection region is called the level of significance of the test. It is the probability that the test procedure will result in a Type I error .

The probability of making a Type II error is too complicated to discuss in a beginning text, so we will say no more about it than this: for a fixed sample size, choosing $alpha$ smaller in order to reduce the chance of making a Type I error has the effect of increasing the chance of making a Type II error . The only way to simultaneously reduce the chances of making either kind of error is to increase the sample size.

Standardizing the Test Statistic

Hypotheses testing will be considered in a number of contexts, and great unification as well as simplification results when the relevant sample statistic is standardized by subtracting its mean from it and then dividing by its standard deviation. The resulting statistic is called a standardized test statistic . In every situation treated in this and the following two chapters the standardized test statistic will have either the standard normal distribution or Student’s $t$-distribution.

Definition: hypothesis test

A standardized test statistic for a hypothesis test is the statistic that is formed by subtracting from the statistic of interest its mean and dividing by its standard deviation.

For example, reviewing Example $\PageIndex{3}$, if instead of working with the sample mean $\overline{X}$ we instead work with the test statistic

\[\frac{\overline{X}-8.0}{0.067} \nonumber \]

then the distribution involved is standard normal and the critical values are just $\pm z_{0.05}$. The extra work that was done to find that $C=7.89$ and $C′=8.11$ is eliminated. In every hypothesis test in this book the standardized test statistic will be governed by either the standard normal distribution or Student’s $t$-distribution. Information about rejection regions is summarized in the following tables:

Every instance of hypothesis testing discussed in this and the following two chapters will have a rejection region like one of the six forms tabulated in the tables above.

No matter what the context a test of hypotheses can always be performed by applying the following systematic procedure, which will be illustrated in the examples in the succeeding sections.

Systematic Hypothesis Testing Procedure: Critical Value Approach

Identify the null and alternative hypotheses.
Identify the relevant test statistic and its distribution.
Compute from the data the value of the test statistic.
Construct the rejection region.
Compare the value computed in Step 3 to the rejection region constructed in Step 4 and make a decision. Formulate the decision in the context of the problem, if applicable.

The procedure that we have outlined in this section is called the “Critical Value Approach” to hypothesis testing to distinguish it from an alternative but equivalent approach that will be introduced at the end of Section 8.3.

Key Takeaway

A test of hypotheses is a statistical process for deciding between two competing assertions about a population parameter.
The testing procedure is formalized in a five-step procedure.

Scientific Methods

What is Hypothesis?

We have heard of many hypotheses which have led to great inventions in science. Assumptions that are made on the basis of some evidence are known as hypotheses. In this article, let us learn in detail about the hypothesis and the type of hypothesis with examples.

A hypothesis is an assumption that is made based on some evidence. This is the initial point of any investigation that translates the research questions into predictions. It includes components like variables, population and the relation between the variables. A research hypothesis is a hypothesis that is used to test the relationship between two or more variables.

Characteristics of Hypothesis

Following are the characteristics of the hypothesis:

The hypothesis should be clear and precise to consider it to be reliable.
If the hypothesis is a relational hypothesis, then it should be stating the relationship between variables.
The hypothesis must be specific and should have scope for conducting more tests.
The way of explanation of the hypothesis must be very simple and it should also be understood that the simplicity of the hypothesis is not related to its significance.

Sources of Hypothesis

Following are the sources of hypothesis:

The resemblance between the phenomenon.
Observations from past studies, present-day experiences and from the competitors.
Scientific theories.
General patterns that influence the thinking process of people.

Types of Hypothesis

There are six forms of hypothesis and they are:

Simple hypothesis
Complex hypothesis
Directional hypothesis
Non-directional hypothesis
Null hypothesis
Associative and casual hypothesis

Simple Hypothesis

It shows a relationship between one dependent variable and a single independent variable. For example – If you eat more vegetables, you will lose weight faster. Here, eating more vegetables is an independent variable, while losing weight is the dependent variable.

Complex Hypothesis

It shows the relationship between two or more dependent variables and two or more independent variables. Eating more vegetables and fruits leads to weight loss, glowing skin, and reduces the risk of many diseases such as heart disease.

