Use the same data from the previous exercise in this exercise.

a. Explain why it is necessary to conduct a post hoc test such as a Tukey HSD test when an ANOVA is statistically significant.

b. Conduct a Tukey HSD test. Show all calculations.

c. Explain why we cannot assume that two groups have the same means when we fail to reject the null hypothesis using a Tukey HSD test. Refer to the current example in your answer.

Previous exercise

Irwin and colleagues (2004) conducted research on adherence to an exercise regimen. We give an overview of the study in exercise 12.38. Here are the data:

<5 sessions: 155, 120, 130

5–8 sessions: 199, 160, 184

9–12 sessions: 230, 214, 195, 209

Exercise 12.38

Irwin and colleagues (2004) conducted a study on adherence to an exercise program. 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 researchers assessed the number of minutes of exercise per week for all participants. Assume that you plan to do Bonferroni post hoc comparisons if the ANOVA is statistically significant.