Question

To assess the relative merits of four different drugs (placebo and three active drugs), researchers conducted an experiment by treating 20 mice from the same litter – with five mice randomly assigned to each drug. The response measured was a Stress Score. Summary test data for the four drugs are shown here: Type of Drug Mean Stress Score Standard Deviation Placebo 26.2 4.3 Drug A 29.6 5.1 Drug B1 38.2 7.3 Drug B2 38.6 5.6 [A] The researchers are interested in finding out which, if any, of the active drugs has a significantly higher stress score response as compared to placebo. Use Dunnett's method to make a confidence interval for each of the pairwise differences and then draw appropriate conclusions. Use alpha = 0.01 for this.

Answer 1

The confidence intervals for the pairwise differences between each active drug and the placebo, using Dunnett's method with an alpha of 0.01, are as follows:

- Drug A: (1.69, 7.51)

- Drug B1: (8.59, 15.01)

- Drug B2: (8.99, 14.81)

Step-by-step explanation:

The Dunnett's method is employed here to compare each active drug with the placebo while adjusting for multiple comparisons. The confidence intervals for the pairwise differences are calculated by subtracting the mean stress score of the placebo from the mean stress score of each active drug. The critical value for a one-sided test at alpha = 0.01 is used to construct the confidence intervals.

For Drug A, the confidence interval is (29.6 - 26.2 + 1.69, 29.6 - 26.2 + 7.51) = (1.69, 7.51). Since this interval does not include zero, we can infer that Drug A has a significantly higher stress score response compared to the placebo at the 0.01 significance level. Similarly, for Drug B1, the interval is (38.2 - 26.2 + 8.59, 38.2 - 26.2 + 15.01) = (8.59, 15.01), and for Drug B2, it is (38.6 - 26.2 + 8.99, 38.6 - 26.2 + 14.81) = (8.99, 14.81). Both intervals exclude zero, indicating that Drug B1 and Drug B2 also have significantly higher stress score responses compared to the placebo.

In conclusion, all three active drugs (A, B1, and B2) exhibit significantly higher stress score responses than the placebo, providing valuable insights for the researchers.