Use statistical software to perform Tukey's test to determine which pairwise means differ for the data presented in Example 3 using a familywise error rate of \(\alpha=0.05\).

Approach We will use Minitab to perform Tukey's test. The steps for performing this test using either Minitab or StatCrunch can be found in the Technology Step-by-Step.

Data from Example 3

We presented data for an experimental drug that was meant to increase HDL cholesterol. The data are represented in Table 13 for convenience.

HDL cholesterol levels are known to have a distribution that is approximately normal. Verify that the largest sample standard deviation of any cell is no more than twice the smallest sample standard deviation of any cell.
Use Minitab to test whether there is an interaction effect between the drug dosage and age.
If the null hypothesis of no interaction is not rejected, determine whether there is sufficient evidence to conclude that the mean increase in HDL cholesterol is different (i) among each drug dosage group, (ii) for each age group.

Table 13 Age Placebo Drug Dosage 5 mg 10 mg 18 to 39 years 4 3 -1 9 5 6 14 12 10 40 or older 3 2 0 3 6 7 10 8 7