a. Run an analysis of variance on group differences in Gain scores. (You may have already
done this in Chapter 14.)
b. Now run the analysis on Posttest scores, ignoring Pretest scores.
c. Finally, run the analysis on Posttest scores using Pretest as the covariate.
d. How do these three answers relate to one another, and what do they show about the dif-
ferences and similarities between analysis of covariance and the treatment of gain (or
change) scores?
e. Calculate h^2 on Groups for the analysis of covariance.
f. Calculate dfor the contrast on the two therapy groups (ignoring the control group)
using adjusted means.
16.25 Write up the results of Everitt’s experiment, including effect sizes.Discussion Questions
16.26 I initially thought of creating an analysis of variance example from the example in Chapter 14,
Section 14.7. I could have used Sex and Group as the independent variables, posttest scores
as the dependent variable, and pretest scores as the covariate (ignoring FU6 and FU12 en-
tirely). This would have made a very bad example for the analysis of covariance. Why
would that be? Is there any way in which we might be able to salvage the study as an analy-
sis of covariance example?
16.27 I said that in any experiment where we have pretest and posttest scores we could either look
at the difference scores (compared across groups) or use the pretest as a covariate. These
two analyses will be equivalent only when the slope relating posttest to pretest scores is
1.00. How likely do you think it is that such a condition would be met (or at least approxi-
mated)? What does b 5 1.00 actually imply?
16.28 Make up or find an example with respect to Exercise 16.25 where the slope is not nearly 1.0.
Analyze it using both the analysis of covariance and a t test on difference scores. Do either of
these analyses make sense?Exercises 627Group Pretest Posttest Gain
2 78.1 81.4 3.3
2 70.5 81.8 11.3
2 77.3 77.3 0.0
2 85.2 84.2 2 1.0
2 86.0 75.4 2 10.6
2 84.1 79.5 2 4.6
2 79.7 73.0 2 6.7
2 85.5 88.3 2.8
2 84.4 84.7 0.3
2 79.6 81.4 1.8
2 77.5 81.2 3.7
2 72.3 88.2 15.9
2 89.0 78.8 2 10.2
3 83.8 95.2 11.4
3 83.3 94.3 11.0Group Pretest Posttest Gain
3 86.0 91.5 5.5
3 82.5 91.9 9.4
3 86.7 100.3 13.6
3 79.6 76.7 2 2.9
3 76.9 76.8 2 0.1
3 94.2 101.6 7.4
3 73.4 94.9 21.5
3 80.5 75.2 2 5.3
3 81.6 77.8 2 3.8
3 82.1 95.5 13.4
3 77.6 90.7 13.1
3 83.5 92.5 9.0
3 89.9 93.8 3.9
3 86.0 91.7 5.7
3 87.3 98.0 10.7