Directional Hypothesis

It shows how a researcher is intellectual and committed to a particular outcome. The relationship between the variables can also predict its nature. For example- children aged four years eating proper food over a five-year period are having higher IQ levels than children not having a proper meal. This shows the effect and direction of the effect.

Non-directional Hypothesis

It is used when there is no theory involved. It is a statement that a relationship exists between two variables, without predicting the exact nature (direction) of the relationship.

Null Hypothesis

It provides a statement which is contrary to the hypothesis. It’s a negative statement, and there is no relationship between independent and dependent variables. The symbol is denoted by “H O ”.

Associative and Causal Hypothesis

Associative hypothesis occurs when there is a change in one variable resulting in a change in the other variable. Whereas, the causal hypothesis proposes a cause and effect interaction between two or more variables.

Examples of Hypothesis

Following are the examples of hypotheses based on their types:

Consumption of sugary drinks every day leads to obesity is an example of a simple hypothesis.
All lilies have the same number of petals is an example of a null hypothesis.
If a person gets 7 hours of sleep, then he will feel less fatigue than if he sleeps less. It is an example of a directional hypothesis.

Functions of Hypothesis

Following are the functions performed by the hypothesis:

Hypothesis helps in making an observation and experiments possible.
It becomes the start point for the investigation.
Hypothesis helps in verifying the observations.
It helps in directing the inquiries in the right direction.

How will Hypothesis help in the Scientific Method?

Researchers use hypotheses to put down their thoughts directing how the experiment would take place. Following are the steps that are involved in the scientific method:

Formation of question
Doing background research
Creation of hypothesis
Designing an experiment
Collection of data
Result analysis
Summarizing the experiment
Communicating the results

Frequently Asked Questions – FAQs

What is hypothesis.

A hypothesis is an assumption made based on some evidence.

Give an example of simple hypothesis?

What are the types of hypothesis.

Types of hypothesis are:

Associative and Casual hypothesis

State true or false: Hypothesis is the initial point of any investigation that translates the research questions into a prediction.

Define complex hypothesis..

A complex hypothesis shows the relationship between two or more dependent variables and two or more independent variables.

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Meaning of hypothesis in English

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abstraction
afterthought
anthropocentrism
anti-Darwinian
exceptionalism
foundation stone
great minds think alike idiom
non-dogmatic
non-empirical
non-material
non-practical
social Darwinism
supersensible
the domino theory

hypothesis | American Dictionary

Hypothesis | business english, examples of hypothesis, translations of hypothesis.

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have irons in the fire

to be involved with many activities or jobs at the same time or to make certain that there are always several possibilities available

Binding, nailing, and gluing: talking about fastening things together

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Statistics > Machine Learning

Title: extending mean-field variational inference via entropic regularization: theory and computation.

Abstract: Variational inference (VI) has emerged as a popular method for approximate inference for high-dimensional Bayesian models. In this paper, we propose a novel VI method that extends the naive mean field via entropic regularization, referred to as $\Xi$-variational inference ($\Xi$-VI). $\Xi$-VI has a close connection to the entropic optimal transport problem and benefits from the computationally efficient Sinkhorn algorithm. We show that $\Xi$-variational posteriors effectively recover the true posterior dependency, where the dependence is downweighted by the regularization parameter. We analyze the role of dimensionality of the parameter space on the accuracy of $\Xi$-variational approximation and how it affects computational considerations, providing a rough characterization of the statistical-computational trade-off in $\Xi$-VI. We also investigate the frequentist properties of $\Xi$-VI and establish results on consistency, asymptotic normality, high-dimensional asymptotics, and algorithmic stability. We provide sufficient criteria for achieving polynomial-time approximate inference using the method. Finally, we demonstrate the practical advantage of $\Xi$-VI over mean-field variational inference on simulated and real data.

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6 Common Leadership Styles — and How to Decide Which to Use When

Rebecca Knight

Being a great leader means recognizing that different circumstances call for different approaches.

