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Hypothesis Testing | A Step-by-Step Guide with Easy Examples

Published on November 8, 2019 by Rebecca Bevans . Revised on June 22, 2023.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics . It is most often used by scientists to test specific predictions, called hypotheses, that arise from theories.

There are 5 main steps in hypothesis testing:

• State your research hypothesis as a null hypothesis and alternate hypothesis (H o ) and (H a  or H 1 ).
• Collect data in a way designed to test the hypothesis.
• Perform an appropriate statistical test .
• Decide whether to reject or fail to reject your null hypothesis.
• Present the findings in your results and discussion section.

Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps.

Table of contents

Step 1: state your null and alternate hypothesis, step 2: collect data, step 3: perform a statistical test, step 4: decide whether to reject or fail to reject your null hypothesis, step 5: present your findings, other interesting articles, frequently asked questions about hypothesis testing.

After developing your initial research hypothesis (the prediction that you want to investigate), it is important to restate it as a null (H o ) and alternate (H a ) hypothesis so that you can test it mathematically.

The alternate hypothesis is usually your initial hypothesis that predicts a relationship between variables. The null hypothesis is a prediction of no relationship between the variables you are interested in.

• H 0 : Men are, on average, not taller than women. H a : Men are, on average, taller than women.

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For a statistical test to be valid , it is important to perform sampling and collect data in a way that is designed to test your hypothesis. If your data are not representative, then you cannot make statistical inferences about the population you are interested in.

There are a variety of statistical tests available, but they are all based on the comparison of within-group variance (how spread out the data is within a category) versus between-group variance (how different the categories are from one another).

If the between-group variance is large enough that there is little or no overlap between groups, then your statistical test will reflect that by showing a low p -value . This means it is unlikely that the differences between these groups came about by chance.

Alternatively, if there is high within-group variance and low between-group variance, then your statistical test will reflect that with a high p -value. This means it is likely that any difference you measure between groups is due to chance.

Your choice of statistical test will be based on the type of variables and the level of measurement of your collected data .

• an estimate of the difference in average height between the two groups.
• a p -value showing how likely you are to see this difference if the null hypothesis of no difference is true.

Based on the outcome of your statistical test, you will have to decide whether to reject or fail to reject your null hypothesis.

In most cases you will use the p -value generated by your statistical test to guide your decision. And in most cases, your predetermined level of significance for rejecting the null hypothesis will be 0.05 – that is, when there is a less than 5% chance that you would see these results if the null hypothesis were true.

In some cases, researchers choose a more conservative level of significance, such as 0.01 (1%). This minimizes the risk of incorrectly rejecting the null hypothesis ( Type I error ).

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The results of hypothesis testing will be presented in the results and discussion sections of your research paper , dissertation or thesis .

In the results section you should give a brief summary of the data and a summary of the results of your statistical test (for example, the estimated difference between group means and associated p -value). In the discussion , you can discuss whether your initial hypothesis was supported by your results or not.

In the formal language of hypothesis testing, we talk about rejecting or failing to reject the null hypothesis. You will probably be asked to do this in your statistics assignments.

However, when presenting research results in academic papers we rarely talk this way. Instead, we go back to our alternate hypothesis (in this case, the hypothesis that men are on average taller than women) and state whether the result of our test did or did not support the alternate hypothesis.

If your null hypothesis was rejected, this result is interpreted as “supported the alternate hypothesis.”

These are superficial differences; you can see that they mean the same thing.

You might notice that we don’t say that we reject or fail to reject the alternate hypothesis . This is because hypothesis testing is not designed to prove or disprove anything. It is only designed to test whether a pattern we measure could have arisen spuriously, or by chance.

If we reject the null hypothesis based on our research (i.e., we find that it is unlikely that the pattern arose by chance), then we can say our test lends support to our hypothesis . But if the pattern does not pass our decision rule, meaning that it could have arisen by chance, then we say the test is inconsistent with our hypothesis .

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Normal distribution
• Descriptive statistics
• Measures of central tendency
• Correlation coefficient

Methodology

• Cluster sampling
• Stratified sampling
• Types of interviews
• Cohort study
• Thematic analysis

Research bias

• Implicit bias
• Cognitive bias
• Survivorship bias
• Availability heuristic
• Nonresponse bias
• Regression to the mean

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

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What is Hypothesis Testing? Types and Methods

• Soumyaa Rawat
• Jul 23, 2021

Hypothesis Testing  

Hypothesis testing is the act of testing a hypothesis or a supposition in relation to a statistical parameter. Analysts implement hypothesis testing in order to test if a hypothesis is plausible or not. 

In data science and statistics , hypothesis testing is an important step as it involves the verification of an assumption that could help develop a statistical parameter. For instance, a researcher establishes a hypothesis assuming that the average of all odd numbers is an even number. 

In order to find the plausibility of this hypothesis, the researcher will have to test the hypothesis using hypothesis testing methods. Unlike a hypothesis that is ‘supposed’ to stand true on the basis of little or no evidence, hypothesis testing is required to have plausible evidence in order to establish that a statistical hypothesis is true. 

Perhaps this is where statistics play an important role. A number of components are involved in this process. But before understanding the process involved in hypothesis testing in research methodology, we shall first understand the types of hypotheses that are involved in the process. Let us get started! 

Types of Hypotheses

In data sampling, different types of hypothesis are involved in finding whether the tested samples test positive for a hypothesis or not. In this segment, we shall discover the different types of hypotheses and understand the role they play in hypothesis testing.

Alternative Hypothesis

Alternative Hypothesis (H1) or the research hypothesis states that there is a relationship between two variables (where one variable affects the other). The alternative hypothesis is the main driving force for hypothesis testing. 

It implies that the two variables are related to each other and the relationship that exists between them is not due to chance or coincidence. 

When the process of hypothesis testing is carried out, the alternative hypothesis is the main subject of the testing process. The analyst intends to test the alternative hypothesis and verifies its plausibility.

Null Hypothesis

The Null Hypothesis (H0) aims to nullify the alternative hypothesis by implying that there exists no relation between two variables in statistics. It states that the effect of one variable on the other is solely due to chance and no empirical cause lies behind it. 

The null hypothesis is established alongside the alternative hypothesis and is recognized as important as the latter. In hypothesis testing, the null hypothesis has a major role to play as it influences the testing against the alternative hypothesis. 

(Must read: What is ANOVA test? )

Non-Directional Hypothesis

The Non-directional hypothesis states that the relation between two variables has no direction. 

Simply put, it asserts that there exists a relation between two variables, but does not recognize the direction of effect, whether variable A affects variable B or vice versa. 

Directional Hypothesis

The Directional hypothesis, on the other hand, asserts the direction of effect of the relationship that exists between two variables. 

Herein, the hypothesis clearly states that variable A affects variable B, or vice versa. 

Statistical Hypothesis

A statistical hypothesis is a hypothesis that can be verified to be plausible on the basis of statistics. 

By using data sampling and statistical knowledge, one can determine the plausibility of a statistical hypothesis and find out if it stands true or not. 

(Related blog: z-test vs t-test )

Performing Hypothesis Testing  

Now that we have understood the types of hypotheses and the role they play in hypothesis testing, let us now move on to understand the process in a better manner. 

In hypothesis testing, a researcher is first required to establish two hypotheses - alternative hypothesis and null hypothesis in order to begin with the procedure. 

To establish these two hypotheses, one is required to study data samples, find a plausible pattern among the samples, and pen down a statistical hypothesis that they wish to test. 

A random population of samples can be drawn, to begin with hypothesis testing. Among the two hypotheses, alternative and null, only one can be verified to be true. Perhaps the presence of both hypotheses is required to make the process successful. 

At the end of the hypothesis testing procedure, either of the hypotheses will be rejected and the other one will be supported. Even though one of the two hypotheses turns out to be true, no hypothesis can ever be verified 100%. 

(Read also: Types of data sampling techniques )

Therefore, a hypothesis can only be supported based on the statistical samples and verified data. Here is a step-by-step guide for hypothesis testing.

Establish the hypotheses

First things first, one is required to establish two hypotheses - alternative and null, that will set the foundation for hypothesis testing. 

These hypotheses initiate the testing process that involves the researcher working on data samples in order to either support the alternative hypothesis or the null hypothesis. 

Generate a testing plan

Once the hypotheses have been formulated, it is now time to generate a testing plan. A testing plan or an analysis plan involves the accumulation of data samples, determining which statistic is to be considered and laying out the sample size. 

All these factors are very important while one is working on hypothesis testing.

Analyze data samples

As soon as a testing plan is ready, it is time to move on to the analysis part. Analysis of data samples involves configuring statistical values of samples, drawing them together, and deriving a pattern out of these samples. 

While analyzing the data samples, a researcher needs to determine a set of things -

Significance Level - The level of significance in hypothesis testing indicates if a statistical result could have significance if the null hypothesis stands to be true.

Testing Method - The testing method involves a type of sampling-distribution and a test statistic that leads to hypothesis testing. There are a number of testing methods that can assist in the analysis of data samples. 

Test statistic - Test statistic is a numerical summary of a data set that can be used to perform hypothesis testing.

P-value - The P-value interpretation is the probability of finding a sample statistic to be as extreme as the test statistic, indicating the plausibility of the null hypothesis. 

Infer the results

The analysis of data samples leads to the inference of results that establishes whether the alternative hypothesis stands true or not. When the P-value is less than the significance level, the null hypothesis is rejected and the alternative hypothesis turns out to be plausible. 

Methods of Hypothesis Testing

As we have already looked into different aspects of hypothesis testing, we shall now look into the different methods of hypothesis testing. All in all, there are 2 most common types of hypothesis testing methods. They are as follows -

Frequentist Hypothesis Testing

The frequentist hypothesis or the traditional approach to hypothesis testing is a hypothesis testing method that aims on making assumptions by considering current data. 

The supposed truths and assumptions are based on the current data and a set of 2 hypotheses are formulated. A very popular subtype of the frequentist approach is the Null Hypothesis Significance Testing (NHST). 

The NHST approach (involving the null and alternative hypothesis) has been one of the most sought-after methods of hypothesis testing in the field of statistics ever since its inception in the mid-1950s. 

Bayesian Hypothesis Testing

A much unconventional and modern method of hypothesis testing, the Bayesian Hypothesis Testing claims to test a particular hypothesis in accordance with the past data samples, known as prior probability, and current data that lead to the plausibility of a hypothesis. 

The result obtained indicates the posterior probability of the hypothesis. In this method, the researcher relies on ‘prior probability and posterior probability’ to conduct hypothesis testing on hand. 

On the basis of this prior probability, the Bayesian approach tests a hypothesis to be true or false. The Bayes factor, a major component of this method, indicates the likelihood ratio among the null hypothesis and the alternative hypothesis. 

The Bayes factor is the indicator of the plausibility of either of the two hypotheses that are established for hypothesis testing.  

(Also read - Introduction to Bayesian Statistics ) 

To conclude, hypothesis testing, a way to verify the plausibility of a supposed assumption can be done through different methods - the Bayesian approach or the Frequentist approach. 

Although the Bayesian approach relies on the prior probability of data samples, the frequentist approach assumes without a probability. A number of elements involved in hypothesis testing are - significance level, p-level, test statistic, and method of hypothesis testing. 

(Also read: Introduction to probability distributions )

A significant way to determine whether a hypothesis stands true or not is to verify the data samples and identify the plausible hypothesis among the null hypothesis and alternative hypothesis. 

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Hypothesis Testing – A Complete Guide with Examples

Published by Alvin Nicolas at August 14th, 2021 , Revised On October 26, 2023

In statistics, hypothesis testing is a critical tool. It allows us to make informed decisions about populations based on sample data. Whether you are a researcher trying to prove a scientific point, a marketer analysing A/B test results, or a manufacturer ensuring quality control, hypothesis testing plays a pivotal role. This guide aims to introduce you to the concept and walk you through real-world examples.

What is a Hypothesis and a Hypothesis Testing?

A hypothesis is considered a belief or assumption that has to be accepted, rejected, proved or disproved. In contrast, a research hypothesis is a research question for a researcher that has to be proven correct or incorrect through investigation.

What is Hypothesis Testing?

Hypothesis testing  is a scientific method used for making a decision and drawing conclusions by using a statistical approach. It is used to suggest new ideas by testing theories to know whether or not the sample data supports research. A research hypothesis is a predictive statement that has to be tested using scientific methods that join an independent variable to a dependent variable.  

Example: The academic performance of student A is better than student B

Characteristics of the Hypothesis to be Tested

A hypothesis should be:

• Clear and precise
• Capable of being tested
• Able to relate to a variable
• Stated in simple terms
• Consistent with known facts
• Limited in scope and specific
• Tested in a limited timeframe
• Explain the facts in detail

What is a Null Hypothesis and Alternative Hypothesis?

A  null hypothesis  is a hypothesis when there is no significant relationship between the dependent and the participants’ independent  variables . 

In simple words, it’s a hypothesis that has been put forth but hasn’t been proved as yet. A researcher aims to disprove the theory. The abbreviation “Ho” is used to denote a null hypothesis.

If you want to compare two methods and assume that both methods are equally good, this assumption is considered the null hypothesis.

Example: In an automobile trial, you feel that the new vehicle’s mileage is similar to the previous model of the car, on average. You can write it as: Ho: there is no difference between the mileage of both vehicles. If your findings don’t support your hypothesis and you get opposite results, this outcome will be considered an alternative hypothesis.

If you assume that one method is better than another method, then it’s considered an alternative hypothesis. The alternative hypothesis is the theory that a researcher seeks to prove and is typically denoted by H1 or HA.

If you support a null hypothesis, it means you’re not supporting the alternative hypothesis. Similarly, if you reject a null hypothesis, it means you are recommending the alternative hypothesis.

