Procedure for hypothesis testing

Let’s go through the steps of hypothesis testing using an example scenario. Suppose we want to test whether a new drug has a significant effect on reducing blood pressure.

Step 1: Formulate Hypotheses

• Null Hypothesis (0H0​): The new drug has no effect on blood pressure. μnew drug​−μplacebo​=0
• Alternative Hypothesis (1H1​ or Ha​): The new drug has a significant effect on reducing blood pressure. μnew drug​−μplacebo​<0

Step 2: Choose a Significance Level (�α)

• Commonly chosen levels are 0.05, 0.01, or 0.10. Let’s choose α=0.05 for this example.

Step 3: Collect and Analyze Data

• Collect data on blood pressure for two groups: one treated with the new drug and the other with a placebo.

Step 4: Choose a Statistical Test

• Based on the nature of the data, choose an appropriate statistical test. Let’s assume we are using a t-test for comparing means.

Step 5: Calculate Test Statistic

• Calculate the t-statistic based on the sample data.

Step 6: Determine Critical Region or P-value

• For a one-tailed test with a significance level of 0.05, find the critical t-value or determine the p-value.
• For example, if using a t-distribution table, the critical t-value for a one-tailed test at α=0.05 with, say, 20 degrees of freedom, might be approximately -1.729.

Step 7: Make a Decision

• If the calculated t-statistic falls in the critical region (beyond -1.729) or if the p-value is less than 0.05, reject the null hypothesis.
• If not, fail to reject the null hypothesis.

Step 8: Draw Conclusions

• Based on the decision, conclude whether there is enough evidence to support the alternative hypothesis or if the null hypothesis cannot be rejected.

Example Detailed Explanation:

Suppose we have collected blood pressure data for two groups: the new drug group (mean = 120 mmHg) and the placebo group (mean = 130 mmHg). We perform a t-test, and the calculated t-statistic is -2.5.

Calculation:

• Null Hypothesis (H0​): μnew drug​−μplacebo​=0
• Alternative Hypothesis (H1​): μnew drug​−μplacebo​<0
• t-Statistic: -2.5

Decision:

• For a one-tailed test at α=0.05 with, say, 20 degrees of freedom, the critical t-value might be approximately -1.729.
• Since -2.5 < -1.729, the t-statistic falls in the critical region.
• Therefore, we reject the null hypothesis.

Conclusion:

• There is enough evidence at the 0.05 significance level to suggest that the new drug has a significant effect in reducing blood pressure compared to the placebo.

This detailed example illustrates each step in the hypothesis testing process, emphasizing the importance of formulating clear hypotheses, choosing an appropriate significance level, analyzing data, and drawing meaningful conclusions based on statistical evidence.