Chapter 12, Problem 7P

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 III is substantially larger than the means for the other two treatments. To create the following data, we started with the values from problem 6 and subtracted 3 points to each score in treatment III. Notice that subtracting 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 6.

  

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 $\eta$² for these data compare with the values obtained in problem 6?

b. Use an ANOVA with $\alpha$ = .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 $\eta$² to measure the effect size for this study. (Does your answer agree with your prediction in part a?)