EXAMPLE 12.28

Power of a reading comprehension study. Suppose that a study on reading comprehension for three different teaching methods has 10 students in each group. How likely is this study to detect differences in the mean responses? A previous study performed in a different setting found sample means of 41, 47, and 44, and the pooled standard deviation was 7. Based on these results, we will use μ₁ = 41, μ₂ = 47, μ₃ = 44, and σ = 7 in a calculation of power. The n_i are equal, so is simply the average of the :

683

The noncentrality parameter is, therefore,

Because there are three groups with 10 observations per group, DFG = 2 and DFE = 27. The critical value for ⍺ = 0.05 is F* = 3.35. The power is, therefore,

1 − PROBF(3.35, 2, 27, 3.67) = 0.3486

The chance that we reject the ANOVA H₀ at the 5% significance level given these population means and standard deviation is slightly less than 35%.