Example: In an automobile trial, you feel that the new vehicle’s mileage is better than the previous model of the vehicle. You can write it as; Ha: the two vehicles have different mileage. On average/ the fuel consumption of the new vehicle model is better than the previous model.

If a null hypothesis is rejected during the hypothesis test, even if it’s true, then it is considered as a type-I error. On the other hand, if you don’t dismiss a hypothesis, even if it’s false because you could not identify its falseness, it’s considered a type-II error.

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How to Conduct Hypothesis Testing?

Here is a step-by-step guide on how to conduct hypothesis testing.

Step 1: State the Null and Alternative Hypothesis

Once you develop a research hypothesis, it’s important to state it is as a Null hypothesis (Ho) and an Alternative hypothesis (Ha) to test it statistically.

A null hypothesis is a preferred choice as it provides the opportunity to test the theory. In contrast, you can accept the alternative hypothesis when the null hypothesis has been rejected.

Example: You want to identify a relationship between obesity of men and women and the modern living style. You develop a hypothesis that women, on average, gain weight quickly compared to men. Then you write it as: Ho: Women, on average, don’t gain weight quickly compared to men. Ha: Women, on average, gain weight quickly compared to men.

Step 2: Data Collection

Hypothesis testing follows the statistical method, and statistics are all about data. It’s challenging to gather complete information about a specific population you want to study. You need to  gather the data  obtained through a large number of samples from a specific population. 

Example: Suppose you want to test the difference in the rate of obesity between men and women. You should include an equal number of men and women in your sample. Then investigate various aspects such as their lifestyle, eating patterns and profession, and any other variables that may influence average weight. You should also determine your study’s scope, whether it applies to a specific group of population or worldwide population. You can use available information from various places, countries, and regions.

Step 3: Select Appropriate Statistical Test

There are many  types of statistical tests , but we discuss the most two common types below, such as One-sided and two-sided tests.

Note: Your choice of the type of test depends on the purpose of your study 

One-sided Test

In the one-sided test, the values of rejecting a null hypothesis are located in one tail of the probability distribution. The set of values is less or higher than the critical value of the test. It is also called a one-tailed test of significance.

Example: If you want to test that all mangoes in a basket are ripe. You can write it as: Ho: All mangoes in the basket, on average, are ripe. If you find all ripe mangoes in the basket, the null hypothesis you developed will be true.

Two-sided Test

In the two-sided test, the values of rejecting a null hypothesis are located on both tails of the probability distribution. The set of values is less or higher than the first critical value of the test and higher than the second critical value test. It is also called a two-tailed test of significance. 

Example: Nothing can be explicitly said whether all mangoes are ripe in the basket. If you reject the null hypothesis (Ho: All mangoes in the basket, on average, are ripe), then it means all mangoes in the basket are not likely to be ripe. A few mangoes could be raw as well.

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Step 4: Select the Level of Significance

When you reject a null hypothesis, even if it’s true during a statistical hypothesis, it is considered the  significance level . It is the probability of a type one error. The significance should be as minimum as possible to avoid the type-I error, which is considered severe and should be avoided. 

If the significance level is minimum, then it prevents the researchers from false claims. 

The significance level is denoted by  P,  and it has given the value of 0.05 (P=0.05)

If the P-Value is less than 0.05, then the difference will be significant. If the P-value is higher than 0.05, then the difference is non-significant.

Example: Suppose you apply a one-sided test to test whether women gain weight quickly compared to men. You get to know about the average weight between men and women and the factors promoting weight gain.

Step 5: Find out Whether the Null Hypothesis is Rejected or Supported

After conducting a statistical test, you should identify whether your null hypothesis is rejected or accepted based on the test results. It would help if you observed the P-value for this.

Example: If you find the P-value of your test is less than 0.5/5%, then you need to reject your null hypothesis (Ho: Women, on average, don’t gain weight quickly compared to men). On the other hand, if a null hypothesis is rejected, then it means the alternative hypothesis might be true (Ha: Women, on average, gain weight quickly compared to men. If you find your test’s P-value is above 0.5/5%, then it means your null hypothesis is true.

Step 6: Present the Outcomes of your Study

The final step is to present the  outcomes of your study . You need to ensure whether you have met the objectives of your research or not. 

In the discussion section and  conclusion , you can present your findings by using supporting evidence and conclude whether your null hypothesis was rejected or supported.

In the result section, you can summarise your study’s outcomes, including the average difference and P-value of the two groups.

If we talk about the findings, our study your results will be as follows:

Example: In the study of identifying whether women gain weight quickly compared to men, we found the P-value is less than 0.5. Hence, we can reject the null hypothesis (Ho: Women, on average, don’t gain weight quickly than men) and conclude that women may likely gain weight quickly than men.

Did you know in your academic paper you should not mention whether you have accepted or rejected the null hypothesis? 

Always remember that you either conclude to reject Ho in favor of Haor   do not reject Ho . It would help if you never rejected  Ha  or even  accept Ha .

Suppose your null hypothesis is rejected in the hypothesis testing. If you conclude  reject Ho in favor of Haor   do not reject Ho,  then it doesn’t mean that the null hypothesis is true. It only means that there is a lack of evidence against Ho in favour of Ha. If your null hypothesis is not true, then the alternative hypothesis is likely to be true.

Example: We found that the P-value is less than 0.5. Hence, we can conclude reject Ho in favour of Ha (Ho: Women, on average, don’t gain weight quickly than men) reject Ho in favour of Ha. However, rejected in favour of Ha means (Ha: women may likely to gain weight quickly than men)

Frequently Asked Questions

What are the 3 types of hypothesis test.

The 3 types of hypothesis tests are:

• One-Sample Test : Compare sample data to a known population value.
• Two-Sample Test : Compare means between two sample groups.
• ANOVA : Analyze variance among multiple groups to determine significant differences.

What is a hypothesis?

A hypothesis is a proposed explanation or prediction about a phenomenon, often based on observations. It serves as a starting point for research or experimentation, providing a testable statement that can either be supported or refuted through data and analysis. In essence, it’s an educated guess that drives scientific inquiry.

What are null hypothesis?

A null hypothesis (often denoted as H0) suggests that there is no effect or difference in a study or experiment. It represents a default position or status quo. Statistical tests evaluate data to determine if there’s enough evidence to reject this null hypothesis.

What is the probability value?

The probability value, or p-value, is a measure used in statistics to determine the significance of an observed effect. It indicates the probability of obtaining the observed results, or more extreme, if the null hypothesis were true. A small p-value (typically <0.05) suggests evidence against the null hypothesis, warranting its rejection.

What is p value?

The p-value is a fundamental concept in statistical hypothesis testing. It represents the probability of observing a test statistic as extreme, or more so, than the one calculated from sample data, assuming the null hypothesis is true. A low p-value suggests evidence against the null, possibly justifying its rejection.

What is a t test?

A t-test is a statistical test used to compare the means of two groups. It determines if observed differences between the groups are statistically significant or if they likely occurred by chance. Commonly applied in research, there are different t-tests, including independent, paired, and one-sample, tailored to various data scenarios.

When to reject null hypothesis?

Reject the null hypothesis when the test statistic falls into a predefined rejection region or when the p-value is less than the chosen significance level (commonly 0.05). This suggests that the observed data is unlikely under the null hypothesis, indicating evidence for the alternative hypothesis. Always consider the study’s context.

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The Craft of Writing a Strong Hypothesis

Table of Contents

Writing a hypothesis is one of the essential elements of a scientific research paper. It needs to be to the point, clearly communicating what your research is trying to accomplish. A blurry, drawn-out, or complexly-structured hypothesis can confuse your readers. Or worse, the editor and peer reviewers.

A captivating hypothesis is not too intricate. This blog will take you through the process so that, by the end of it, you have a better idea of how to convey your research paper's intent in just one sentence.

What is a Hypothesis?

The first step in your scientific endeavor, a hypothesis, is a strong, concise statement that forms the basis of your research. It is not the same as a thesis statement , which is a brief summary of your research paper .

The sole purpose of a hypothesis is to predict your paper's findings, data, and conclusion. It comes from a place of curiosity and intuition . When you write a hypothesis, you're essentially making an educated guess based on scientific prejudices and evidence, which is further proven or disproven through the scientific method.

The reason for undertaking research is to observe a specific phenomenon. A hypothesis, therefore, lays out what the said phenomenon is. And it does so through two variables, an independent and dependent variable.

The independent variable is the cause behind the observation, while the dependent variable is the effect of the cause. A good example of this is “mixing red and blue forms purple.” In this hypothesis, mixing red and blue is the independent variable as you're combining the two colors at your own will. The formation of purple is the dependent variable as, in this case, it is conditional to the independent variable.

Different Types of Hypotheses‌

Types of hypotheses

Some would stand by the notion that there are only two types of hypotheses: a Null hypothesis and an Alternative hypothesis. While that may have some truth to it, it would be better to fully distinguish the most common forms as these terms come up so often, which might leave you out of context.

Apart from Null and Alternative, there are Complex, Simple, Directional, Non-Directional, Statistical, and Associative and casual hypotheses. They don't necessarily have to be exclusive, as one hypothesis can tick many boxes, but knowing the distinctions between them will make it easier for you to construct your own.

1. Null hypothesis

A null hypothesis proposes no relationship between two variables. Denoted by H 0 , it is a negative statement like “Attending physiotherapy sessions does not affect athletes' on-field performance.” Here, the author claims physiotherapy sessions have no effect on on-field performances. Even if there is, it's only a coincidence.

2. Alternative hypothesis

Considered to be the opposite of a null hypothesis, an alternative hypothesis is donated as H1 or Ha. It explicitly states that the dependent variable affects the independent variable. A good  alternative hypothesis example is “Attending physiotherapy sessions improves athletes' on-field performance.” or “Water evaporates at 100 °C. ” The alternative hypothesis further branches into directional and non-directional.

• Directional hypothesis: A hypothesis that states the result would be either positive or negative is called directional hypothesis. It accompanies H1 with either the ‘<' or ‘>' sign.
• Non-directional hypothesis: A non-directional hypothesis only claims an effect on the dependent variable. It does not clarify whether the result would be positive or negative. The sign for a non-directional hypothesis is ‘≠.'

3. Simple hypothesis

A simple hypothesis is a statement made to reflect the relation between exactly two variables. One independent and one dependent. Consider the example, “Smoking is a prominent cause of lung cancer." The dependent variable, lung cancer, is dependent on the independent variable, smoking.

4. Complex hypothesis

In contrast to a simple hypothesis, a complex hypothesis implies the relationship between multiple independent and dependent variables. For instance, “Individuals who eat more fruits tend to have higher immunity, lesser cholesterol, and high metabolism.” The independent variable is eating more fruits, while the dependent variables are higher immunity, lesser cholesterol, and high metabolism.

5. Associative and casual hypothesis

Associative and casual hypotheses don't exhibit how many variables there will be. They define the relationship between the variables. In an associative hypothesis, changing any one variable, dependent or independent, affects others. In a casual hypothesis, the independent variable directly affects the dependent.

6. Empirical hypothesis

Also referred to as the working hypothesis, an empirical hypothesis claims a theory's validation via experiments and observation. This way, the statement appears justifiable and different from a wild guess.

Say, the hypothesis is “Women who take iron tablets face a lesser risk of anemia than those who take vitamin B12.” This is an example of an empirical hypothesis where the researcher  the statement after assessing a group of women who take iron tablets and charting the findings.

7. Statistical hypothesis

The point of a statistical hypothesis is to test an already existing hypothesis by studying a population sample. Hypothesis like “44% of the Indian population belong in the age group of 22-27.” leverage evidence to prove or disprove a particular statement.

Characteristics of a Good Hypothesis

Writing a hypothesis is essential as it can make or break your research for you. That includes your chances of getting published in a journal. So when you're designing one, keep an eye out for these pointers:

• A research hypothesis has to be simple yet clear to look justifiable enough.
• It has to be testable — your research would be rendered pointless if too far-fetched into reality or limited by technology.
• It has to be precise about the results —what you are trying to do and achieve through it should come out in your hypothesis.
• A research hypothesis should be self-explanatory, leaving no doubt in the reader's mind.
• If you are developing a relational hypothesis, you need to include the variables and establish an appropriate relationship among them.
• A hypothesis must keep and reflect the scope for further investigations and experiments.

Separating a Hypothesis from a Prediction

Outside of academia, hypothesis and prediction are often used interchangeably. In research writing, this is not only confusing but also incorrect. And although a hypothesis and prediction are guesses at their core, there are many differences between them.

A hypothesis is an educated guess or even a testable prediction validated through research. It aims to analyze the gathered evidence and facts to define a relationship between variables and put forth a logical explanation behind the nature of events.

Predictions are assumptions or expected outcomes made without any backing evidence. They are more fictionally inclined regardless of where they originate from.

For this reason, a hypothesis holds much more weight than a prediction. It sticks to the scientific method rather than pure guesswork. "Planets revolve around the Sun." is an example of a hypothesis as it is previous knowledge and observed trends. Additionally, we can test it through the scientific method.

Whereas "COVID-19 will be eradicated by 2030." is a prediction. Even though it results from past trends, we can't prove or disprove it. So, the only way this gets validated is to wait and watch if COVID-19 cases end by 2030.

Finally, How to Write a Hypothesis

Quick tips on writing a hypothesis

1.  Be clear about your research question

A hypothesis should instantly address the research question or the problem statement. To do so, you need to ask a question. Understand the constraints of your undertaken research topic and then formulate a simple and topic-centric problem. Only after that can you develop a hypothesis and further test for evidence.

