EXAMPLE 14.27 The Effect of Fewer Subjects

CASE 14.2 The reading comprehension study described in Case 14.2 had 22 subjects in each group. Suppose that a similar study has only 10 subjects per group. How likely is this study to detect differences in the mean responses that are similar in size to those observed in the actual study?

Based on the results of the actual study, we calculate the power for the alternative , with . The are equal, so is simply the average of the :

The noncentrality parameter is, therefore,

Because there are three groups with 10 observations per group, and . The critical value for is . The power is, therefore,

The chance that we reject the ANOVA at the 5% significance level is only about 35%.