The first step in conducting a hypothesis test is to write the hypothesis statements that are going to be tested. For each test you will have a null hypothesis (H0) and an alternative hypothesis (Ha).

How to conduct a hypothesis test

A hypothesis is a statement that proposes a relationship between variables or an explanation for a phenomenon. It is an essential part of the scientific method and is used to guide the research process. Here are the steps for writing a hypothesis:

1. Identify the research question: Before writing a hypothesis, you need to identify the research question you want to answer.
2. State the null hypothesis: The null hypothesis (H0) is the default assumption that there is no significant difference or relationship between variables. It is usually stated first and is used to compare against the alternative hypothesis (Ha).
3. State the alternative hypothesis: The alternative hypothesis (Ha) is the opposite of the null hypothesis and proposes a specific relationship or difference between variables.
4. Determine the type of hypothesis: There are two types of hypotheses: directional and nondirectional. A directional hypothesis predicts the direction of the relationship or difference between variables (e.g., “increased exercise will result in decreased body weight”). A nondirectional hypothesis does not predict the direction of the relationship or difference (e.g., “there will be a difference in body weight between the exercise group and the control group”).
5. Make sure your hypothesis is testable: A hypothesis must be testable and falsifiable through empirical evidence.

6. Refine and revise the hypothesis: After stating the hypothesis, refine and revise it based on feedback and further research.

 

Example of a hypothesis

Research question: Does sleep affect memory consolidation?

Null hypothesis: There is no significant difference in memory consolidation between individuals who sleep for 8 hours versus those who sleep for 4 hours.

Alternative hypothesis: Individuals who sleep for 8 hours will have better memory consolidation than those who sleep for 4 hours.

Type of hypothesis: Directional

This hypothesis could be tested through an experimental study in which participants are randomly assigned to either an 8-hour or 4-hour sleep condition and then tested on a memory task. The results could be analyzed to determine if there is a significant difference in memory consolidation between the two conditions.

So, now we know that When writing hypotheses there are three things that we need to know:

• (1) the parameter that we are testing
• (2) the direction of the test (non-directional, right-tailed or left-tailed), and
• (3) the value of the hypothesized parameter.

Now you know that, when writing hypotheses there are three things that we need to know: (1) the parameter that we are testing (2) the direction of the test (non-directional, right-tailed or left-tailed), and (3) the value of the hypothesized parameter.

• We can write hypotheses for a single mean (µ), paired means(µd), a single proportion (p), the difference between two independent means (µ1-µ2), the difference between two proportions (p1-p2), a simple linear regression slope (β), and a correlation (ρ).
• The research question will give us the information necessary to determine if the test is two-tailed (e.g., “different from,” “not equal to”), right-tailed (e.g., “greater than,” “more than”), or left-tailed (e.g., “less than,” “fewer than”).
• The research question will also give us the hypothesized parameter value. This is the number that goes in the hypothesis statements (i.e., µ0 and p0). For the difference between two groups, regression, and correlation, this value is typically 0.

One Group Mean

 

1. Null Hypothesis: The population mean is equal to a specific value. Alternative Hypothesis: The population mean is not equal to a specific value. Example: H0: µ = 50, Ha: µ ≠ 50
2. Null Hypothesis: The population mean is less than or equal to a specific value. Alternative Hypothesis: The population mean is greater than a specific value. Example: H0: µ ≤ 10, Ha: µ > 10
3. Null Hypothesis: The population mean is greater than or equal to a specific value. Alternative Hypothesis: The population mean is less than a specific value. Example: H0: µ ≥ 80, Ha: µ < 80

Paired Means

1. Null Hypothesis: The mean difference between two paired samples is equal to zero. Alternative Hypothesis: The mean difference between two paired samples is not equal to zero. Example: H0: µd = 0, Ha: µd ≠ 0
2. Null Hypothesis: The mean difference between two paired samples is less than or equal to zero. Alternative Hypothesis: The mean difference between two paired samples is greater than zero. Example: H0: µd ≤ 0, Ha: µd > 0
3. Null Hypothesis: The mean difference between two paired samples is greater than or equal to zero. Alternative Hypothesis: The mean difference between two paired samples is less than zero. Example: H0: µd ≥ 2, Ha: µd < 2

