Concluding a hypothesis test involves making a decision about your null hypothesis based on the evidence you've gathered and analyzed. It's a two-part process, determining whether to reject or fail to reject the null hypothesis and interpreting the implications for your alternative hypothesis.
The Two-Part Conclusion Process
The conclusion of hypothesis testing consists of the following two essential components:
-
Decision Regarding the Null Hypothesis: Make a clear determination about whether you reject or fail to reject the null hypothesis (H0). You never "accept" the null hypothesis; you either have enough evidence to reject it, or you don't.
-
Interpretation in Context of the Alternative Hypothesis: State whether there is or is not sufficient evidence to support the alternative hypothesis (H1 or Ha). Your conclusion should be easily understandable in the context of the original research question.
Key Concepts
Before diving into the specific scenarios, let's review some key concepts:
- Null Hypothesis (H0): A statement that there is no effect or no difference. It's the statement you're trying to disprove.
- Alternative Hypothesis (H1 or Ha): A statement that contradicts the null hypothesis. It's what you're trying to find evidence for.
- P-value: The probability of obtaining results as extreme as, or more extreme than, the observed results, assuming the null hypothesis is true.
- Significance Level (α): A pre-determined threshold for statistical significance (commonly 0.05). If the p-value is less than α, we reject the null hypothesis.
Conclusion Scenarios
Here's how the conclusion process works based on the p-value and significance level:
| Scenario | Decision about H0 | Interpretation regarding H1 |
|---|---|---|
| p-value ≤ α | Reject the null hypothesis (H0) | There is enough evidence to support the alternative hypothesis (H1) |
| p-value > α | Fail to reject the null hypothesis (H0) | There is not enough evidence to support the alternative hypothesis (H1) |
Examples
Let's illustrate this with examples:
Example 1:
- Research Question: Is a new drug effective in lowering blood pressure?
- H0: The drug has no effect on blood pressure.
- H1: The drug lowers blood pressure.
- α: 0.05
- P-value: 0.03
Conclusion: Since the p-value (0.03) is less than α (0.05), we reject the null hypothesis. There is enough evidence to support the claim that the drug lowers blood pressure.
Example 2:
- Research Question: Is there a difference in exam scores between students who use a new study method and those who don't?
- H0: There is no difference in exam scores.
- H1: There is a difference in exam scores.
- α: 0.05
- P-value: 0.10
Conclusion: Since the p-value (0.10) is greater than α (0.05), we fail to reject the null hypothesis. There is not enough evidence to support the claim that there is a difference in exam scores between the two groups.
Important Considerations
- Practical Significance vs. Statistical Significance: A statistically significant result doesn't always mean it's practically significant. The effect size might be small, even if it's statistically significant.
- Type I and Type II Errors: Remember the possibility of making a wrong decision. A Type I error is rejecting a true null hypothesis, and a Type II error is failing to reject a false null hypothesis.
- Context is Key: Always interpret your results in the context of your research question and the limitations of your study.
In summary, concluding a hypothesis test requires deciding to reject or fail to reject the null hypothesis based on the p-value and significance level, followed by a clear statement regarding the evidence for the alternative hypothesis, keeping practical significance and potential errors in mind.
