12.40 Power calculations for planning a study. You are planning a new eye gaze study for a different university than that studied in Example 12.15 (page 663). From Example 12.15, 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 12.9, we found the pooled standard error to be 1.68. Because the power of the F test decreases as the standard deviation increases, use σ = 2.0 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 μ₁ = 3.2, μ₂ = 3.7, μ₃ = 3.0 and μ₄ = 4.0.