Hypothesis testing is a statistical procedure used to test assumptions or hypotheses about a population parameter. It involves formulating a null hypothesis (H0) and an alternative hypothesis (Ha), collecting data, and determining whether the evidence is strong enough to reject the null hypothesis.

The primary purpose of hypothesis testing is to make inferences about a population based on a sample of data. It allows researchers and analysts to quantify the likelihood that observed differences or relationships in the data occurred by chance rather than reflecting a true effect in the population.

Steps of Hypothesis Testing

Let’s walk through how to do a hypothesis test, one step at a time.

Step 1: State your hypotheses

The first step is to formulate your research question into two competing hypotheses:

• Null Hypothesis (H₀): This is a statement of no effect or no difference. It’s the hypothesis that the test seeks to either reject or fail to reject.
• Alternative Hypothesis (H₁ or Ha): This is a statement that contradicts the null hypothesis. It reflects the claim or effect you want to test for in the population.

Example:

• H₀: The average weight of apples is 150 grams.
• H₁: The average weight of apples is not 150 grams.

Step 2: Set the significance level (α)

• The significance level (α) is the probability of rejecting the null hypothesis when it is true (Type I error). Common values are 0.05, 0.01, or 0.10, but it should be chosen before conducting the test.

Example:
Set α = 0.05, which means you are willing to accept a 5% chance of incorrectly rejecting the null hypothesis.

Step 3: Choose the appropriate statistical test

Select a statistical test based on the type of data and the hypothesis. The choice depends on factors such as:

• Data type (continuous, categorical, etc.)
• Distribution of the data (normal, non-normal)
• Sample size
• Number of groups being compared

Common tests include:

• t-tests (for comparing means)

• chi-square tests (for categorical data)

• ANOVA (for comparing means of multiple groups)

Example:
A t-test might be used if you are testing the mean of a small sample and don’t know the population standard deviation.

Step 4: Determine the decision rule (critical region)

• Based on the chosen significance level (α) and the test statistic, determine the critical value(s) from the relevant statistical distribution (like the Z or t-distribution). The decision rule tells you the threshold beyond which the null hypothesis will be rejected.
• If your test statistic exceeds the critical value (or falls into the rejection region), you reject the null hypothesis.

Example:
If α = 0.05, the critical value for a two-tailed test might be ±1.96 for a Z-test. If your test statistic is greater than 1.96 or less than -1.96, reject the null hypothesis.

Step 5: Collect data and compute the test statistic

• Gather sample data and calculate the test statistic (e.g., Z or t value). This involves using the sample data to calculate a statistic that can then be compared to the critical value.

Example:
Suppose you calculate a t-statistic from the sample data and find that it equals 2.5.

Step 6: Make a decision

Compare the p-value to the predetermined significance level (α), which is typically set at 0.05. The decision rule is as follows:

• If p-value ≤ α: Reject the null hypothesis, suggesting evidence supports the alternative hypothesis.
• If p-value > α: Fail to reject the null hypothesis, suggesting insufficient evidence to support the alternative hypothesis.

It’s important to note that failing to reject the null hypothesis doesn’t prove it’s true; it simply means there’s not enough evidence to conclude otherwise.

Example:
If the computed t-statistic (2.5) is greater than the critical value (1.96), you reject the null hypothesis.

Step 7: Draw a Conclusion

Report the results, including the test statistic, p-value, and conclusion. Discuss whether the findings support the initial hypothesis and their implications. When presenting results, consider:

• Providing context for the study.
• Clearly stating the hypotheses.
• Reporting the test statistic and p-value.
• Interpreting the results in plain language.
• Discussing the practical significance of the findings.