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• How to Write a Strong Hypothesis | Steps & Examples

How to Write a Strong Hypothesis | Steps & Examples

Published on May 6, 2022 by Shona McCombes . Revised on November 20, 2023.

A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection .

Example: Hypothesis

Daily apple consumption leads to fewer doctor’s visits.

Table of contents

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, other interesting articles, frequently asked questions about writing hypotheses.

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).

Variables in hypotheses

Hypotheses propose a relationship between two or more types of variables .

• An independent variable is something the researcher changes or controls.
• A dependent variable is something the researcher observes and measures.

If there are any control variables , extraneous variables , or confounding variables , be sure to jot those down as you go to minimize the chances that research bias  will affect your results.

In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .

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Step 1. Ask a question

Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.

Step 2. Do some preliminary research

Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.

At this stage, you might construct a conceptual framework to ensure that you’re embarking on a relevant topic . This can also help you identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalize more complex constructs.

Step 3. Formulate your hypothesis

Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.

4. Refine your hypothesis

You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:

• The relevant variables
• The specific group being studied
• The predicted outcome of the experiment or analysis

5. Phrase your hypothesis in three ways

To identify the variables, you can write a simple prediction in  if…then form. The first part of the sentence states the independent variable and the second part states the dependent variable.

In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.

If you are comparing two groups, the hypothesis can state what difference you expect to find between them.

6. Write a null hypothesis

If your research involves statistical hypothesis testing , you will also have to write a null hypothesis . The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .

• H 0 : The number of lectures attended by first-year students has no effect on their final exam scores.
• H 1 : The number of lectures attended by first-year students has a positive effect on their final exam scores.

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

• Sampling methods
• Simple random sampling
• Stratified sampling
• Cluster sampling
• Likert scales
• Reproducibility

 Statistics

• Null hypothesis
• Statistical power
• Probability distribution
• Effect size
• Poisson distribution

Research bias

• Optimism bias
• Cognitive bias
• Implicit bias
• Hawthorne effect
• Anchoring bias
• Explicit bias

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.

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.

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Essentials Of Statistics For The Behavioral Sciences

Frederick j gravetter, larry b. wallnau, lori-ann b. forzano, james e. witnauer, introduction to hypothesis testing - all with video answers.

Chapter Questions

Does a hypothesis test allow a researcher to claim that an alternative hypothesis is true? Explain your answer.

Identify the four steps of a hypothesis test as presented in this chapter.

Suppose that a researcher is interested in the effect of a new college preparation course on scores for a standardized critical thinking test with a population mean of $\mu=20$. Students receive training in the course and later receive the standardized test. The researcher wants to test the hypothesis that the course affected test scores. a. In words, state the null and alternative hypotheses as they relate to the treatment in this example. b. Use symbols to state the null and alternative hypothesis.

Define the alpha level and the critical region for a hypothesis test.

Define a Type I error and a Type II error and explain the consequences of each. Which type of error is worse? Why?

If the alpha level is changed from $\alpha=.05$ to $\alpha=.01$ : a. What happens to the boundaries for the critical region? b. What happens to the probability of a Type I error?

Explain how each of the following influences the value of the $z$-score in a hypothesis test. a. Increasing the size of the treatment effect. b. Increasing the population standard deviation. c. Increasing the number of scores in the sample.

According to the CDC (2016), the average life expectancy of someone with diabetes is $\mu=72$ years, $\sigma=14$. Suppose that a sample of $n=64$ people diagnosed with diabetes who received a blood glucose monitoring implant had an average life expectancy of $M=76$ years. Test the hypothesis that the glucose monitoring implant changes life expectancy. Assume a two-tailed test, $\alpha=.05$.

The National Study of Student Engagement (Indiana University, 2018) reports that the average, full-time college senior in the United States spends only $\mu=15, \sigma=9$, hours per week preparing for classes by reading, doing homework, studying, etc. A state university develops a program that is designed to increase student motivation to study. A sample of $n=36$ students completes the program and later reports that they spend $M=18$ hours per week studying. The university would like to test whether the program increased time spent preparing for class. a. Assuming a two-tailed test, state the null and alternative hypotheses in a sentence that includes the two variables being examined. b. Using the standard four-step procedure, conduct a two-tailed hypothesis test with $\alpha=.05$ to evaluate the effect of the program.

The personality characteristics of business leaders (e.g., CEOs) are related to the operations of the businesses that they lead (Oreg \& Berson, 2018). Traits like openness to experience are related to positive financial outcomes and other traits are related to negative financial outcomes for their businesses. Suppose that a board of directors is interested in evaluating the personality of their leadership. Among a sample of $n=16$ managers, the sample mean of the openness to experiences dimension of personality was $M=4.50$. Assuming that $\mu=4.24$ and $\sigma=1.05$ (Cobb-Clark \& Schurer, 2012), use a two-tailed hypothesis test with $\alpha=.05$ to test the hypothesis that this company's business leaders' openness to experience is different from the population.