2. Carry out a recce

Once you have your research's foundation laid out, it would be best to conduct preliminary research. Go through previous theories, academic papers, data, and experiments before you start curating your research hypothesis. It will give you an idea of your hypothesis's viability or originality.

Making use of references from relevant research papers helps draft a good research hypothesis. SciSpace Discover offers a repository of over 270 million research papers to browse through and gain a deeper understanding of related studies on a particular topic. Additionally, you can use SciSpace Copilot , your AI research assistant, for reading any lengthy research paper and getting a more summarized context of it. A hypothesis can be formed after evaluating many such summarized research papers. Copilot also offers explanations for theories and equations, explains paper in simplified version, allows you to highlight any text in the paper or clip math equations and tables and provides a deeper, clear understanding of what is being said. This can improve the hypothesis by helping you identify potential research gaps.

3. Create a 3-dimensional hypothesis

Variables are an essential part of any reasonable hypothesis. So, identify your independent and dependent variable(s) and form a correlation between them. The ideal way to do this is to write the hypothetical assumption in the ‘if-then' form. If you use this form, make sure that you state the predefined relationship between the variables.

In another way, you can choose to present your hypothesis as a comparison between two variables. Here, you must specify the difference you expect to observe in the results.

4. Write the first draft

Now that everything is in place, it's time to write your hypothesis. For starters, create the first draft. In this version, write what you expect to find from your research.

Clearly separate your independent and dependent variables and the link between them. Don't fixate on syntax at this stage. The goal is to ensure your hypothesis addresses the issue.

5. Proof your hypothesis

After preparing the first draft of your hypothesis, you need to inspect it thoroughly. It should tick all the boxes, like being concise, straightforward, relevant, and accurate. Your final hypothesis has to be well-structured as well.

Research projects are an exciting and crucial part of being a scholar. And once you have your research question, you need a great hypothesis to begin conducting research. Thus, knowing how to write a hypothesis is very important.

Now that you have a firmer grasp on what a good hypothesis constitutes, the different kinds there are, and what process to follow, you will find it much easier to write your hypothesis, which ultimately helps your research.

Now it's easier than ever to streamline your research workflow with SciSpace Discover . Its integrated, comprehensive end-to-end platform for research allows scholars to easily discover, write and publish their research and fosters collaboration.

It includes everything you need, including a repository of over 270 million research papers across disciplines, SEO-optimized summaries and public profiles to show your expertise and experience.

If you found these tips on writing a research hypothesis useful, head over to our blog on Statistical Hypothesis Testing to learn about the top researchers, papers, and institutions in this domain.

Frequently Asked Questions (FAQs)

1. what is the definition of hypothesis.

According to the Oxford dictionary, a hypothesis is defined as “An idea or explanation of something that is based on a few known facts, but that has not yet been proved to be true or correct”.

2. What is an example of hypothesis?

The hypothesis is a statement that proposes a relationship between two or more variables. An example: "If we increase the number of new users who join our platform by 25%, then we will see an increase in revenue."

3. What is an example of null hypothesis?

A null hypothesis is a statement that there is no relationship between two variables. The null hypothesis is written as H0. The null hypothesis states that there is no effect. For example, if you're studying whether or not a particular type of exercise increases strength, your null hypothesis will be "there is no difference in strength between people who exercise and people who don't."

4. What are the types of research?

• Fundamental research

• Applied research

• Qualitative research

• Quantitative research

• Mixed research

• Exploratory research

• Longitudinal research

• Cross-sectional research

• Field research

• Laboratory research

• Fixed research

• Flexible research

• Action research

• Policy research

• Classification research

• Comparative research

• Causal research

• Inductive research

• Deductive research

5. How to write a hypothesis?

• Your hypothesis should be able to predict the relationship and outcome.

• Avoid wordiness by keeping it simple and brief.

• Your hypothesis should contain observable and testable outcomes.

• Your hypothesis should be relevant to the research question.

6. What are the 2 types of hypothesis?

• Null hypotheses are used to test the claim that "there is no difference between two groups of data".

• Alternative hypotheses test the claim that "there is a difference between two data groups".

7. Difference between research question and research hypothesis?

A research question is a broad, open-ended question you will try to answer through your research. A hypothesis is a statement based on prior research or theory that you expect to be true due to your study. Example - Research question: What are the factors that influence the adoption of the new technology? Research hypothesis: There is a positive relationship between age, education and income level with the adoption of the new technology.

8. What is plural for hypothesis?

The plural of hypothesis is hypotheses. Here's an example of how it would be used in a statement, "Numerous well-considered hypotheses are presented in this part, and they are supported by tables and figures that are well-illustrated."

9. What is the red queen hypothesis?

The red queen hypothesis in evolutionary biology states that species must constantly evolve to avoid extinction because if they don't, they will be outcompeted by other species that are evolving. Leigh Van Valen first proposed it in 1973; since then, it has been tested and substantiated many times.

10. Who is known as the father of null hypothesis?

The father of the null hypothesis is Sir Ronald Fisher. He published a paper in 1925 that introduced the concept of null hypothesis testing, and he was also the first to use the term itself.

11. When to reject null hypothesis?

You need to find a significant difference between your two populations to reject the null hypothesis. You can determine that by running statistical tests such as an independent sample t-test or a dependent sample t-test. You should reject the null hypothesis if the p-value is less than 0.05.

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• Hypothesis Testing: Definition, Uses, Limitations + Examples

Hypothesis testing is as old as the scientific method and is at the heart of the research process. 

Research exists to validate or disprove assumptions about various phenomena. The process of validation involves testing and it is in this context that we will explore hypothesis testing. 

What is a Hypothesis? 

A hypothesis is a calculated prediction or assumption about a population parameter based on limited evidence. The whole idea behind hypothesis formulation is testing—this means the researcher subjects his or her calculated assumption to a series of evaluations to know whether they are true or false. 

Typically, every research starts with a hypothesis—the investigator makes a claim and experiments to prove that this claim is true or false . For instance, if you predict that students who drink milk before class perform better than those who don’t, then this becomes a hypothesis that can be confirmed or refuted using an experiment.  

Read: What is Empirical Research Study? [Examples & Method]

What are the Types of Hypotheses? 

1. simple hypothesis.

Also known as a basic hypothesis, a simple hypothesis suggests that an independent variable is responsible for a corresponding dependent variable. In other words, an occurrence of the independent variable inevitably leads to an occurrence of the dependent variable. 

Typically, simple hypotheses are considered as generally true, and they establish a causal relationship between two variables. 

Examples of Simple Hypothesis  

• Drinking soda and other sugary drinks can cause obesity. 
• Smoking cigarettes daily leads to lung cancer.

2. Complex Hypothesis

A complex hypothesis is also known as a modal. It accounts for the causal relationship between two independent variables and the resulting dependent variables. This means that the combination of the independent variables leads to the occurrence of the dependent variables . 

Examples of Complex Hypotheses  

• Adults who do not smoke and drink are less likely to develop liver-related conditions.
• Global warming causes icebergs to melt which in turn causes major changes in weather patterns.

3. Null Hypothesis

As the name suggests, a null hypothesis is formed when a researcher suspects that there’s no relationship between the variables in an observation. In this case, the purpose of the research is to approve or disapprove this assumption. 

Examples of Null Hypothesis

• This is no significant change in a student’s performance if they drink coffee or tea before classes. 
• There’s no significant change in the growth of a plant if one uses distilled water only or vitamin-rich water. 

Read: Research Report: Definition, Types + [Writing Guide]

4. Alternative Hypothesis 

To disapprove a null hypothesis, the researcher has to come up with an opposite assumption—this assumption is known as the alternative hypothesis. This means if the null hypothesis says that A is false, the alternative hypothesis assumes that A is true. 

An alternative hypothesis can be directional or non-directional depending on the direction of the difference. A directional alternative hypothesis specifies the direction of the tested relationship, stating that one variable is predicted to be larger or smaller than the null value while a non-directional hypothesis only validates the existence of a difference without stating its direction. 

Examples of Alternative Hypotheses  

• Starting your day with a cup of tea instead of a cup of coffee can make you more alert in the morning. 
• The growth of a plant improves significantly when it receives distilled water instead of vitamin-rich water. 

5. Logical Hypothesis

Logical hypotheses are some of the most common types of calculated assumptions in systematic investigations. It is an attempt to use your reasoning to connect different pieces in research and build a theory using little evidence. In this case, the researcher uses any data available to him, to form a plausible assumption that can be tested. 

Examples of Logical Hypothesis

• Waking up early helps you to have a more productive day. 
• Beings from Mars would not be able to breathe the air in the atmosphere of the Earth. 

6. Empirical Hypothesis  

After forming a logical hypothesis, the next step is to create an empirical or working hypothesis. At this stage, your logical hypothesis undergoes systematic testing to prove or disprove the assumption. An empirical hypothesis is subject to several variables that can trigger changes and lead to specific outcomes. 

Examples of Empirical Testing 

• People who eat more fish run faster than people who eat meat.
• Women taking vitamin E grow hair faster than those taking vitamin K.

7. Statistical Hypothesis

When forming a statistical hypothesis, the researcher examines the portion of a population of interest and makes a calculated assumption based on the data from this sample. A statistical hypothesis is most common with systematic investigations involving a large target audience. Here, it’s impossible to collect responses from every member of the population so you have to depend on data from your sample and extrapolate the results to the wider population. 

Examples of Statistical Hypothesis  

• 45% of students in Louisiana have middle-income parents. 
• 80% of the UK’s population gets a divorce because of irreconcilable differences.

What is Hypothesis Testing? 

Hypothesis testing is an assessment method that allows researchers to determine the plausibility of a hypothesis. It involves testing an assumption about a specific population parameter to know whether it’s true or false. These population parameters include variance, standard deviation, and median. 

Typically, hypothesis testing starts with developing a null hypothesis and then performing several tests that support or reject the null hypothesis. The researcher uses test statistics to compare the association or relationship between two or more variables. 

Explore: Research Bias: Definition, Types + Examples

Researchers also use hypothesis testing to calculate the coefficient of variation and determine if the regression relationship and the correlation coefficient are statistically significant.

How Hypothesis Testing Works

The basis of hypothesis testing is to examine and analyze the null hypothesis and alternative hypothesis to know which one is the most plausible assumption. Since both assumptions are mutually exclusive, only one can be true. In other words, the occurrence of a null hypothesis destroys the chances of the alternative coming to life, and vice-versa. 

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What Are The Stages of Hypothesis Testing?  

To successfully confirm or refute an assumption, the researcher goes through five (5) stages of hypothesis testing; 

• Determine the null hypothesis
• Specify the alternative hypothesis
• Set the significance level
• Calculate the test statistics and corresponding P-value
• Draw your conclusion
• Determine the Null Hypothesis

Like we mentioned earlier, hypothesis testing starts with creating a null hypothesis which stands as an assumption that a certain statement is false or implausible. For example, the null hypothesis (H0) could suggest that different subgroups in the research population react to a variable in the same way. 

• Specify the Alternative Hypothesis

Once you know the variables for the null hypothesis, the next step is to determine the alternative hypothesis. The alternative hypothesis counters the null assumption by suggesting the statement or assertion is true. Depending on the purpose of your research, the alternative hypothesis can be one-sided or two-sided. 

Using the example we established earlier, the alternative hypothesis may argue that the different sub-groups react differently to the same variable based on several internal and external factors. 

• Set the Significance Level

Many researchers create a 5% allowance for accepting the value of an alternative hypothesis, even if the value is untrue. This means that there is a 0.05 chance that one would go with the value of the alternative hypothesis, despite the truth of the null hypothesis. 

Something to note here is that the smaller the significance level, the greater the burden of proof needed to reject the null hypothesis and support the alternative hypothesis.

Explore: What is Data Interpretation? + [Types, Method & Tools]

• Calculate the Test Statistics and Corresponding P-Value 

Test statistics in hypothesis testing allow you to compare different groups between variables while the p-value accounts for the probability of obtaining sample statistics if your null hypothesis is true. In this case, your test statistics can be the mean, median and similar parameters. 

If your p-value is 0.65, for example, then it means that the variable in your hypothesis will happen 65 in100 times by pure chance. Use this formula to determine the p-value for your data: 

• Draw Your Conclusions

After conducting a series of tests, you should be able to agree or refute the hypothesis based on feedback and insights from your sample data.  

Applications of Hypothesis Testing in Research

Hypothesis testing isn’t only confined to numbers and calculations; it also has several real-life applications in business, manufacturing, advertising, and medicine. 

In a factory or other manufacturing plants, hypothesis testing is an important part of quality and production control before the final products are approved and sent out to the consumer. 

During ideation and strategy development, C-level executives use hypothesis testing to evaluate their theories and assumptions before any form of implementation. For example, they could leverage hypothesis testing to determine whether or not some new advertising campaign, marketing technique, etc. causes increased sales. 

In addition, hypothesis testing is used during clinical trials to prove the efficacy of a drug or new medical method before its approval for widespread human usage. 

What is an Example of Hypothesis Testing?

An employer claims that her workers are of above-average intelligence. She takes a random sample of 20 of them and gets the following results: 

Mean IQ Scores: 110

Standard Deviation: 15 

Mean Population IQ: 100

Step 1: Using the value of the mean population IQ, we establish the null hypothesis as 100.

Step 2: State that the alternative hypothesis is greater than 100.

Step 3: State the alpha level as 0.05 or 5% 

Step 4: Find the rejection region area (given by your alpha level above) from the z-table. An area of .05 is equal to a z-score of 1.645.

Step 5: Calculate the test statistics using this formula

Z = (110–100) ÷ (15÷√20) 

10 ÷ 3.35 = 2.99 

If the value of the test statistics is higher than the value of the rejection region, then you should reject the null hypothesis. If it is less, then you cannot reject the null. 

