For Exercises 14.1 and 14.2, see pages 717718; for 14.3 and 14.4, see page 720; for 14.5 and 14.6, see page 722; for 14.7, see page 724; for 14.8 and 14.9, see page 726; for 14.10 to 14.13, see pages 728728; for 14.14 and 14.15, see page 731; for 14.16 to 14.19, see page 739; for 14.20 and 14.21, see page 740; for 14.22 and 14.23, see page 741; for 14.24 and 14.25, see page 742; for 14.26 and 14.27, see page 743; for 14.28 and 14.29, see page 744; and for 14.30 and 14.31, see page 748.

Question 14.30

14.30 Power calculations for planning a study.

You are planning a new eye gaze study for a different university than that studied in Example 14.13 (pages 729731). From Example 14.13, we know that the standard deviations for the four groups considered in that study were 1.75, 1.72, 1.53, and 1.67. In Figure 14.9, we found the pooled standard error to be 1.68. Because the power of the test decreases as the standard deviation increases, use for the calculations in this exercise. This choice leads to sample sizes that are perhaps a little larger than we need but prevents us from choosing sample sizes that are too small to detect the effects of interest. You would like to conclude that the population means are different when and .

  1. Pick several values for (the number of students that you will select from each group) and calculate the power of the ANOVA test for each of your choices.
  2. Plot the power versus the sample size. Describe the general shape of the plot.
  3. What choice of would you choose for your study? Give reasons for your answer.