Hypothesis Testing Process

Hypothesis testing is a systematic method used in statistics to determine whether there is enough evidence in a sample to infer a conclusion about a population.

1. Formulate the Hypotheses

The first step is to define the two hypotheses:

• Null Hypothesis (H_0​): Represents the assumption of no effect, relationship, or difference. It acts as the default statement to be tested.

  Example: “The new drug has no effect on blood pressure.”

• Alternative Hypothesis (H_1​): Represents what the researcher seeks to prove, suggesting an effect, relationship, or difference.

  Example: “The new drug significantly lowers blood pressure.”

2. Choose the Significance Level (α)

The significance level determines the threshold for rejecting the null hypothesis. Common choices include $\alpha =0.05$ (5%) or if $\alpha =0.01$ (1%). This value indicates the probability of rejecting H_0​ when it is true (Type I error).

3. Select the Appropriate Test

Choose a statistical test based on:

• The type of data (e.g., categorical, continuous).
• The sample size.
• The assumptions about the data distribution (e.g., normal distribution).

  Examples include t-tests, z-tests, chi-square tests, and ANOVA.

4. Collect and Summarize Data

Gather the sample data, ensuring it is representative of the population. Calculate the sample statistic (e.g., mean, proportion) relevant to the hypothesis being tested.

5. Compute the Test Statistic

Using the sample data, compute the test statistic (e.g., t-value, z-value) based on the chosen test. This statistic helps determine how far the sample data deviates from what is expected under H_0​.

6. Determine the P-Value

The p-value is the probability of observing the sample results (or more extreme) if H0H_0H0​ is true.

• If p-value ≤ $\alpha$: Reject H_0​ in favor of H_1​.
• If p-value > $\alpha$: Fail to reject H_0​.

7. Draw a Conclusion

Based on the p-value and test statistic, decide whether to reject or fail to reject H0H_0H0​.

• Reject H_0​: There is sufficient evidence to support H_1​.
• Fail to Reject H_0​: There is insufficient evidence to support H_1​.

8. Report the Results

Clearly communicate the findings, including the hypotheses, significance level, test statistic, p-value, and conclusion. This ensures transparency and allows others to validate the results.