In this case, 2.99 > 1.645 so we reject the null. 

Importance/Benefits of Hypothesis Testing 

The most significant benefit of hypothesis testing is it allows you to evaluate the strength of your claim or assumption before implementing it in your data set. Also, hypothesis testing is the only valid method to prove that something “is or is not”. Other benefits include: 

• Hypothesis testing provides a reliable framework for making any data decisions for your population of interest. 
• It helps the researcher to successfully extrapolate data from the sample to the larger population. 
• Hypothesis testing allows the researcher to determine whether the data from the sample is statistically significant. 
• Hypothesis testing is one of the most important processes for measuring the validity and reliability of outcomes in any systematic investigation. 
• It helps to provide links to the underlying theory and specific research questions.

Criticism and Limitations of Hypothesis Testing

Several limitations of hypothesis testing can affect the quality of data you get from this process. Some of these limitations include: 

• The interpretation of a p-value for observation depends on the stopping rule and definition of multiple comparisons. This makes it difficult to calculate since the stopping rule is subject to numerous interpretations, plus “multiple comparisons” are unavoidably ambiguous. 
• Conceptual issues often arise in hypothesis testing, especially if the researcher merges Fisher and Neyman-Pearson’s methods which are conceptually distinct. 
• In an attempt to focus on the statistical significance of the data, the researcher might ignore the estimation and confirmation by repeated experiments.
• Hypothesis testing can trigger publication bias, especially when it requires statistical significance as a criterion for publication.
• When used to detect whether a difference exists between groups, hypothesis testing can trigger absurd assumptions that affect the reliability of your observation.

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Hypothesis Testing

When you conduct a piece of quantitative research, you are inevitably attempting to answer a research question or hypothesis that you have set. One method of evaluating this research question is via a process called hypothesis testing , which is sometimes also referred to as significance testing . Since there are many facets to hypothesis testing, we start with the example we refer to throughout this guide.

An example of a lecturer's dilemma

Two statistics lecturers, Sarah and Mike, think that they use the best method to teach their students. Each lecturer has 50 statistics students who are studying a graduate degree in management. In Sarah's class, students have to attend one lecture and one seminar class every week, whilst in Mike's class students only have to attend one lecture. Sarah thinks that seminars, in addition to lectures, are an important teaching method in statistics, whilst Mike believes that lectures are sufficient by themselves and thinks that students are better off solving problems by themselves in their own time. This is the first year that Sarah has given seminars, but since they take up a lot of her time, she wants to make sure that she is not wasting her time and that seminars improve her students' performance.

The research hypothesis

The first step in hypothesis testing is to set a research hypothesis. In Sarah and Mike's study, the aim is to examine the effect that two different teaching methods – providing both lectures and seminar classes (Sarah), and providing lectures by themselves (Mike) – had on the performance of Sarah's 50 students and Mike's 50 students. More specifically, they want to determine whether performance is different between the two different teaching methods. Whilst Mike is skeptical about the effectiveness of seminars, Sarah clearly believes that giving seminars in addition to lectures helps her students do better than those in Mike's class. This leads to the following research hypothesis:

Before moving onto the second step of the hypothesis testing process, we need to take you on a brief detour to explain why you need to run hypothesis testing at all. This is explained next.

Sample to population

If you have measured individuals (or any other type of "object") in a study and want to understand differences (or any other type of effect), you can simply summarize the data you have collected. For example, if Sarah and Mike wanted to know which teaching method was the best, they could simply compare the performance achieved by the two groups of students – the group of students that took lectures and seminar classes, and the group of students that took lectures by themselves – and conclude that the best method was the teaching method which resulted in the highest performance. However, this is generally of only limited appeal because the conclusions could only apply to students in this study. However, if those students were representative of all statistics students on a graduate management degree, the study would have wider appeal.

In statistics terminology, the students in the study are the sample and the larger group they represent (i.e., all statistics students on a graduate management degree) is called the population . Given that the sample of statistics students in the study are representative of a larger population of statistics students, you can use hypothesis testing to understand whether any differences or effects discovered in the study exist in the population. In layman's terms, hypothesis testing is used to establish whether a research hypothesis extends beyond those individuals examined in a single study.

Another example could be taking a sample of 200 breast cancer sufferers in order to test a new drug that is designed to eradicate this type of cancer. As much as you are interested in helping these specific 200 cancer sufferers, your real goal is to establish that the drug works in the population (i.e., all breast cancer sufferers).

As such, by taking a hypothesis testing approach, Sarah and Mike want to generalize their results to a population rather than just the students in their sample. However, in order to use hypothesis testing, you need to re-state your research hypothesis as a null and alternative hypothesis. Before you can do this, it is best to consider the process/structure involved in hypothesis testing and what you are measuring. This structure is presented on the next page .

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How to Write a Great Hypothesis

Hypothesis 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, operational definitions, types of hypotheses, hypotheses examples.

• Collecting Data

Frequently Asked Questions

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.

One hypothesis example would be a study designed to look at the relationship between sleep deprivation and test performance might have a hypothesis that states: "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."

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. It is only at this point that researchers 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 a number of 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 wisdom 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.

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.

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.

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

In order to measure this variable, the researcher must devise a measurement that assesses aggressive behavior without harming other people. In this situation, the researcher might utilize a simulated task to measure aggressiveness.

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 that there is a relationship between one independent variable and one dependent variable.
• Complex hypothesis : This type of hypothesis suggests a relationship between three or more variables, such as two independent variables and a dependent variable.
• 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 sample of the population 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."
• Complex hypothesis: "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."

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:

• "Children who receive a new reading intervention will have scores different than students who do not receive the intervention."
• "There will be no difference in scores on a memory recall task between children and adults."

Examples of an alternative hypothesis:

• "Children who receive a new reading intervention will perform better than students who did not receive the intervention."
• "Adults will perform better on a memory task than children." 

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 it would be impossible or difficult to  conduct an experiment . 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 then be used to look at how the variables are related. This type of 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.

A Word From Verywell

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.

Some examples of how to write a hypothesis include:

• "Staying up late will lead to worse test performance the next day."
• "People who consume one apple each day will visit the doctor fewer times each year."
• "Breaking study sessions up into three 20-minute sessions will lead to better test results than a single 60-minute study session."

The four parts of a hypothesis are:

• The research question
• The independent variable (IV)
• The dependent variable (DV)
• The proposed relationship between the IV and DV

Castillo M. The scientific method: a need for something better? . AJNR Am J Neuroradiol. 2013;34(9):1669-71. doi:10.3174/ajnr.A3401

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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• Fundamental Analysis

Hypothesis to Be Tested: Definition and 4 Steps for Testing with Example

What Is Hypothesis Testing?

Hypothesis testing, sometimes called significance testing, is an act in statistics whereby an analyst tests an assumption regarding a population parameter. The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis.

Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data. Such data may come from a larger population, or from a data-generating process. The word "population" will be used for both of these cases in the following descriptions.

Key Takeaways

• Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data.
• The test provides evidence concerning the plausibility of the hypothesis, given the data.
• Statistical analysts test a hypothesis by measuring and examining a random sample of the population being analyzed.
• The four steps of hypothesis testing include stating the hypotheses, formulating an analysis plan, analyzing the sample data, and analyzing the result.

How Hypothesis Testing Works

In hypothesis testing, an  analyst  tests a statistical sample, with the goal of providing evidence on the plausibility of the null hypothesis.

Statistical analysts test a hypothesis by measuring and examining a random sample of the population being analyzed. All analysts use a random population sample to test two different hypotheses: the null hypothesis and the alternative hypothesis.

The null hypothesis is usually a hypothesis of equality between population parameters; e.g., a null hypothesis may state that the population mean return is equal to zero. The alternative hypothesis is effectively the opposite of a null hypothesis (e.g., the population mean return is not equal to zero). Thus, they are mutually exclusive , and only one can be true. However, one of the two hypotheses will always be true.

The null hypothesis is a statement about a population parameter, such as the population mean, that is assumed to be true.

4 Steps of Hypothesis Testing

All hypotheses are tested using a four-step process:

• The first step is for the analyst to state the hypotheses.
• The second step is to formulate an analysis plan, which outlines how the data will be evaluated.
• The third step is to carry out the plan and analyze the sample data.
• The final step is to analyze the results and either reject the null hypothesis, or state that the null hypothesis is plausible, given the data.

Real-World Example of Hypothesis Testing

If, for example, a person wants to test that a penny has exactly a 50% chance of landing on heads, the null hypothesis would be that 50% is correct, and the alternative hypothesis would be that 50% is not correct.

Mathematically, the null hypothesis would be represented as Ho: P = 0.5. The alternative hypothesis would be denoted as "Ha" and be identical to the null hypothesis, except with the equal sign struck-through, meaning that it does not equal 50%.

A random sample of 100 coin flips is taken, and the null hypothesis is then tested. If it is found that the 100 coin flips were distributed as 40 heads and 60 tails, the analyst would assume that a penny does not have a 50% chance of landing on heads and would reject the null hypothesis and accept the alternative hypothesis.

If, on the other hand, there were 48 heads and 52 tails, then it is plausible that the coin could be fair and still produce such a result. In cases such as this where the null hypothesis is "accepted," the analyst states that the difference between the expected results (50 heads and 50 tails) and the observed results (48 heads and 52 tails) is "explainable by chance alone."

Some staticians attribute the first hypothesis tests to satirical writer John Arbuthnot in 1710, who studied male and female births in England after observing that in nearly every year, male births exceeded female births by a slight proportion. Arbuthnot calculated that the probability of this happening by chance was small, and therefore it was due to “divine providence.”

What is Hypothesis Testing?

Hypothesis testing refers to a process used by analysts to assess the plausibility of a hypothesis by using sample data. In hypothesis testing, statisticians formulate two hypotheses: the null hypothesis and the alternative hypothesis. A null hypothesis determines there is no difference between two groups or conditions, while the alternative hypothesis determines that there is a difference. Researchers evaluate the statistical significance of the test based on the probability that the null hypothesis is true.

What are the Four Key Steps Involved in Hypothesis Testing?

Hypothesis testing begins with an analyst stating two hypotheses, with only one that can be right. The analyst then formulates an analysis plan, which outlines how the data will be evaluated. Next, they move to the testing phase and analyze the sample data. Finally, the analyst analyzes the results and either rejects the null hypothesis or states that the null hypothesis is plausible, given the data.

What are the Benefits of Hypothesis Testing?

Hypothesis testing helps assess the accuracy of new ideas or theories by testing them against data. This allows researchers to determine whether the evidence supports their hypothesis, helping to avoid false claims and conclusions. Hypothesis testing also provides a framework for decision-making based on data rather than personal opinions or biases. By relying on statistical analysis, hypothesis testing helps to reduce the effects of chance and confounding variables, providing a robust framework for making informed conclusions.

What are the Limitations of Hypothesis Testing?

Hypothesis testing relies exclusively on data and doesn’t provide a comprehensive understanding of the subject being studied. Additionally, the accuracy of the results depends on the quality of the available data and the statistical methods used. Inaccurate data or inappropriate hypothesis formulation may lead to incorrect conclusions or failed tests. Hypothesis testing can also lead to errors, such as analysts either accepting or rejecting a null hypothesis when they shouldn’t have. These errors may result in false conclusions or missed opportunities to identify significant patterns or relationships in the data.

The Bottom Line

Hypothesis testing refers to a statistical process that helps researchers and/or analysts determine the reliability of a study. By using a well-formulated hypothesis and set of statistical tests, individuals or businesses can make inferences about the population that they are studying and draw conclusions based on the data presented. There are different types of hypothesis testing, each with their own set of rules and procedures. However, all hypothesis testing methods have the same four step process, which includes stating the hypotheses, formulating an analysis plan, analyzing the sample data, and analyzing the result. Hypothesis testing plays a vital part of the scientific process, helping to test assumptions and make better data-based decisions.

Sage. " Introduction to Hypothesis Testing. " Page 4.

Elder Research. " Who Invented the Null Hypothesis? "

Formplus. " Hypothesis Testing: Definition, Uses, Limitations and Examples. "

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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.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

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A Beginner’s Guide to Hypothesis Testing in Business

• 30 Mar 2021

Becoming a more data-driven decision-maker can bring several benefits to your organization, enabling you to identify new opportunities to pursue and threats to abate. Rather than allowing subjective thinking to guide your business strategy, backing your decisions with data can empower your company to become more innovative and, ultimately, profitable.

If you’re new to data-driven decision-making, you might be wondering how data translates into business strategy. The answer lies in generating a hypothesis and verifying or rejecting it based on what various forms of data tell you.

Below is a look at hypothesis testing and the role it plays in helping businesses become more data-driven.

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What Is Hypothesis Testing?

To understand what hypothesis testing is, it’s important first to understand what a hypothesis is.

A hypothesis or hypothesis statement seeks to explain why something has happened, or what might happen, under certain conditions. It can also be used to understand how different variables relate to each other. Hypotheses are often written as if-then statements; for example, “If this happens, then this will happen.”

Hypothesis testing , then, is a statistical means of testing an assumption stated in a hypothesis. While the specific methodology leveraged depends on the nature of the hypothesis and data available, hypothesis testing typically uses sample data to extrapolate insights about a larger population.

Hypothesis Testing in Business

When it comes to data-driven decision-making, there’s a certain amount of risk that can mislead a professional. This could be due to flawed thinking or observations, incomplete or inaccurate data , or the presence of unknown variables. The danger in this is that, if major strategic decisions are made based on flawed insights, it can lead to wasted resources, missed opportunities, and catastrophic outcomes.

