In How It Works 12.1, we conducted a one-way between-groups ANOVA on an abbreviated data set from research by Irwin and colleagues (2004) on adherence to an exercise regimen. Participants were asked to attend a monthly group education program to help them change their exercise behavior. Attendance was taken and participants were divided into three categories: those who attended fewer than 5 sessions, those who attended between 5 and 8 sessions, and those who attended between 9 and 12 sessions. The dependent variable was number of minutes of exercise per week. Here are the data once again:

5 sessions: 155, 120, 130 5–8 sessions: 199, 160, 184 9–12 sessions: 230, 214, 195, 209

a. What conclusion did you draw in step 6 of the ANOVA? Why could you not be more specific in your conclusion? That is, why is an additional test necessary when our ANOVA is statistically significant?

b. Conduct a Tukey HSD test for this example.

State your conclusions based on this test. Show all calculations.

c. If we did not reject the null hypothesis for every possible pair of means, then why can’t we conclude that the two means are the same?