Research suggests that the most effective leaders adapt their style to different circumstances — be it a change in setting, a shift in organizational dynamics, or a turn in the business cycle. But what if you feel like you’re not equipped to take on a new and different leadership style — let alone more than one? In this article, the author outlines the six leadership styles Daniel Goleman first introduced in his 2000 HBR article, “Leadership That Gets Results,” and explains when to use each one. The good news is that personality is not destiny. Even if you’re naturally introverted or you tend to be driven by data and analysis rather than emotion, you can still learn how to adapt different leadership styles to organize, motivate, and direct your team.

Much has been written about common leadership styles and how to identify the right style for you, whether it’s transactional or transformational, bureaucratic or laissez-faire. But according to Daniel Goleman, a psychologist best known for his work on emotional intelligence, “Being a great leader means recognizing that different circumstances may call for different approaches.”

RK Rebecca Knight is a journalist who writes about all things related to the changing nature of careers and the workplace. Her essays and reported stories have been featured in The Boston Globe, Business Insider, The New York Times, BBC, and The Christian Science Monitor. She was shortlisted as a Reuters Institute Fellow at Oxford University in 2023. Earlier in her career, she spent a decade as an editor and reporter at the Financial Times in New York, London, and Boston.

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What's The Real Meaning Of Fortnight By Taylor Swift & Post Malone? Here's Our Theory

Ahead of its release, Swifties noticed some subtle Joe Alwyn shade in the tracklist for "The Tortured Poets Department," but is "Fortnight," Taylor Swift's lead single featuring Post Malone, about the actor? It would be ironic if this were the case as a fortnight is a period of two weeks and her relationship with Alwyn was her longest.

The biggest hint that the song is about someone else is the lyric, "I touched you for only a fortnight." This indicates that Swift is singing about a fleeting romance. Before this major clue, Swift reveals that she's been feeling blue with references to the worst day of the week and month of the year. "All my mornings are Monday stuck in an endless February," she sings in a breathy voice over a hypnotic, dreamy track that's evocative of the Cyndi Lauper classic "Time After Time." Swift seemingly reveals that her short-lived romance is the result of trying to pull herself out of a sorrowful state. It's a hair-of-the-dog situation, as the cause of her woe is also her remedy. "I took the miracle move on drug, the effects were temporary," she confesses. So, the guy she's most likely repeating the cycle of heartbreak with is her rumored ex-boyfriend Matt Healy . Swift's purported relationship with The 1975's lead singer was brief, but a source told The Sun that what they had was "something electric." Interestingly, there's some electricity used in the teaser footage for the "Fortnight" music video.

Taylor Swift looks the part of a tortured Victorian-era poet

Taylor Swift opens "Fortnight" by singing, "I was s'posed to be sent away / But they forgot to come and get me." The striking black-and-white imagery in her "Fortnight" music video teaser makes it obvious that she's referencing being institutionalized, but it seems she wasn't forgotten in the video; she's shown strapped into an electroshock therapy machine like those that were once used on asylum patients. Swift clearly wants fans to focus on the lyric, "I love you, it's ruining my life," as it's repeated over and over again on a typewriter a la "The Shining." Could these words refer to Matt Healy's sketchy past and the backlash from Swifties disappointed in their idol for seemingly falling for someone like him?

View this post on Instagram A post shared by Taylor Swift (@taylorswift)

In the teaser, Swift is dressed in a Victorian-era mourning gown, which is a reminder of the tortured, Victorian-era poet that she's distantly related to : Emily Dickinson. Another scene shows her with thin eyebrows like those sported by silent film stars. Another track on "The Tortured Poets Department" shares its name with one of these actors, "Clara Bow." The tragic "It Girl" of her era was once institutionalized . Swifties have also pointed out similarities between the video and the movie "Poor Things," which stars Swift's good friend Emma Stone . They can look for more Easter eggs and hidden messages when the full music video drops on April 19 at 8 p.m. ET.

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Mystery Taylor Swift Mural Appears in Chicago Featuring 'Error 321' Easter Egg: What Does It Mean?

The pop superstar will release her 11th studio album 'The Tortured Poets Department' on Friday, April 19

James Devaney/GC Images

With Taylor Swift 's new album The Tortured Poets Department coming out soon, it's time for Swifties to put on their sleuthing caps and decode some Easter eggs .