The real value of hypothesis testing in business is that it allows professionals to test their theories and assumptions before putting them into action. This essentially allows an organization to verify its analysis is correct before committing resources to implement a broader strategy.

As one example, consider a company that wishes to launch a new marketing campaign to revitalize sales during a slow period. Doing so could be an incredibly expensive endeavor, depending on the campaign’s size and complexity. The company, therefore, may wish to test the campaign on a smaller scale to understand how it will perform.

In this example, the hypothesis that’s being tested would fall along the lines of: “If the company launches a new marketing campaign, then it will translate into an increase in sales.” It may even be possible to quantify how much of a lift in sales the company expects to see from the effort. Pending the results of the pilot campaign, the business would then know whether it makes sense to roll it out more broadly.

Related: 9 Fundamental Data Science Skills for Business Professionals

Key Considerations for Hypothesis Testing

1. alternative hypothesis and null hypothesis.

In hypothesis testing, the hypothesis that’s being tested is known as the alternative hypothesis . Often, it’s expressed as a correlation or statistical relationship between variables. The null hypothesis , on the other hand, is a statement that’s meant to show there’s no statistical relationship between the variables being tested. It’s typically the exact opposite of whatever is stated in the alternative hypothesis.

For example, consider a company’s leadership team that historically and reliably sees $12 million in monthly revenue. They want to understand if reducing the price of their services will attract more customers and, in turn, increase revenue.

In this case, the alternative hypothesis may take the form of a statement such as: “If we reduce the price of our flagship service by five percent, then we’ll see an increase in sales and realize revenues greater than $12 million in the next month.”

The null hypothesis, on the other hand, would indicate that revenues wouldn’t increase from the base of $12 million, or might even decrease.

Check out the video below about the difference between an alternative and a null hypothesis, and subscribe to our YouTube channel for more explainer content.

2. Significance Level and P-Value

Statistically speaking, if you were to run the same scenario 100 times, you’d likely receive somewhat different results each time. If you were to plot these results in a distribution plot, you’d see the most likely outcome is at the tallest point in the graph, with less likely outcomes falling to the right and left of that point.

With this in mind, imagine you’ve completed your hypothesis test and have your results, which indicate there may be a correlation between the variables you were testing. To understand your results' significance, you’ll need to identify a p-value for the test, which helps note how confident you are in the test results.

In statistics, the p-value depicts the probability that, assuming the null hypothesis is correct, you might still observe results that are at least as extreme as the results of your hypothesis test. The smaller the p-value, the more likely the alternative hypothesis is correct, and the greater the significance of your results.

3. One-Sided vs. Two-Sided Testing

When it’s time to test your hypothesis, it’s important to leverage the correct testing method. The two most common hypothesis testing methods are one-sided and two-sided tests , or one-tailed and two-tailed tests, respectively.

Typically, you’d leverage a one-sided test when you have a strong conviction about the direction of change you expect to see due to your hypothesis test. You’d leverage a two-sided test when you’re less confident in the direction of change.

4. Sampling

To perform hypothesis testing in the first place, you need to collect a sample of data to be analyzed. Depending on the question you’re seeking to answer or investigate, you might collect samples through surveys, observational studies, or experiments.

A survey involves asking a series of questions to a random population sample and recording self-reported responses.

Observational studies involve a researcher observing a sample population and collecting data as it occurs naturally, without intervention.

Finally, an experiment involves dividing a sample into multiple groups, one of which acts as the control group. For each non-control group, the variable being studied is manipulated to determine how the data collected differs from that of the control group.

Learn How to Perform Hypothesis Testing

Hypothesis testing is a complex process involving different moving pieces that can allow an organization to effectively leverage its data and inform strategic decisions.

If you’re interested in better understanding hypothesis testing and the role it can play within your organization, one option is to complete a course that focuses on the process. Doing so can lay the statistical and analytical foundation you need to succeed.

Do you want to learn more about hypothesis testing? Explore Business Analytics —one of our online business essentials courses —and download our Beginner’s Guide to Data & Analytics .

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HYPOTHESIS TESTING IN RESEARCH METHODOLOGY: A REVIEW

Hypothesis is usually considered as the principal instrument in research. It plays a major role in research. Its main function is to suggest new experiments and observations. It occupies a very small space in the thesis. A researcher cannot proceed in the research work without formulating one or more than one hypothesis. Hypothesis brings clarity, specificity and focus to a research problem. There are two types of hypothesis which are called the Null Hypothesis and the Alternative Hypothesis. There are four steps in hypothesis testing. After getting the results, the researcher tests whether the collected facts support the hypothesis formulated or not. There exist a number of statistical tools like ttest, F-test, chi-square test, D-W test, etc., to test the validity of hypothesis. Hypothesis testing shows whether the hypothesis should be accepted or rejected. It has been rightly said that “You torture the data until they confess”. This paper include the introduction, steps of hypothesis testing, function of hypothesis and testing of hypothesis.

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Fly-ash bricks are well known bricks. Fly-ash bricks are slow but surely replacing conventional clay bricks for wall constructions. It is green and environmentally friendly material. Fly ash brick is a really good option against Clay brick. It is green and environmentally friendly material. The fly ash bricks are comparatively lighter in weight and stronger and less costly than common clay bricks. Fly- ash Bricks is low value and high volume product and transporting it over long distances is uneconomical. But due to less awareness of fly ash bricks the different agencies of the construction wing using clay bricks. This research paper presents a comparison of fly-ash bricks and clay bricks. Based on Fly-ash bricks and clay bricks the data collected, Data will be collected through questionnaires and personal interviews targeting residential building and infrastructure projects. We can easily able to analysis of fly ash bricks and clay bricks by using Chi-square test through statistical methods (SPSS SOFTWARE).

Yapang Jamir

Analysis of variance (ANOVA) is the method used to compare continuous measurements to determine if the measurements are sampled from the same or different distributions. It is an analytical tool used to determine the significance of factors on measurements by looking at the relationship between a quantitative "response variable" and a proposed explanatory "factor." This method is similar to the process of comparing the statistical difference between two samples, in that it invokes the concept of hypothesis testing. Instead of comparing two samples, however, a variable is correlated with one or more explanatory factors, typically using the F-statistic. From this F-statistic, the P-value can be calculated to see if the difference is significant. For example, if the P-value is low (P-value<0.05 or P-value<0.01-this depends on desired level of significance), then there is a low probability that the two groups are the same. The method is highly versatile in that it can be used to analyze complicated systems, with numerous variables and factors. INTRODUCTION ANOVA is a quantitative research method that tests hypotheses that are made about differences between two or more means. If independent estimates of variance can be obtained from the data, ANOVA compares the means of different groups by analyzing comparisons of variance estimates. There are two models for ANOVA, the fixed effects model, and the random effects model (in the latter, the treatments are not fixed). ANOVA is a very useful technique for testing the equality of more than two means of population. The word analysis of variance is used because the technique involves first finding out the total variation among the observation in the collection data, then assigning causes of components of variation to various factors and finally drawing conclusion about the equality of means. It also used to test the significance of a regression equation as a whole i.e., whether all the equation are equal to zero. Factor analysis is the process by which a complicated system of many variables is simplified by completely defining it with a smaller number of "factors." If these factors can be studied and determined, they can be used to predict the value of the variables in a system.

This paper aimed at studying the factors that affect the academic achievement of students at the Faculty of Sciences and Humanities, Thadiq, Shaqraa University-KSA. Multinomial Logistic Regression (M. Lo.R.) was used to analyze the data. A significant relationship was found between academic achievement and the studied factors. The variables father's educational status, mother's educational status, existence of desire in the specialization (EDS), existence of somebody helps in the study, the average number of hours of revision per day has an effect on the students’ academic achievement. Nearly 56 % of student academic achievement depends upon all the fifteen studied variables. Nearly 50 % of student academic achievement depends upon the five variables that mentioned above. The results of the present study can be made use of in planning for the enhancement of a student's academic achievement. Similar studies in other faculties are needed to support the results reached in the present study.

محمدحسن فرج

This paper aims at studying the factors that affect academic achievement of the student in Faculty of Sciences and Humanities (Thadiq) -Shaqraa University-KSA. The Logistic Regression (Lo.R.) was used to analyze the data. The important result was, there is significant relationship between the academic achievement of the student on one hand and the studied factors on the other hand. In consequence of the above mentioned results, there are two discussions: The first is to conduct similar studies in the other faculties, and the second is to take the advantages of this study in the planning and improvement of student's academic rate.

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Research Article

Liking music with and without sadness: Testing the direct effect hypothesis of pleasurable negative emotion

Roles Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Resources, Validation, Visualization, Writing – original draft, Writing – review & editing

* E-mail: [email protected]

Affiliation Empirical Musicology Laboratory, School of the Arts and Media, UNSW Australia, Sydney, NSW, Australia

• Emery Schubert

• Published: April 10, 2024
• https://doi.org/10.1371/journal.pone.0299115
• Reader Comments

Negative emotion evoked in listeners of music can produce intense pleasure, but we do not fully understand why. The present study addressed the question by asking participants (n = 50) to self-select a piece of sadness-evoking music that was loved. The key part of the study asked participants to imagine that the felt sadness could be removed. Overall participants reported performing the task successfully. They also indicated that the removal of the sadness reduced their liking of the music, and 82% of participants reported that the evoked sadness also adds to the enjoyment of the music. The study provided evidence for a “Direct effect hypothesis”, which draws on the multicomponent model of emotion, where a component of the negative emotion is experienced as positive during music (and other aesthetic) experiences. Earlier evidence of a mediator, such as ‘being moved’, as the source of enjoyment was reinterpreted in light of the new findings. Instead, the present study applied a semantic overlap explanation, arguing that sadness primes emotions that share meaning with sadness, such as being-moved. The priming occurs if the overlap in meaning is sufficient. The degree of semantic overlap was defined empirically. The present study therefore suggests that mediator-based explanations need to be treated with caution both as a finding of the study, and because of analytic limitations in earlier research that are discussed in the paper.

Citation: Schubert E (2024) Liking music with and without sadness: Testing the direct effect hypothesis of pleasurable negative emotion. PLoS ONE 19(4): e0299115. https://doi.org/10.1371/journal.pone.0299115

Editor: Maja Vukadinovic, Novi Sad School of Business, SERBIA

Received: December 5, 2023; Accepted: February 5, 2024; Published: April 10, 2024

Copyright: © 2024 Emery Schubert. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: Data contain potentially identifying or sensitive participant information because open ended responses about personal experiences to music could have been reported. The decision to restrict data sharing was part of the approval given by the institutional ethics committee. The email contact for the institutional ethics advisory committee that granted approval for this design is [email protected] .

Funding: Initials of the authors who received each award: ES Grant numbers awarded to each author: FT120100053 (ES) The full name of each funder: Australian Research Council URL of each funder website: https://www.arc.gov.au/ Did the sponsors or funders play any role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript?: No.

Competing interests: The authors have declared that no competing interests exist.

Introduction

A considerable portion of the population (estimates ranging from around 25% to 50%) will report that music they love can also make them feel negative emotions such as sadness [ 1 – 6 ]. This finding has mystified researchers. How can a loved activity simultaneously produce a negative feeling, and yet lead the same individual to eagerly seek out the experience?

The Indirect effect hypothesis

Much theorising has been proposed to explain the conundrum as it applies to music listening and the contemplation of the arts in general. A dominating approach argues that the ‘sadness’ (the negative emotion that is the focus of the current investigation, and one that has received much attention) evoked by the music serves some non-negative purpose. The negative emotion is not in and of itself enjoyed. We will refer to such explanations as part of the ‘Indirect effect hypothesis’, meaning that a negative emotion such as sadness itself cannot or should not directly play a role in the generation of pleasure. The Indirect effect hypothesis is old, with written origins in Aristotle’s concept of catharsis from 4 th century BCE–where certain negative emotions in response to the arts act as a psychic cleanser, which removes bad or negative emotions from the soul [ 7 , 8 ]. The enduring concept of catharsis suggests an Indirect effect hypothesis because the negative emotion itself is not enjoyed directly. Rather, it is the cleansing, or the product of the cleansing that feels good. (Please note that in this article, the terms enjoyment, pleasure, feels-good, preferred, loved and liked are treated, more or less, as substitutable synonyms; see [ 9 ]) The negative impact of the emotion is thus compensated for by the positive effect on the soul or, in early 21 st century parlance, the mind.

A more recent version of the Indirect effect hypothesis is that sadness produces pleasure indirectly by triggering an intermediary step, sometimes referred to as a ‘mediator’. ‘Being moved’, for example, has been reported as the underlying reason for listening to otherwise sad music. Being moved can be seen as consisting of positive aspects, in addition to negative aspects [ 10 – 13 ]. It is the positive aspects of being moved that are responsible for the pleasure of the otherwise sadness-inducing music. Such explanations argue that the negative emotion occurs alongside a mediator, and so itself is not the direct cause of the positive aspects of the experience, thus eradicating the paradoxical aspect of the phenomenon.

A common technique to test the Indirect effect hypothesis is to ask participants to listen to a piece of music and rate the felt sadness and enjoyment experienced, in addition to rating the alleged mediator. If the enjoyment ratings are correlated with the mediator, and provided this correlation is overall stronger than is sadness with enjoyment, we have evidence, albeit correlational, that the mediator is the direct cause of the liking, not the sadness, supporting the Indirect effect hypothesis. To date, being moved has produced the strongest evidence of mediating sadness [ 3 , 14 – 16 ]. But other contenders that have been proposed, including beauty, wonder and nostalgia [for an overview, see 3 , 17 ].