Ackerman and Goldsmith (2011) report that students who study from a screen (smartphone, tablet, or computer) tended to have lower quiz scores than students who studied the same material from printed pages. To test this finding, a professor identifies a sample of $n=16$ students who used the electronic version of the course textbook and determines that this sample had an average score of $M=72.5$ on the final exam. During the previous three years, the final exam scores for the general population of students taking the course averaged $\mu=77$ with a standard deviation of $\sigma=8$ and formed a roughly normal distribution. The professor would like to use the sample to determine whether students studying from an electronic screen had exam scores that are significantly different from those for the general population. a. Assuming a two-tailed test, state the null and alternative hypotheses in a sentence that includes the two variables being examined. b. Using the standard four-step procedure, conduct a two-tailed hypothesis test with $\alpha=.05$ to evaluate the effect of studying from an electronic screen.

Childhood participation in sports, cultural groups, and youth groups appears to be related to improved self-esteem for adolescents (McGee, Williams, Howden-Chapman, Martin, \& Kawachi, 2006). In a representative study, a sample of $n=100$ adolescents with a history of group participation is given a standardized self-esteem questionnaire. For the general population of adolescents, scores on this questionnaire form a normal distribution with a mean of $\mu=50$ and a standard deviation of $\sigma=15$. The sample of groupparticipation adolescents had an average of $M=53.8$. a. Does this sample provide enough evidence to conclude that self-esteem scores for these adolescents are significantly different from those of the general population? Use a two-tailed test with $\alpha=.05$. b. Compute Cohen's $d$ to measure the size of the difference. c. Write a sentence describing the outcome of the hypothesis test and the measure of effect size as it would appear in a research report.

A random sample is selected from a normal population with a mean of $\mu=20$ and a standard deviation of $\sigma=10$. After a treatment is administered to the individuals in the sample, the sample mean is found to be $M=25$. a. If the sample consists of $n=25$ scores, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with $\alpha=.05$. b. If the sample consists of $n=4$ scores, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with $\alpha=.05$. c. Comparing your answers for parts a and b, explain how the size of the sample influences the outcome of a hypothesis test.

A random sample of $n=9$ scores is selected from a normal population with a mean of $\mu=100$. After a treatment is administered to the individuals in the sample, the sample mean is found to be $M=106$. a. If the population standard deviation is $\sigma=10$, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with $\alpha=.05$. b. Repeat part a, assuming a one-tailed test with $\alpha=.05$. c. If the population standard deviation is $\sigma=12$, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with $\alpha=.05$. d. Repeat part c, assuming a one-tailed test with $\alpha=.05$. e. Comparing your answers for parts a through d, explain how the magnitude of the standard deviation and the number of tails in the hypothesis influence the outcome of a hypothesis test.

A random sample is selected from a normal population with a mean of $\mu=40$ and a standard deviation of $\sigma=10$. After a treatment is administered to the individuals in the sample, the sample mean is found to be $M=46$. a. How large a sample is necessary for this sample mean to be statistically significant? Assume a twotailed test with $\alpha=.05$. b. If the sample mean were $M=43$, what sample size is needed to be significant for a two-tailed test with $\alpha=.05$ ?

Researchers at a weather center in the northeastern United States recorded the number of $90^{\circ}$ Fahrenheit days each year since records first started in 1875 . The numbers form a normal-shaped distribution with a mean of $\mu=9.6$ and a standard deviation of $\sigma=1.9$. To see if the data showed any evidence of global warming, they also computed the mean number of $90^{\circ}$ days for the most recent $n=4$ years and obtained $M=12.25$. Do the data indicate that the past four years have had significantly more $90^{\circ}$ days than would be expected for a random sample from this population? Use a one-tailed test with $\alpha=.05$.

A high school teacher has designed a new course intended to help students prepare for the mathematics section of the SAT. A sample of $n=20$ students is recruited for the course and, at the end of the year, each student takes the SAT. The average score for this sample is $M=562$. For the general population, scores on the SAT are standardized to form a normal distribution with $\mu=500$ and $\sigma=100$. a. Can the teacher conclude that students who take the course score significantly higher than the general population? Use a one-tailed test with $\alpha=.01$. b. Compute Cohen's $d$ to estimate the size of the effect. c. Write a sentence demonstrating how the results of the hypothesis test and the measure of effect size would appear in a research report.