Several days before the Friday, April 19 release of the pop superstar's 11th studio album, mysterious murals have begun popping up in Chicago that include repetition of the text "TTPD" and "13." Fans were quick to recognize the nods to the puzzle-loving singer, 34, and took photos of the visuals, which they shared on social media .

According to viral posts from fans, the murals include a QR code, which links to a YouTube Short on Swift's official YouTube that includes the text "Error 321" as it's spelled out in a typewriter-like font, as well as the number 13 beneath it.

Swifties may remember that "Error 321" first appeared just before the singer-songwriter announced The Tortured Poets Department at the 2024 Grammys in February.

Moments before she revealed a new album was on the way while accepting the gramophone for best pop vocal album , her website went dark to include the error code and the text "hneriergrd," which fans discovered was an anagram for "red herring."

Although it's yet to be confirmed what the significance of "Error 321" is, it often indicates an error in communication across telephone lines, fax machines, etcetera.

As the release of The Tortured Poets Department approaches, Swift has teased the effort with a handful of Easter eggs, including a countdown clock that launched with her favorite number, 13 , and posts on social media featuring snippets of lyrics.

During the total solar eclipse on Monday, April 8, she posted a clip on her Instagram Stories featuring the line, "Crowd goes wild at her fingertips/Half moonshine, Full eclipse," and a link to pre-order her new record.

Fans have speculated that the LP will largely be about heartbreak, as it comes nearly a year following her break-up with her former boyfriend of six years, Joe Alywn .

The "Karma" singer also recently curated a set of playlists for Apple Music featuring songs from throughout her discography as they're broken into the "five stages of heartbreak:" denial, anger, bargaining, depression and acceptance.

Frazer Harrison/Getty

Shortly after the hitmaker announced her follow-up to 2022's Midnights was on the way, she unveiled the tracklist on Instagram .

The Tortured Poets Department is set to include 16 songs, with additional tracks on various deluxe versions. It'll also feature appearances from two special guests: Florence and the Machine and Post Malone .

Never miss a story — sign up for PEOPLE's free daily newsletter to stay up-to-date on the best of what PEOPLE has to offer, from celebrity news to compelling human interest stories.

Swift's frequent collaborator Jack Antonoff is said to have worked with her on much of the album, and it seems as though another one of her recurrent producers, Aaron Dessner , also contributed to the project.

When the "Cruel Summer" singer teased additional lyrics and a limited edition vinyl pressing of the LP, it appeared as though most of his name could be seen on an image of the physical copy at the pre-order link.

The Tortured Poets Department is due out on Friday, April 19.