Limitations of the Indirect effect hypothesis

An inherent weakness of Indirect effect hypothesis, and in particular the mediator-based explanation, is that it does not consider the phenomenal experience of the individual who claims that they both experience sadness, and that the sadness itself, for them, forms at least part of the pleasure [e.g., 6 ]. There are also limitations with research methods that are used to test the mediator explanation in the extant literature, as elucidated in the Method section.

Another limitation specifically concerns the mediator driven approach because it does not explain why the negative emotion would be present at all if it is the mediator that is driving the pleasure. If music is pleasurable because it is moving, and not because it evokes sadness, why would the listener not just seek the music that is moving but not sadness evoking? Is it because the mediator generates the negative (sad) emotion, as a by-product? But this would suggest that the occurrence of enjoyed negative emotion experiences such as sadness in response to music should be nothing more than an outlier, and be rarely reported as an enjoyed part of the experience (presumably well under the 25% of reports that are typical of published research, as indicated at the Introduction). Mediation theory therefore only explains why listeners claim to enjoy felt negative emotions to a limited extent. An alternative explanation is worth considering, and here the Direct effect hypothesis is proposed.

The Direct effect hypothesis

The Direct effect hypothesis argues that there is something intrinsic about felt negative emotion evoked by music that attracts the listener, without mandating a mediator or some factor outside the negative emotion itself. The presence of accompanying affects (such as being moved) are not excluded, but they are not essential. One line of research that supports this hypothesis is the link between individual differences and enjoyment of sad music. Such research does not exclude the Indirect effect account, but it does suggest that individual factors attract the listener to sadness in music, raising the possibility that there is something peculiar about some negative emotions that allow them to be enjoyed in their own right.

Strong contenders for the disposition of people who enjoy the sadness evoked by music are empathisers, fantasisers, ruminators, those who demonstrate an openness to experience, and those with a high propensity to fall into states of absorption [ 2 , 3 , 16 , 18 – 22 ]. Current thinking is that these personal characteristics, especially empathising, absorption and openness to experience, allow the individual to connect with fictional narratives while suspending disbelief, and so exhibit a good capacity to “make-believe” [ 23 , 24 ], a capacity which generalises to emotions in music listening [e.g., see 16 , 25 – 27 ]. This explanation also presents an alternative theoretical perspective to the above cited literature, because rather than presenting sadness as a mere by-product of mediation or as a means to some beneficial end, the sadness can be ‘enjoyed’ for its own sake (directly). It is not real-sadness, but a make-believe, or aesthetic, kind of sadness, still experienced as sadness, but with some real-life negative aspect of the sadness not triggered [ 28 ].

The Direct effect hypothesis has a theoretical foundation. Emotion researchers such as Frijda [ 29 ] and Scherer [ 30 ] have conceptualised emotion as consisting of multiple phases or components operating in synchrony. This view is both reflective of contemporary understandings of emotion, and defined networks in the brain. In one instantiation of a componential model, Sander, Grandjean and Scherer [ 31 ] proposed five components/networks of emotion building on Scherer’s model: ‘Expression’ (e.g., a facial expression that communicates the emotion), ‘Action Tendency’ (e.g., motivation to approach toward, or flee from the cause of the emotion), ‘Autonomic Reaction’ (e.g., changed heart rate), ‘Feeling’ (what the emotion feels-like, such as ‘I feel sadness’) and ‘Elicitation’ (the internally triggered cause of the emotion through interpretation of environmental situation, association and instinct) such as prolonged loneliness eliciting sadness.

In the case of the enjoyment of negative emotions Schubert [ 32 ] proposed that when contemplating aesthetic stimuli the Action tendency component of an emotion is experienced as positive (motivation to approach) while other components remain as they would for real-life, non-aesthetic experiences of such emotions. The individual is not compelled to act in a withdrawn or aversive manner to the stimulus or event under contemplation because the perceiver has an implicit awareness that it is presented in an aesthetic or make-believe context. This dissociated response occurs because the individual has an intrinsic understanding of the safe, make-believe context in which the causal stimulus/event is perceived [ 33 – 35 ].

Limitations of the direct effect hypothesis

The Direct effect hypothesis of enjoyment of negative emotion has arguably been difficult to test. If emotions happen to be correlated (such as sadness and being moved), researchers typically take this as an indication in favour of the Indirect effect hypothesis. But such interpretations do not exclude the possibility that the enjoyment directly stems from the sadness. While there is some evidence that those who enjoy negative emotion in music are indeed enjoying the negative emotion, there has been little systematic investigation of the experiential aspect of enjoyment of negative emotion in music. Other approaches to falsifying the Direct effect hypothesis are needed.

The approach taken in the present research is in the form of an ‘empirical thought experiment’, which has origins in so-called experimental philosophy [ 36 ]. Thought experiments, also referred to as mental simulation or ‘prefactual thinking’, rely on the participant’s capacity to imagine a situation and provide a response to that situation. The method can be particularly useful when a real-life stimulus-effect manipulation of interest is not possible or ethically compromising [e.g., 37 ]. It has been applied successfully to the empirical investigation of a range or research questions [ 38 ] and, of relevance here, to scenarios involving mental simulation of emotions [ 39 – 42 ].

Probing listeners to mentally simulate manipulating aspects of sadness induced by music is a simple approach to address both the Direct and Indirect effect hypotheses of enjoyment of experienced negative emotion in music. In brief, if a listener reports experiencing the sadness induced by a piece of music as pleasurable, the thought experiment to address the question of interest (to test if the sadness is the cause of the pleasure) is to ask the participant to imagine that the felt sadness, and only the felt sadness, can somehow be removed. If enjoyment is consequently diminished (as a result of the mentally simulated, excised sadness), the Direct effect hypothesis will be supported. Assurances would need to be set in place that the sadness was experienced (felt) and not just expressed by the music [ 43 ], and that the music was responsible for triggering the sadness, not some (extramusical) association (as discussed in the Method section).

The aim of this study was to investigate whether negative emotion in music, in this case sadness, can be both experienced and enjoyed. Two competing hypotheses were tested:

H1 –the Indirect effect hypothesis, which predicts that: Sadness removed from a liked piece of music will increase or not change enjoyment. This is because it is not the sadness that is enjoyed, but something external to the sadness, such as being moved or some other mediator.

H2 –the Direct effect hypothesis predicts that: Sadness removed from a liked piece of sadness will decrease enjoyment. This is because the sadness itself is somehow enjoyed, regardless of the impact of correlated variables (such as being moved, etc.).

Methodological and data analysis issues

This preamble to the method examines four key issues encountered in extant methods and data-analysis conventions stemming from controversy about use of experimenter- versus participant-selected stimuli. These issues are: Confounding extramusical association, Phenomenon of interest, Demand characteristics and Prospective mediators. This is followed by a discussion of problems that have emerged in experimenter-selected stimulus, and, as a result, a justification for the use of participant-selected music is then presented.

Confounding extramusical association.

There has been growing consensus that investigations of enjoyed sadness in music should be assessed through experimenter-selected music. Participant- or ‘self’-selected music has the disadvantage that the music can have personal or other non-musical associations, meaning that it is not the music that is directly responsible for triggering sadness, but previously formed, ‘extramusical’ associations with the music. Self-selected music could therefore lead to confounding extramusical associations that evoke sadness: the music acting as a mere go-between with the external cause of the sadness and the experience of sadness, and therefore potentially lead to false conclusion of negative emotion being caused by the music. Furthermore, self-selected music does not assure that findings would be generalisable to other participants who did not self-select the same piece. Self-selected music is inevitably music that is familiar. Personal meanings and associations with familiar music could well lead to idiosyncratic responses, peculiar to one or a small number of individuals [for a detailed discussion on limitations in use of familiar music, see 44 ].

Although one of the main drivers for using experimenter-selected music is to avoid confounding extramusical associations , it is possible that even for unfamiliar (experimenter-selected) music a participant will have an emotional response to music because it triggers an external factor, rather than emanating from the music itself [ 45 ]. For example, while Day and Thompson [ 46 ] found that familiar music is more successful at evoking visual imagery (and hence increasing the likelihood of extramusical emotional associations), they also observed the important role of fluency, where music that is complex (low in fluency) is more likely to trigger visual imagery than music that is less complex (high in fluency), regardless of familiarity. Furthermore, autobiographical memories have been reported to be triggered by unfamiliar music, although to a lesser extent than familiar music [ 47 , 48 , see also 49 ]. Thus experimenter-selected music can help to diminish the likelihood of data pollution through confounding extramusical associations , even if not eliminate it.

Phenomenon of interest.

Use of unfamiliar music that is rated by an independent panel, or some other means, as evoking sadness and being pleasurable has been proposed to remedy the problem of confounding extramusical association [e.g., 14 , 16 ]. However, this approach also has its shortcomings. Others deciding what music is likely to evoke sadness will not necessarily evoke sadness to a sufficient degree in a randomly sampled participant to address the phenomenon of interest (enjoyment of evoked negative emotion in music). It is well documented that familiar music can evoke stronger emotions than unfamiliar music, with self-selected music being a particularly effective way to elicit the strong emotions [e.g., 43 , 50 – 56 ]. Similarly, others deciding what music someone likes is riddled with problems. Music preference calls into play several factors such as familiarity [ 57 ], making the assumption of an absolute, objective rating of pleasure in response to a given piece of music problematic. This constitutes a considerable drawback of experimenter-selected design because additional precautions need to be taken to assure that participant experiences capture the phenomenon of interest (both strong liking and experiencing of sadness), as discussed below.

Demand characteristics.

Another problem with self-selected music is that it may attract demand characteristics bias. This bias can occur when the participant infers the research question [ 58 , 59 ]. For self-selected music the research objective can be inferred by the participant, in particular if they are asked to select music that they love that also evokes sadness. In this situation, the participant may guess that the study is concerned with enjoyment and experiencing sadness. If consciously or subconsciously they wish to please the experimenter, they may inflate their assessment of the amount of enjoyment the music generates or the amount of sadness it evokes or both. Furthermore, during participant recruiting, if mention is made that people are sought who experience sadness in response to loved music, it is self-evident that the participant pool will be biased, because only those who have the targeted experience are likely to participate, overlooking the opportunity to estimate how common the phenomenon is in a general population.

Prospective mediators.

Overall, the studies adopting experimenter-selected designs have used interval rating scale measurements of the variables of interest (enjoyment, sadness, and the prospective mediator variables, such as being moved). In addition, other variables are rated to help reduce the likelihood that the participant will successfully intuit the aim of the study, and to capture information about alternative, prospective mediators. Interval rating scales have the advantage of being convenient for correlation based data processing procedures, such as statistical mediation analysis [ 60 ].

Problems with experiment-selected designs.

Although research using experimenter-selected music designs have claimed to manage several methodological problems identified in self-selected music designs to address the current research question, as summarised above, experimenter-selected stimuli based approaches nevertheless have their own limitations (some overlapping with self-selected music approaches).

As mentioned above, experimenter-selected music is less likely to evoke strong emotions compared with self-selected music, and so it is possible that a person who is capable of experiencing intense sadness in response to loved music will not have that experience for music selected by the best-intentioned experimenter. Even with self-selected music, some studies have shown that only about one quarter to one third of participants report experiencing negative emotions such as sadness in response to music they love (see Introduction ). Schubert (6) used the self-selection approach while considerably circumventing the problem of demand characteristics. He asked participants to select a piece of music that they love, but not revealing the research interest in negative emotions. As it turned out, about one third (25/73) of the participants spontaneously reported experiencing negative emotions, with specific mention made of sadness in 12/72 (i.e., one sixth of) cases (p. 17). In that study it was not clear, however, whether the sadness emanated from the music itself, or through some confounding extramusical association . Nevertheless the method mitigated demand characteristics bias, and above all, it ensured that the piece selected was highly liked, something which experimenter-selected approaches rarely guarantee. Konečni [ 61 ] also argued that fully-fledged aesthetic experiences in response to music are rare even under regular listening circumstances. Therefore, the phenomenon of interest would occur in an even smaller proportion of cases in studies applying experimenter-selected music, even if the stimuli have been previously screened for sadness evocation and enjoyment by individuals other than the participant them/her/himself.

Another related limitation of studies using experimenter-selected pieces concerns the response format itself, which commonly employs an integer-based rating scale for each of the affective variables of interest. The problem is not the use of rating scales per se , but the tradition of publishing rating scale results. Studies typically report scale (i.e., item) mean (X) and standard deviation (SD) scores, and/or the correlation coefficient (usually the Pearson product moment coefficient, r) for pairs of variables. The chief problem with such reporting is they imply assumptions about the distribution of the responses. Providing these descriptive statistics, and in particular when the data are then applied to parametric statistical analysis procedures, infers that the distribution of the data are normal, have homogenous variance and are linear [ 62 , p. 311]. If these assumptions are taken at face value, it means that the density of responses diminish as data points are located further away from the mean, with the diminution per scale step being more rapid when the standard deviation is small. Consequently, when there is no explicit information provided about the nature of the distribution, the number of responses that meet the criterion for the phenomenon of interest could be relatively small, and risk not providing statistically sufficient power for meaningful analysis. A simple visual diagnosis can be made through scatterplots of felt sadness versus liking ratings. The decision needs to be made as to where the cut off mark is for sadness and liking scores above which count as satisfying the phenomenon of interest .

This weakness in extant research constitutes the most serious problem of the mediation-based explanation, which, to the author’s knowledge, has exclusively employed experimenter-selected stimuli and use of interval rating scales with X/SD/r reporting, assuming that any amount of sadness evoked by a piece of music should be proportionally implicated in its enjoyment. The assumption is incorrect because it asserts that a linear relationship is evidence of the phenomenon of interest . In fact, the phenomenon of interest is not concerned with enjoyed that accompanies low levels of sadness because when sadness levels are low, other reasons for enjoying the music are still perfectly viable. Evidence of this problem is reflected to some extent by the generally low correlations reported between sadness and liking scores, usually with a small effect size [r < .3, see 63 ]. When the correlation coefficient is small, no conclusion can be drawn about the phenomenon of interest because low correlation only reveals a lack of (non-zero) linearity, rather than information about the modality of the bivariate distribution. That is, a small correlation coefficient provides no information regarding the location of the mode of the distribution, or whether a desirable mode (also) exists in the high sadness, high liking region of the distribution.

