In How It Works 11.1, 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 we 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 the ANOVA is statistically significant? 

b. Conduct a Tukey HSD test for this example. State your conclusio ns based on this test. Show all calculations. 

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