# Empirical Direction in Design and Analysis

By Norman H. Anderson | Go to book overview

EXERCISES FOR CHAPTER 13
1. In the numerical example of Ancova Idealized of Section 13.2.1:
 1 Draw a graph to show how “the Ancova adjustment increases Y E by 2 points, decreases YC by 2 points.” 2 Do the same assuming treatment E increases Y by a constant c for each subject. 3 Redo (a) using Equation 4.
2. a. Repeat the graphic analysis of part (a) of the previous exercise to show how Ancova would reach wrong conclusions if the estimate of b1 was lower than its true value, say b1 =.6. Estimate graphically the apparent difference between E and C, and check using Equation 4. How does this relate to evaluation of Head Start programs?
 b. Repeat (a) assuming treatment E adds 1 point to each subject's score.
3. The error variances for Anova and Ancova, denoted σ2ε and σ2ε, respectively, obey the relation (Winer et al., 1991, p. 741):where ρ is the Y−X correlation. For moderate df, the df ratio at the right is close to 1. Ignore this term and plot a graph of the ratio of the two error terms as a function of ρ. How would you describe this trend? What does this mean for experimental design?4. To calculate power for Ancova, use Equations 3–5 in Chapter 4 for Anova. Replace the error variance, in Equation 4, by the Ancova error variance from the previous exercise.P wishes to study emotional arousal in three kinds of stress situations, but is uncertain how many subjects to run. He guesses the true means are 1, 2, and 4, with an error variance of 6. He plans to measure arousal before and after the experimental stress, the before measure to be used as a covariate. Tentatively, P considers n = 9.
 1 Show that power is about.57,.64,.70, and.78 for ρ = 0,.3,.45, and.6. Comment. 2 Guesstimate similarly the 95% confidence interval for difference between two means for each of the four correlations in (a). What problem do they raise for P? 3 What changes in the experimental design might P consider?

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