For the preceding problem you should find that there are significant differences among the three treatments.

One reason for the significance is that the sample variances are relatively small. To create the following data, we kept the same sample means that appeared in problem 19 but doubled the SS values within each sample.

Treatment I II III n 5 6 n 5 6 n 5 6 N 5 18 M 5 1 M 5 2 M 5 6 G 5 54 SS 5 120 SS 5 130 SS 5 80 SX2 5 576

a. Calculate the sample variance for each of the three samples. Describe how these sample variances compare with those from problem 19.

b. Predict how the increase in sample variance should influence the outcome of the analysis. That is, how will the F-ratio for these data compare with the value obtained in problem 19?

c. Use an ANOVA with a 5 .05 to determine whether there are any significant differences among the three treatment means. (Does your answer agree with your prediction in part b?)