For the preceding problem you should find that there are significant differences among the three treatments. The primary reason for the significance is that the mean for treatment I is substantially smaller than the means for the other two treatments. To create the following data, we started with the values from problem 7 and added 3 points to each score in treatment I.
Recall that adding a constant causes the mean to change but has no influence on the variability of the sample. In the resulting data the mean differences are much smaller than those in problem 7.
I II III
n 6 n 6 n 6
M 4 M 5 M 6 N 18
T 24 T 30 T 36 G 90
SS 30 SS 35 SS 40 ΣX2 567
a. Before you begin any calculations, predict how the change in the data should influence the outcome of the analysis. That is, how will the F-ratio and the value of η2 for these data compare with the values obtained in problem 7?
b. Use an ANOVA with α .05 to determine whether there are any significant differences among the three treatment means. (Does your answer agree with your prediction in part a?)
c. Calculate η2 to measure the effect size for this study. (Does your answer agree with your prediction in part a?)