Following are two separate (hypothetical) sets of data that are somewhat exaggerated to help clarify the procedures underlying analysis of variance. In each case, the experimenter is interested in conditions that affect the number of errors made by participants on a simple clerical task that must be performed quickly. Group 1 listens to upbeat dance music while performing the tasks; Group 2 listens to soothing, New Age music; and Group 3 listens to white noise (e.g., the steady hum of a machine in the background).

a. By inspection, in which case would you guess that the difference among groups is more likely to be statistically significant? Why?

b. Carry out the analysis of variance for Experiment 1. Are the results significant at the .05 level? Calculate eta squared.

c. Carry out the analysis of variance for Experiment 2. Are these results significant at the .05 level? Calculate eta squared.

d. Briefly describe why the F ratio and eta squared statistics differ dramatically for the two experiments even though the sample means (i.e., 2, 6, and 4) are the same in both cases.

e. Calculate an unbiased estimate of ω² for whichever experiment is significant.

Experiment 2 Experiment 1 Group 1 Group 2 Group 3 Group 1 Group 2 Group 3 1 10 10 3 8 9. 3 3 4 3 6. 3 10 6. 4 2 4 653 mm 2.