Screen time and use of social media are related to negative mental health outcomes, including suicidal thoughts (Twenge, Joiner, Rogers, \& Martin, 2018). In a national survey of adolescents, the mean number of depressive symptoms was $\mu=2.06, \sigma=1.00$. Suppose that a researcher recruits $n=25$ participants and instructs them to visit friends or family instead of using social media. The researcher observes that the average number of depressive symptoms is $M=1.66$ after the intervention. a. Test the hypothesis that the treatment reduced the number of depressive symptoms. Use a one-tailed test with $\alpha=.05$. b. If the researcher wants to reduce the likelihood of a Type 1 error, what should they do? c. Compute Cohen's $d$ to estimate the size of the effect. d. Write a sentence demonstrating how the results of the hypothesis test and the measure of effect size would appear in a research report.

Suppose that a treatment effect increases both the mean and the standard deviation of a measurement. Can a hypothesis test with $z$ be conducted? Explain your answer.

After examining over one million online restaurant reviews and the associated weather conditions, Bakhshi, Kanuparthy, and Gilbert (2014) reported significantly higher ratings during moderate weather compared to very hot or very cold conditions. To verify this result, a researcher collected a sample of $n=25$ reviews of local restaurants over an unusually hot period during July and August and obtained an average rating of $M=7.29$. The complete set of reviews during the previous year averaged $\mu=7.52$ with a standard deviation of $\sigma=0.60$. a. Can the researcher conclude that reviews during hot weather are significantly lower than the general population average? Use a one-tailed test with $\alpha=.05$. b. Compute Cohen's $d$ to measure effect size for this study. c. Write a sentence demonstrating how the outcome of the hypothesis test and the measure of effect size would appear in a research report.

A researcher is evaluating the influence of a treatment using a sample selected from a normally distributed population with a mean of $\mu=50$ and a standard deviation of $\sigma=10$. The researcher expects $a+5$-point treatment effect and plans to use a two-tailed hypothesis test with $\alpha=.05$. a. Compute the power of the test if the researcher uses a sample of $n=4$ individuals (see Example 8.6). b. Compute the power of the test if the researcher uses a sample of $n=25$ individuals.

Telles, Singh, and Balkrishna (2012) reported that yoga training improves finger dexterity. Suppose that a researcher conducts an experiment evaluating the effect of yoga on standardized O'Conner finger dexterity test scores. A sample of $n=4$ participants is selected, and each person receives yoga training before being tested on a standardized dexterity task. Suppose that for the regular population, scores on the dexterity task form a normal distribution with $\mu=50$ and $\sigma=8$. The treatment is expected to increase scores on the test by an average of 3 points. a. If the researcher uses a two-tailed test with $\alpha=.05$, what is the power of the hypothesis test? b. Again, assuming a two-tailed test with $\alpha=.05$, what is the power of the hypothesis test if the sample size were increased to $n=64$ ?

Research has shown that IQ scores have been increasing for years (Flynn, 1984, 1999). The phenomenon is called the Flynn effect and the data indicate that the increase appears to average about 7 points per decade. To examine this effect, a researcher obtains an IQ test with instructions for scoring from 10 years ago and plans to administer the test to a sample of $n=25$ of today's high school students. Ten years ago, the scores on this IQ test produced a standardized distribution with a mean of $\mu=100$ and a standard deviation $\sigma=15$. If there actually has been a 7-point increase in the average IQ during the past ten years, then find the power of the hypothesis test for each of the following. a. The researcher uses a two-tailed hypothesis test with $\alpha=.05$ to determine whether the data indicate a significant change in IQ over the past 10 years. b. The researcher uses a two-tailed hypothesis test with $\alpha=.01$ to determine whether the data indicate a significant increase in IQ over the past 10 years.

Explain how the power of a hypothesis test is influenced by each of the following. Assume that all other factors are held constant. a. Increasing the alpha level from .01 to .05 . b. Changing from a one-tailed test to a two-tailed test. c. Increasing effect size.

Suppose that a researcher is interested in the effect of an exercise program on body weight among men. The researcher expects a treatment effect of 3 pounds after 15 weeks of exercise in the exercise program. In the population, the mean adult body weight for men is $\mu=$ 195.5 pounds, $\sigma=42.0$. For all of the following, assume that $\alpha=.05$, two-tailed. a. State the null and alternative hypotheses using symbols. b. Compute the power of the hypothesis test for a sample $n=2,500$. c. Imagine that the researcher observes a sample mean of $M=192.1$ pounds in a sample of $n=2,500$ participants. Test the hypothesis that the exercise program reduced body weight. Compute Cohen's $d$. d. Repeat part $\mathrm{c}$ with a sample of $n=25$. e. Compute Cohen's $d$ for the results of parts $\mathrm{c}$ and $\mathrm{d}$. Describe the distinction between effect size and statistical significance in these hypothetical studies.