Note: In the above hypotheses, x̄ represents the sample mean, µ represents the population mean, µd represents the mean difference between two paired samples, and H0 and Ha represent the null and alternative hypotheses, respectively

One Group Proportion

1. Null Hypothesis: The proportion of adults who own a car is 60%. Alternative Hypothesis: The proportion of adults who own a car is not 60%. Example: H0: p = 0.60, Ha: p ≠ 0.60
2. Null Hypothesis: The proportion of customers who are satisfied with the service is less than or equal to 0.75. Alternative Hypothesis: The proportion of customers who are satisfied with the service is greater than 0.75. Example: H0: p ≤ 0.75, Ha: p > 0.75
3. Null Hypothesis: The proportion of students who pass the exam is greater than or equal to 0.85. Alternative Hypothesis: The proportion of students who pass the exam is less than 0.85. Example: H0: p ≥ 0.85, Ha: p < 0.85

Difference between Two Independent Means

1. Null Hypothesis (H0): There is no significant difference between the means of two independent groups. Alternative Hypothesis (Ha): There is a significant difference between the means of two independent groups (two-tailed).
2. Null Hypothesis (H0): The mean of the population is less than or equal to a certain value. Alternative Hypothesis (Ha): The mean of the population is greater than the certain value (right-tailed).
3. Null Hypothesis (H0): The mean of the population is greater than or equal to a certain value. Alternative Hypothesis (Ha): The mean of the population is less than the certain value (left-tailed).

Difference between Two Proportions

1. Null Hypothesis (H0): There is no significant difference between the proportions of two independent groups. Alternative Hypothesis (Ha): There is a significant difference between the proportions of two independent groups (two-tailed).

2. Null Hypothesis (H0): The proportion of one group is less than or equal to the proportion of another group. Alternative Hypothesis (Ha): The proportion of one group is greater than the proportion of another group (right-tailed).

3. Null Hypothesis (H0): The proportion of one group is greater than or equal to the proportion of another group. Alternative Hypothesis (Ha): The proportion of one group is less than the proportion of another group (left-tailed).

To test this hypothesis, statistical methods such as a two-sample z-test or chi-square test can be used to determine if the difference between the two proportions is statistically significant or if it could have occurred by chance.

Simple Linear Regression: Slope

1. Null Hypothesis (H0): There is no significant linear relationship between the predictor variable and the response variable. Alternative Hypothesis (Ha): There is a significant linear relationship between the predictor variable and the response variable, and the slope of the regression line is not equal to zero (two-tailed).

2. Null Hypothesis (H0): There is no significant linear relationship between the predictor variable and the response variable or the slope of the regression line is less than or equal to zero. Alternative Hypothesis (Ha): There is a significant positive linear relationship between the predictor variable and the response variable, and the slope of the regression line is greater than zero (right-tailed).

3. Null Hypothesis (H0): There is no significant linear relationship between the predictor variable and the response variable or the slope of the regression line is greater than or equal to zero. Alternative Hypothesis (Ha): There is a significant negative linear relationship between the predictor variable and the response variable, and the slope of the regression line is less than zero (left-tailed).

To test this hypothesis, statistical methods such as a t-test or F-test can be used to determine if the slope of the regression line is significantly different from zero, indicating a significant linear relationship between the predictor and response variables.

Correlation (Pearson’s r)

1. Null Hypothesis (H0): There is no significant linear relationship between the two variables. Alternative Hypothesis (Ha): There is a significant linear relationship between the two variables (two-tailed).

2. Null Hypothesis (H0): There is no significant positive linear relationship between the two variables. Alternative Hypothesis (Ha): There is a significant positive linear relationship between the two variables (right-tailed).

3. Null Hypothesis (H0): There is no significant negative linear relationship between the two variables. Alternative Hypothesis (Ha): There is a significant negative linear relationship between the two variables (left-tailed).

In this context, the Pearson’s correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. A positive r value indicates a positive linear relationship (i.e., as one variable increases, so does the other), while a negative r value indicates a negative linear relationship (i.e., as one variable increases, the other decreases).

To test these hypotheses, statistical methods such as a t-test or z-test can be used to determine if the correlation coefficient is significantly different from zero and whether the relationship is positive or negative.