The primary statistical advantage of including a pretest in a randomized design is to decrease error variance. Suppose we let cr£ 2 represent the error variance in a posttest-only design. As mentioned in the chapter (see Equations 49 and 56), it can be shown that in a randomized design in which the pretest and posttest have equal variances (often a reasonable assumption), the error variances for ANCOVA and a gain score analysis are where p is the population correlation within groups between the pretest and the posttest. A graduate student is planning a randomized study in which he anticipates that and cr£ — 20 (these figures correspond to a large effect size). He plans to use 10 subjects per group. Find the power the student would have with each approach (posttest only, ANCOVA, and gain scores) in each of the following situations (assuming a = .05 , and equal variances for the pretest and posttest): a. p = 0 b. p = .3 c. p = .5 d. p = .7 e. What overall conclusion(s) do you draw here? where oe is to be understood as referring to the error standard deviation of the approach being used.)

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