In short, by not diagnosing the nature of the bivariate response distribution, the analytic approaches adopted for currently available experimenter-selected designs potentially exclude cases of high evoked sadness that accompany high liking, meaning that they have not captured the phenomenon of interest and so cannot make conclusions about it, or should do so with caution. One solution for future research employing ratings for all variables of interest while maintaining the advantages of the experimenter-selected stimuli approach is to recruit a sufficiently large random sample so that enough cases happen to fall in the desired range spontaneously. However, using self-selected music is more efficient because the phenomenon of interest is achieved by categorical self-selection.

Using self-selected stimuli–justification.

With the above arguments, the stimulus self-selection approach can be justified provided some modifications are made to the way the approach has been applied in the past. These are itemised here in six points. Based on the above overview, the main innovations to note are points 2, 3c, 3d and 4. Square bracketed text following each point indicates the main methodological issue(s) discussed above that are addressed by each of the proposed actions.

• Correspondence used for recruiting participants is not to indicate that the study is concerned with experiencing sadness in music, its enjoyment, or both [as per recommendations by 58 , 59 ]. [Demand characteristics]
• During the study, request that the participant selects music that is loved, not just liked, to ensure that the desired (high) liking category of music is attained [ 64 ]. [Phenomenon of interest]
• that the music is highly liked,
• the sadness is indeed felt,
• the sadness emanates directly from the music, and not through extramusical association, and
• the experienced sadness is implicated in the enjoyment of the music. [Confounding extramusical association; Phenomenon of interest]
• A control condition is employed, for example where instead of requesting sadness-evoking music, music evoking another emotion that is not paradoxical is requested, such as a mediator proposed in previous research. An obvious choice is moving music (that is loved). [Demand characteristics; Phenomenon of interest]
• A number of affect terms, including sadness and the control condition emotion should be added to a list of emotions rated in both test and control conditions to allow for comparison, and help identify prospective mediators. [Prospective mediators]
• Since participants are explicitly asked to have potentially powerfully sad emotions evoked, towards the end of the study an additional stimulus is rated that requires evocation of a positive emotion. This satisfies potential ethical concerns where sadness experience could influence mood negatively, and allows the option of further comparisons with affects in the test condition that were prospective mediators. [Prospective mediators]

Participants

103 participants, recruited from an English speaking tertiary institution, consisting mostly of undergraduate music students, completed the study. They were randomly assigned to one of the two conditions. Fifty participants were randomly assigned to the Sadness condition and 53 to the Moving condition in a between-subjects design. The research received ethics approval from the UNSW Australia institutional review board Human Research Advisory Panel B: Arts, Architecture, Design and Law. Participants were recruited from June 4, 2021 until June 9, 2021. Consent to participate was provided at the opening of the online survey, with a checkbox selected if the participant agreed to participate. No minors participated in the study.

The Qualtrics survey platform ( https://www.qualtrics.com ) was used for human data collection. Self-selected music was identified through online links searched for and reported within the survey by the participant. The participant used an electronic device, such as a laptop, iPad or tablet. They were encouraged to wear earphones to listen to music, but this was not enforced. Affect terms consisted of a list of terms that are drawn from Schindler, Hosoya [ 65 ] and Schubert [ 66 ], as presented in the Procedures.

Prior to commencing the study, informed consent was requested verbally through the online interface, with all participants being asked to read an online participant information sheet, which included information about being free to withdraw from the study at any time. They were informed that their data would be treated confidentially, and were encouraged to ask questions if needed, and then to indicate if they wished to commence the study. Participants were randomly assigned into a Sadness (test) or Moving (control) condition. We describe the sadness condition here, but the moving condition is identical, except that ‘sad’ and ‘sadness’ is replaced with ‘moved’/’being moved’ and ‘movingness’ (respectively). Otherwise, where grammatically straight-forward ‘[CONDITION]’ is shown, which was replaced by ‘sadness’ or ‘moved’/’being moved’, depending on the assigned condition. After the tasks for the test or control condition were completed, all participants were invited to select another piece, but this time one that made them feel happy. Although this step of the study was completed by all participants, it will be referred to as the Happy ‘condition’ for convenience. The steps of the study are listed below. They followed one another in sequence, and the participant could not return to a step once they had answered the questions in that step and progressed.

• Participants were asked to self-select a piece that they both loved and that evoked sadness. They were encouraged to think about this for a few minutes if necessary. For those who could not come up with a piece that met these criteria, some alternative pieces were proposed, from which they could select, or, have further opportunity to select another piece. Details of the piece were collected.
• Enjoyment of the piece was rated: "How much do you like this piece?” (anchors: 0 = dislike it a lot; 100 = like it a lot)
• Open-ended felt emotions requested: “Please indicate in as much detail as possible any emotions that you feel in response to this piece. Be sure to include [CONDITION], of course.” (Free text response.)
• Affects felt . 26 felt affect terms were rated on a 3-point scale (A lot, A little, Not felt) on the extent to which each terms was felt. The wording of each terms was presented to the participant as—1: Being absorbed/completely immersed in the music; 2. Anger; 3. A sense of awe; 4. Feeling of beauty; 5. Calm; 6. Chills; 7. Compassion; 8. Empathy; 9. Euphoria; 10. Fear; 11. A feeling that is sublime; 12. Goosebumps; 13. Grief; 14. Happiness; 15. Joy; 16. Being moved; 17. Nostalgia; 18. Peacefulness; 19. Powerful feelings; 20. Release or relief (sometimes referred to as ’Catharsis’); 21. Sadness; 22. Tears/wanting to cry/feeling like crying/actually crying; 23. Tenderness; 24. Transcendence; 25. Tragedy; 26. Wonder.
• Confirm felt and direct . Confirm that: Affect terms marked as present in the previous step (‘A lot’ or ‘A little’) were (a) felt and (b) that they were triggered directly by the music, not by thoughts, memories, images, etc. (Yes/No for each of (a) and (b)).
• I would like the piece a LITTLE LESS;
• It would make NO DIFFERENCE;
• I would like the piece a LITTLE MORE;
• I would like the piece a LOT MORE.
• Affects that add to liking . The same 26 Affect terms listed in step iv were rated on a 3-point scale (Adds to the pleasure, Does not add to the pleasure, Don’t know/not relevant) to assess whether the “the felt emotions add to the liking, pleasure, attraction or enjoyment”.
• Cooling down. The above procedure was repeated for a self-selected happy piece, but without any ratings of the 26 Affect terms requested (i.e. steps iv, v & vii excluded).
• Background (age, gender, music background) data were collected after which the participant was thanked and farewelled.

Some researchers, such as [ 67 , 68 ], treat the concepts of affect and emotion as distinct. In the present study the distinction is partly made for the convenience of distinguishing between participant open-ended response in step iii (emotion) versus their selection from a predetermined list of terms in steps iv, v & vii (affect). The term ‘emotion’ rather than ‘affect’ was used in all of these instruction steps because the former term was considered better understood by participants, regardless of whether referred to as emotion or affect in this article.

Data validation

Participant profile by condition..

Inferential tests demonstrated that the Sadness and Moving groups were statistically identical in terms of gender, age and years of music lessons ( Table 1 ). Also comparable across the groups was the overall rating of liking, averaging over 90 on a 0–100 scale, with upper quartiles (Q3) demonstrating a ceiling effect in both conditions which supports the use of self-selected music for generating high levels of pleasure.

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https://doi.org/10.1371/journal.pone.0299115.t001

Check that the emotion was felt and evoked emotion was directly due to the music.

There was overall high confirmation that the emotions were felt (over 96% of participants) and over 90% of participants in both conditions confirmed that the sadness was triggered intrinsically by the music (not triggered by something outside the music). See Table 1 for breakdown by condition. Overall, participants from both conditions were successful at experiencing the target emotion (Sadness or Being moved) and confirmed that, as requested, the music was directly responsible for triggering the emotion, rather than due to some extramusical factor. All participants were retained for further analysis.

Most frequently reported music excerpts.

All participants selected a piece that met the music selection criteria. Although researcher-suggested pieces were prepared in case a participant could not identify a self-selected piece meeting the criteria, none of the participants requested the researcher-suggested option, and so the research-suggested options were never used in the study. A selection of the self-selected items is presented in Table 2 , showing composers/artists reported by at least three participants across the cohort, and listing the works reported at least twice across the cohort. Interesting similarities can be observed across conditions, with composers Beethoven, Chopin and Debussy, and artists Taylor Swift and Bon Iver appearing in the Moving and Sad conditions. Furthermore, for the Beethoven, two pieces were mentioned in both of these conditions: Für Elise and Moonlight Sonata (1st Movement). These selections reflect the shared tastes across the groups, and at the high proportion of musicians, in particular pianists, who participated (all of the more frequently selected Beethoven, Chopin and Debussy pieces were for piano). Table 1 reveals the overall high average years of music lessons reported across the cohort [ 69 ]. These selections also indicate the capacity for the same piece of music to evoke different emotions (being moving and sadness).

https://doi.org/10.1371/journal.pone.0299115.t002

Emotion profile of sad music: Open-ended

After selection of a piece in their assigned condition, participants were asked to provide free descriptions of the emotions they felt in response to the selected piece (self-selected sad or self-selected moving music). The reported terms were pre-processed by identifying all reported emotion terms (participants could report more than one), correcting spelling mistakes, checking context and lemmatizing terms. This was followed by a frequency count of these terms for each condition. The target emotion was expected to be reported frequently in each condition.

Table 3 lists the emotion terms in descending order of frequency for each condition (including the Happy condition, where the same task was requested of participants in both conditions, but for a happy piece), with the most frequent words shown (down to a count of five). The selection of most frequent terms shown with an asterisk in the top rows of the table (above the horizontal cell divider) was determined by the ‘Power Fitted Elbow’ (PFE) technique that builds on word frequency distribution characteristics [ 70 – 73 ]. The expected target emotion (shown in italics font in the table) is reported most frequently in all conditions. Noteworthy is that sad was reported frequently in the Moved condition, while negative emotions were reported exclusively among the most frequently reported Sad condition emotions. Nostalgia was frequently reported in all conditions. In the Sad condition, the lemma Moved (not shown in the table) was mentioned 4 times, but was not reported frequently, according to the PFE criterion. Another interesting finding is that none of the frequently investigated mediator emotions (Being moved, in particular), appear in the most frequently reported items of the Sad condition list (sad, nostalgia, loss, melancholy and lonely). In contrast, the Moved condition did lead to frequent open-ended reporting of sadness.

https://doi.org/10.1371/journal.pone.0299115.t003

Emotion profile of sad music: Felt Affect term ratings

After open-ended responses were reported, participants were asked to indicate the extent to which each of 26 affect terms were felt when listening to the music. Again, the target affect terms were expected to be rated highest. The ratings for each affect term within and between conditions were examined.

Means for each affect term by condition are summarised in Fig 1 . Ratings of the same affect term between conditions were analysed using Bonferroni adjusted independent samples t-tests. Felt sadness was rated higher in the Sad condition, but (non-significantly) higher ratings were given to felt Power, Moved and Absorption ratings in the Sad condition. For the Moved condition the affect term Being moved was rated as the second highest scale (second to Absorption), and the rating was statistically the same as for the rating of Being Moved in the Sad condition. Other differences within and across the two conditions can be observed in Fig 1 . Differences for within conditions are not shown because of the large number that were significantly different at p = .05. The highest scoring (with mean rating in at least one condition > 1.5) affect terms were Absorption, Awe, Beauty, Moved, Power, and Sadness.

https://doi.org/10.1371/journal.pone.0299115.g001

In these data, a relatively high rating of Being moved can be observed in the Sad condition, and it received a higher rating than the target emotion (Sadness) by M = .122, though non-significantly (p = 1.0), which could be taken to support the action of a mediator, being moved, as responsible for the pleasure generated by the music, despite the accompanying rating of sadness.

Affects that add to enjoyment

The above results indicate the presence of emotion during the enjoyable music experience. However this does not necessarily confirm that the emotion itself is implicated in the enjoyment of the music. The next step of the study addressed this with an explicit question about the contribution of each affect term to the enjoyment of the music. The 26 Affect terms were presented again this time to be classified as contributing, not contributing, or being irrelevant to the enjoyment of the music. Table 4 lists the counts across each of the three possibilities for each Affect term, by Condition. Chi-Square tests identified whether the Affect words add to enjoyment of the music by chance or not.

https://doi.org/10.1371/journal.pone.0299115.t004

Significant Chi-square test statistics (at p = .05 with Bonferroni correction) ranged from 15.500 (Fear) to 83.400 (Absorption) for the Moving condition and 14.596 (Fear) to 82.383 (Being moved) for the Sad condition (at p = .05). Chi-Squared tests for Sad and Moving conditions pooled produced statistically significant results for all emotions at p = .05 with Bonferroni correction, ranging from χ 2 = 13.273 (Tragedy) to 158.606 (Being Moved), with second highest χ 2 = 156.85 (for Absorption) and third highest χ 2 = 84.061 (for Sadness).

Self-selected sad music was associated with good likelihood of reporting felt sadness as adding to the pleasure of the experience (83% of response in the Sad condition versus 71% in the Moving condition). The same applies for the affect term rating of Being moved in the Moving condition.