COMMENTS

What is a Hypothesis in Machine Learning?
A hypothesis is an explanation for something. It is a provisional idea, an educated guess that requires some evaluation. A good hypothesis is testable; it can be either true or false. In science, a hypothesis must be falsifiable, meaning that there exists a test whose outcome could mean that the hypothesis is not true.
Hypothesis in Machine Learning
A hypothesis is a function that best describes the target in supervised machine learning. The hypothesis that an algorithm would come up depends upon the data and also depends upon the restrictions and bias that we have imposed on the data. The Hypothesis can be calculated as: Where, y = range. m = slope of the lines. x = domain.
Learning Theories
Learning is the change in the behavior of an organism that is a result of prior experience.[1] Learning theory seeks to explain how individuals acquire, process, retain, and recall knowledge during the process of learning. Environmental, cognitive, and emotional influences, along with prior experiences, play a vital role in comprehending, acquiring, and retaining skills or knowledge.
Hypothesis: Definition, Examples, and Types
A hypothesis is a tentative statement about the relationship between two or more variables. It is a specific, testable prediction about what you expect to happen in a study. It is a preliminary answer to your question that helps guide the research process. Consider a study designed to examine the relationship between sleep deprivation and test ...
What is hypothesis in Machine Learning?
In machine learning, a hypothesis is a mathematical function or model that converts input data into output predictions. The model's first belief or explanation is based on the facts supplied. The hypothesis is typically expressed as a collection of parameters characterizing the behavior of the model. If we're building a model to predict the ...
Hypothesis Testing
Based on your analysis, you decide whether to reject the null hypothesis in favor of the alternative, or fail to reject / Accept the null hypothesis. The significance level, often denoted by $α$, represents the probability of rejecting the null hypothesis when it is actually true.
What is a Hypothesis
Definition: Hypothesis is an educated guess or proposed explanation for a phenomenon, based on some initial observations or data. It is a tentative statement that can be tested and potentially proven or disproven through further investigation and experimentation. Hypothesis is often used in scientific research to guide the design of experiments ...
How to Write a Strong Hypothesis
5. Phrase your hypothesis in three ways. To identify the variables, you can write a simple prediction in if…then form. The first part of the sentence states the independent variable and the second part states the dependent variable. If a first-year student starts attending more lectures, then their exam scores will improve.
Hypothesis Testing in Machine Learning
Alternate hypothesis: Contrary to the null hypothesis, it shows that observation is the result of real effect. P value. It can also be said as evidence or level of significance for the null hypothesis or in machine learning algorithms. It's the significance of the predictors towards the target.
Learning theory
learning theory, any of the proposals put forth to explain changes in behaviour produced by practice, as opposed to other factors, e.g., physiological development. A common goal in defining any psychological concept is a statement that corresponds to common usage. Acceptance of that aim, however, entails some peril.
Learning Theories: Understanding How People Learn
Learning is the change in knowledge, behavior, or understanding that occurs when people make connections between new information and their existing knowledge. Various theories attempt to describe the factors that enable the learning process. Learning does not happen in the same way or at the same time for all students.
What Is a Hypothesis? The Scientific Method
A hypothesis (plural hypotheses) is a proposed explanation for an observation. The definition depends on the subject. In science, a hypothesis is part of the scientific method. It is a prediction or explanation that is tested by an experiment. Observations and experiments may disprove a scientific hypothesis, but can never entirely prove one.
Hypothesis Definition & Meaning
hypothesis: [noun] an assumption or concession made for the sake of argument. an interpretation of a practical situation or condition taken as the ground for action.
Hypothesis in Machine Learning
The hypothesis is one of the commonly used concepts of statistics in Machine Learning. It is specifically used in Supervised Machine learning, where an ML model learns a function that best maps the input to corresponding outputs with the help of an available dataset. In supervised learning techniques, the main aim is to determine the possible ...
HYPOTHESIS
HYPOTHESIS meaning: 1. an idea or explanation for something that is based on known facts but has not yet been proved…. Learn more.
What is Hypothesis
Hypothesis Meaning. A hypothesis is a proposed statement that is testable and is given for something that happens or observed. It is made using what we already know and have seen, and it's the basis for scientific research. ... Having more kids go to early learning classes helps them do better in school when they get older.
Understanding Hypothesis Testing
Hypothesis testing is a statistical method that is used to make a statistical decision using experimental data. Hypothesis testing is basically an assumption that we make about a population parameter. It evaluates two mutually exclusive statements about a population to determine which statement is best supported by the sample data.
Hypothetical Learning Trajectories in Mathematics Education
Definition. Hypothetical learning trajectory is a theoretical model for the design of mathematics instruction. It consists of three components, a learning goal, a set of learning tasks, and a hypothesized learning process. The construct can be applied to instructional units of various lengths (e.g., one lesson, a series of lessons, the learning ...
The Acquisition-Learning Hypothesis: Definition and Criticism
Criticism of the Acquisition-Learning Hypothesis. The first critique of Krashen's Monitor Model is that the hypothesized distinction between acquisition and learning as posited by the acquisition-learning hypothesis, or, more specifically, determining whether the process involved in language production resulted from implicit acquisition or explicit learning, is impossible to prove.
8.1: The Elements of Hypothesis Testing
Two Types of Errors. The format of the testing procedure in general terms is to take a sample and use the information it contains to come to a decision about the two hypotheses. As stated before our decision will always be either. reject the null hypothesis \ (H_0\) in favor of the alternative \ (H_a\) presented, or.
What is Hypothesis
Functions of Hypothesis. Following are the functions performed by the hypothesis: Hypothesis helps in making an observation and experiments possible. It becomes the start point for the investigation. Hypothesis helps in verifying the observations. It helps in directing the inquiries in the right direction.
Effectiveness of assisted learning project based models ...
Based on the calculations performed, it turns out that t count >t (α, dk), meaning that the H O hypothesis is rejected and H 1 is accepted. It can be concluded that there is a positive and significant influence of the Project Based Learning (PjBL) model on students' creativity and digital literacy.
HYPOTHESIS
HYPOTHESIS definition: 1. an idea or explanation for something that is based on known facts but has not yet been proved…. Learn more.
[2404.11509] VC Theory for Inventory Policies
Advances in computational power and AI have increased interest in reinforcement learning approaches to inventory management. This paper provides a theoretical foundation for these approaches and investigates the benefits of restricting to policy structures that are well-established by decades of inventory theory. In particular, we prove generalization guarantees for learning several well-known ...
[2404.09113] Extending Mean-Field Variational Inference via Entropic
Variational inference (VI) has emerged as a popular method for approximate inference for high-dimensional Bayesian models. In this paper, we propose a novel VI method that extends the naive mean field via entropic regularization, referred to as $Ξ$-variational inference ($Ξ$-VI). $Ξ$-VI has a close connection to the entropic optimal transport problem and benefits from the computationally ...
6 Common Leadership Styles
HBR Learning's online leadership training helps you hone your skills with courses like Leading People. Earn badges to share on LinkedIn and your resume. Access more than 40 courses trusted by ...
What's The Real Meaning Of Fortnight By Taylor Swift & Post Malone
Taylor Swift's "The Tortured Poets Department" has landed, and we've got a good idea what her lead single, "Fortnight (feat. Post Malone)," is really about.
Mystery Taylor Swift Mural Appears Featuring 'Error 321' Easter Egg
With Taylor Swift's new album The Tortured Poets Department coming out soon, it's time for Swifties to put on their sleuthing caps and decode some Easter eggs.
What we know about 'The Tortured Poets Department,' according ...
Taylor Swift, the Chairman of the Tortured Poets Department, will soon call into session a meeting where she'll release her latest album. Here's what we know.

