Overview
This lecture explains the final interpretation step in hypothesis testing, focusing on how to compare the P value to the significance level and what that means for making conclusions.
Step Four: Comparing P Value to Significance Level
- The P value (0.0044) is compared to the significance level (α = 0.05).
- If the P value is smaller than the significance level, we reject the null hypothesis.
- If the P value is larger than the significance level, we fail to reject the null hypothesis.
- This comparison step is identical in every hypothesis test, regardless of the context or chapter.
Interpreting Results
- Rejecting the null hypothesis means there is enough evidence to support the alternative hypothesis.
- In the example, since the P value is smaller, we reject the null hypothesis and conclude caffeine therapy lowered the rate of death and disability.
- This step and conclusion structure will be used consistently for all hypothesis testing problems.
Summary Table/Note Recommendation
- When P < α: Reject the null hypothesis; there is enough evidence for the alternative.
- When P > α: Fail to reject the null hypothesis; there is not enough evidence for the alternative.
- Students are encouraged to have this summary on their note sheet for quick reference.
Key Terms & Definitions
- P value — The probability of obtaining test results at least as extreme as the observed results, assuming the null hypothesis is true.
- Significance level (α) — The threshold set by the researcher (commonly 0.05) used to decide whether to reject the null hypothesis.
- Null hypothesis (H₀) — The default assumption that there is no effect or difference.
- Alternative hypothesis (H₁) — The hypothesis that there is an effect or difference.
Action Items / Next Steps
- Add the interpretation rule (P < α → reject H₀, enough evidence; P > α → fail to reject H₀, not enough evidence) to your note sheet.
- Review previous examples (e.g., Section 8.2) to reinforce this step.