All emotions contributed to the enjoyment of the self-selected music, with the exception of Anger, Fear, Tragedy (both conditions for each, though Tragedy was approaching significance), Grief (Moving condition), Euphoria, Sublime, Happiness, Joy, Peacefulness and Wonder (Sad condition for each). Absorption and Being Moved made the most consistently positive contribution to enjoyment of music, with each being reported as contributing to enjoyment by 90% or more of participants regardless of condition ( Table 4 ).

Fewer nominally negative emotions add to enjoyment in the Moving condition, whereas fewer positive emotions add to enjoyment in the Sad condition. Sadness and crying are emotions with nominally negative connotations, but were reported as adding to the pleasure, regardless of the condition.

Additional emotions that add to liking

The 26 Affect terms might not have exhaustively covered all the emotions that could be experienced, or enjoyed. Therefore, a final question invited participants to list any other emotions that added to the enjoyment of the music.

Only one expression was reported by different participants more than once—Hopelessness (3 independent mentions, one in the Moving condition). 72 participants indicated that no additional emotions contributed to enjoyment (36 in the Moving condition and 36 in the Sad condition). A higher proportion of participants who did report additional emotions mentioned ones that could be interpreted as negative in the Sad condition compared to the Moving condition, but because of the heterogeneity of the responses, which included some words that were already among the 26 Affect terms, no strong conclusion can be drawn, except that the set of Affect terms was effective in identifying the feelings implicated in pleasurable musical experiences.

Hypothesis test–Sadness is liked because the music is sad

For the responses to the Sadness removed step, the following scoring was applied to responses: -2 for ‘I would like the piece a LOT LESS’, -1 for ‘I would like the piece a LITTLE LESS’, 1 for ‘I would like the piece a LITTLE MORE’, 2 for ‘I would like the piece a LOT MORE’, and 0 for NO DIFFERENCE. If the Direct effect hypothesis is supported, we would expect liking to reduce when sadness is removed from the experience. The Indirect effect hypothesis, on the other hand, predicts that removal of sadness would not change liking (change of 0) or increase liking. A single sample t-test supported the Direct effect hypothesis, with an overall reduction of .83 (SD = .916) in liking on the scale of -2 to +2 (t(46) = -.6.207, p < .001, Cohen’s-d = .916). For comparison, in the control condition, removal of movingness also led to a reduction in liking (M = -.77, SD = .807, t(51) = -.6872, p < .001, Cohen’s-d = .807). Taken together the data from this step of the study supports the Direct effect hypothesis.

Based on an overall interpretation of the data, the Direct effect hypothesis is supported. In the specific part of the study that tested the hypothesis, the Sadness removed step, participants reported overall significant reduction in pleasure if the felt sadness, and only the felt sadness evoked by the music, were excised. If sadness were not in itself enjoyed, we may have expected participants to attribute non-sad emotions to the enjoyment, or be unable to perform the task. As it turned out, we can confirm that 83% of participants could perform the task and verify that the sadness was specifically enjoyed, suggesting that the phenomenon of interest is empirically demonstrable. To further ascertain if this is a plausible interpretation, the results are interpreted through the alternative, Indirect effect hypothesis, lens by examining whether mediators still play a commensurate or dominant role in the effect.

Mediation explanation

In the results where affect terms were all rated, a term can be viewed as a mediator if its score or count is statistically equal to or higher than the score or count of the target emotion. Based on this criterion, several steps of the study could be interpreted as supporting the presence of a mediator. In the Open-ended felt emotions step Nostalgia, a prospective mediator of sadness-enjoyment, was spontaneously reported ( Table 3 ). However, Being moved was not, despite previous evidence that Being moved is the stronger candidate of the two [ 15 ]. Nostalgia appeared frequently in the Moved condition as well, but in the Moved condition no mediator was expected because the target emotion (being moved) itself already contained an implicitly positive component. Furthermore, Sadness was also frequently reported in the Moved condition, but, again, there is no reason that being moved would require a mediator. The Indirect effect hypothesis does not predict a mediator that is itself negatively valenced. Thus a mediator based explanation for these results is not straight forward.

In the Affects felt step a more credible impact of prospective mediators can be observed. In the Sad condition, Absorbed (rated highest, with M = 1.796), Being moved (rated higher than Sadness by M = .122, though non-significantly [NS], p = 1.0) and Powerful feelings (rated higher than Sadness by M = 0.020, NS p = 1.0) are all rated as high or higher than the target emotion (Sadness). In the Moved condition only Absorbed (M = 1.942) is rated higher than Being moved (by M = .135, NS p = .074). If we set aside the finding for the Moved condition, the mediator-based explanation is supported, triangulating extant evidence that two of these affects (absorbed and moved) are mediators of sadness.

So it is possible to find support for the Indirect-effect hypothesis, and the mediator-based explanation in particular. However, the findings refer to the presence of emotions. There is no assurance that any of the emotions identified are adding to the pleasure, with the exception of the target emotion, since that requirement was made explicit in the procedure.

The Affects that add to liking step addressed the matter. Being moved, Absorption, and Powerful feelings (but not Nostalgia) all had the same or higher counts than the target (Sadness) emotion, indicating that they add to enjoyment in the Sad condition ( Table 4 ). For example, the affect term Being moved was voted as ’adding to pleasure’ by 96% of participants in the Sad condition, compared to the affect term Sadness ’adding to pleasure’ according to 83% of participants. This supports the Indirect effect hypothesis ( Table 4 ).

Here we have the strongest evidence of mediators in explaining enjoyment of sadness, and this aligns with evidence from previous research [as discussed in the introduction, see 17 ]. But Absorption (adds to pleasure according to 92% of participants) also has a higher count than the target emotion (90%) in the Moved condition. Does that mean that Absorption also mediates Being moved? As pointed out above, that seems unlikely because Being moved already contains a positive aspect, and so should not need a mediator. Using the mediator-based explanation, Absorption adding to enjoyment votes should have (at least) been fewer than the votes for Being moved in the Moving condition (which was not the case). Furthermore, in the Sadness condition, the target emotion itself received statistically significant votes as adding to pleasure, meaning that the alleged mediators may not have served any essential purpose in contributing to the enjoyment. The mediation explanation is only able to partially explain the results. An alternative explanation is proposed by applying the concept of ‘semantic overlap’.

Semantic overlap explanation

Semantic overlap is a phenomenon concerned with the mental organisation of concepts and word meanings. Words with similar meanings (synonyms) are more linked with one another in a mental space than words with unrelated meanings. This is often characterised in network inspired models of the mind, foundationally proposed by Quillian and the notion of the semantic network [ 74 , 75 ]. Word meanings are organised in a complex yet systematic manner according to network principles, of particular interest here being through similarities in the meaning of words, where expressions that are more similar in meaning appear ‘closer together’ in the mental network. This means that when a word is triggered (e.g., heard or read), the semantically more closely related words are more primed (ready to be raised to conscious attention) in the mental network than less closely related words. Cognitive linguists by and large agree that words are pointers or approximate representations of concepts and experiences stored in memory [ 76 , 77 ]. The implication is that words can be mapped onto points in multidimensional semantic space, with distance between words reflecting (of interest here) degree of conceptual dissimilarity between the words. Considerable effort has been devoted to organising emotions by similarity [e.g., 78 – 83 ]. Semantic distance may therefore explain why Being moved frequently appears for sad evoking music (a frequently reported result), and the novel findings identified in the present study.

It is possible to estimate the relative semantic distance between the two words moving and sadness by looking up the terms in a published list of words with quantified point estimates of locations in theoretical semantic space. A large such database was developed by Mohammad [ 82 ], where estimates of location in semantic space of some 20,000 English words were produced. The semantic space in that research adopts a conventional representation of the space, particularly relevant for emotions, referred to as ‘VAD’ space. Emotions can be reasonably well expressed in terms of two dimensions, labelled valence (V) and arousal (A), where the former refers to the positive or negative aspect of the word’s meaning (e.g., happy and calm exhibit positive valence, while sad and angry negative) and the degree of activity associated with the word’s meaning (e.g., joyous and furious are high arousal, while calm and sad are low arousal). Some have argued that two dimensions are only partially sufficient for describing the meaning of an emotion [ 81 , 84 – 87 ], and a frequently proposed third dimension is dominance (D) (where words such as angry and energetic exhibit high dominance, while fear and innocuous are low in dominance), leading to the VAD (Valence, Arousal, Dominance) abbreviation for this three dimensional configuration [other examples: 85 , 88 , for a review, see 89 , 90 ]. Mohammad (82) provided numerical VAD scores for each term scaled to a score between 0 and 1 (negative to positive for valence, low to high for arousal and for dominance) based on human ratings. From these data it is possible to estimate the semantic distance between emotions.

Through calculations using the VAD word list published by Mohammad (82), Moved and Sadness have a semantic distance in VAD space of 0.607 units (numbers closer to 0 indicating greater similarity). With Sadness as the reference, positive emotions appearing in the Affect term list have distances that range from 0.852 for Calm to 1.243 for Joy (all greater than the distance between Sadness and Moving), while negative emotions have scores ranging from 0.469 for Grief (closest negative emotion to Sadness from the Affect terms presented) to 0.768 (Anger), which apart from Anger are all closer to Sadness than Moving is to Sadness. That is, Moving has more semantic overlap with Sadness than does Anger and the positive emotions Joy and Happiness, suggesting semantic overlap as a viable alternative to mediation as to why being moved appears in tandem with sadness. The VAD data also suggest that Moving is semantically more closely related to Sadness than Catharsis, since Catharsis has a distance of 0.633 from Sadness (slightly more distant than Moving). High ratings of Moving for a Sad-evoking context can therefore be explained by semantic overlap. Such an interpretation strengthens the case for supporting the Direct effect hypothesis, because being moved need not be treated as surrogate for sadness.

The Direct effect hypothesis proposes that pleasure is experienced by contextualised re-appraisal or ‘dissociation’ of the Action tendency component of an otherwise negative emotion. The consequent positive experience (enjoyment, pleasure, preference) provides another clue for the remaining Affect terms that were rated the same or higher than the target emotion in each condition. The mediation account fails to explain why Sadness was voted (by 71% of participant) as adding to enjoyment in the Moving condition. The mediator based explanation is also poor at explaining why Absorption was reported as adding to enjoyment, and for doing so in both conditions.

The semantic overlap approach can better explain these results, too. Affect terms such as Absorption and Powerful feelings are affects related to enjoyment when experiencing art. Consider the Absorption in Music scale developed by Sandstrom and Russo [ 91 ]. The 34 item scale contains several items related to the pleasure of being engaged with music in different ways [see also 2 , 18 , 92 , 93 ]. Powerful experiences are reported during special, personal experiences that occur during strong positive aesthetic experiences [ 94 – 96 , p. xiv]. That is, the task itself, of identifying a loved piece of music, also produces semantic overlap of these terms. Furthermore, in the Sad condition several positive emotions were reported more frequently as having no relevance to enjoyment, in comparison to the Moved condition: Euphoria (57% in the Sad condition versus 15% in the Moving condition), Happiness (43% vs 8%) and Joy (49% vs 12%). Mediation struggles to explain why purely positive affect terms are not voted as adding to enjoyment. Semantic overlap, on the other hand, suggests that the activation of sadness is more likely to be associated with other negative emotions, while being moved would be more associated with emotions of both positive and negative valence. In addition to the possibly misleading interpretations of enjoyed-sadness in music research employing a mediator-based approach to explaining the phenomenon, discussed in the Method section, semantic overlap offers an explanation of the results that is superior to the mediator-based explanation.

Conclusions

This study investigated whether the experience of sadness, evoked by music, can itself be highly enjoyable. A novel method was applied where participants were asked to imagine how enjoyment would be impacted should the felt sadness somehow be removed. The results demonstrated that sadness is directly implicated in the enjoyment of such music, providing support for the ‘Direct effect hypothesis’. This hypothesis states that when sad music is enjoyed, the sadness itself directly contributes to the enjoyment. A theoretical position has been presumed by the hypothesis–that the experience of sadness contains a component that can be dissociated from regular experience of the negative emotion when contemplating music or any aesthetic event. The presence of emotions such as being moved were explained by the concept of semantic overlap, where an emotion concept is not activated as a lexical singular, but rather as the meaning that the emotion encompasses, or that is spread to other related emotions, according to how similar they are (in this case to the concept of sadness). Being moved is sufficiently close in meaning to sadness to allow it to be activated during a sadness evoking music experience, regardless of the extent to which it is enjoyed, meaning that the presence of an emotion such as being moved does not necessarily explain (and is not needed to explain) why felt sadness can be enjoyed. Absorption is another affect that accompanied loved, sadness-inducing music. This, too, was explained by semantic overlap, with the positive component of the sadness activating other, reasonably nearby, positive affects, including Absorption. The state of absorption may also play a causal role in attraction to music [ 20 , 97 ], and so there could well be some feedback loop between absorption and other aspects of the experience, including evoked emotions. Suggestions were made for further research to test whether the semantic overlap account and the Direct effect hypothesis better characterise enjoyment of negative emotion in music than mediators (such as being moved and absorption) that themselves have a positive component, through which enjoyment is indirectly generated.

The results of the present study were enhanced by applying a modified version of research using self-selected stimuli that minimised demand characteristics, while ensuring that the phenomenon of interest was investigated. Methodologically, the study took the critical step of ensuring that the impact of particular affects on enjoyment of the music were investigated, not just their presence. Future research is likely to continue the more popular method of using experimenter-selected stimuli which are then rated along various affect terms. This paper made recommendations on how such research could be more successful at identifying the phenomenon of interest, and in so doing better address the debate on the enjoyment of felt sadness and other felt negative emotions in music.

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