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How to Write a Great Hypothesis

Hypothesis Format

Hypothesis Types

At a Glance

The Hypothesis in the Scientific Method

Elements of a Good Hypothesis

How to Formulate a Good Hypothesis

The Importance of Operational Definitions

Replicability

Hypothesis Checklist

A few examples of simple hypotheses:

Examples of a complex hypothesis include:

Examples of a null hypothesis include:

Examples of an alternative hypothesis:

Collecting Data on Your Hypothesis

Descriptive Research Methods

Experimental Research Methods

What is hypothesis in Machine Learning?

What is a Hypothesis?

Defining Hypothesis in Machine Learning

Types of Hypotheses in Machine Learning

1. Null Hypothesis

2. Alternative Hypothesis

3. One-tailed Hypothesis

4. Two-tailed Hypothesis

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Hypothesis Testing – A Deep Dive into Hypothesis Testing, The Backbone of Statistical Inference

1. What is Hypothesis Testing?

2. Steps in Hypothesis Testing

2.1. Set up Hypotheses: Null and Alternative

2.2. Choose a Significance Level (α)

2.3. Calculate a test statistic and P-Value

2.4. Make a Decision

3. Example : Testing a new drug.

4. Example in python

5. Conclusion

More Articles

Machine Learning A-Z™: Hands-On Python & R In Data Science

What is a Hypothesis – Types, Examples and Writing Guide

Types of Hypothesis

Research Hypothesis

Null Hypothesis

Alternative Hypothesis

Directional Hypothesis

Non-directional Hypothesis

Statistical Hypothesis

Composite Hypothesis

Empirical Hypothesis

Simple Hypothesis

Complex Hypothesis

Applications of Hypothesis

How to write a Hypothesis

Identify the Research Question

Conduct a Literature Review

Determine the Variables

Formulate the Hypothesis

Write the Null Hypothesis

Refine the Hypothesis

Examples of Hypothesis

Purpose of Hypothesis

When to use Hypothesis

Characteristics of Hypothesis

Advantages of Hypothesis

Limitations of Hypothesis

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Muhammad Hassan

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3 Learning Theories: Understanding How People Learn