Statistical Methods for Psychology

Section 14.7 One Between-Subjects Variable and One Within-Subjects Variable 479

the effects in this analysis are significant. (They would also be significant if we used

instead of .)

Simple Effects

The Interval 3 Group interaction is plotted in Figure 14.2; the interpretation of the data is

relatively clear. It is apparent that the Same group consistently performs above the level of

the other two groups—that is, the conditioned tolerance to midazolam leads to greater ac-

tivity in that group than in the other groups. It is also clear that activity decreases notice-

ably after the first 5-minute interval (during which the drug is having its greatest effect).

The interaction appears to be produced by the fact that the Different group is intermediate

between the other two groups during the first interval, but it is virtually indistinguishable

from the Control group thereafter. In addition, the Same group continues declining until at

least the fourth interval, whereas the other two groups drop precipitously and then level off.

Simple effects will prove useful in interpreting these results, especially in terms of examin-

ing group differences during the first and the last intervals. Simple effects will also be used

to test for differences between intervals within the Control group, but only for purposes of

illustration—it should be clear that Interval differences exist within each group.

As I have suggested earlier, the Greenhouse and Geisser and the Huynh and Feldt ad-

justments to degrees of freedom appear to do an adequate job of correcting for problems

with the sphericity assumption when testing for overall main effects or interactions. How-

ever, a serious question about the adequacy of the adjustment arises when we consider

within-subjects simple effects (Boik, 1981; Harris, 1985). The traditional approach to test-

ing simple effects (see Howell, 1987) involves testing individual within-subjects contrasts

against a pooled error term ( ). If there are problems with the underlying as-

sumption, this error term will sometimes underestimate and sometimes overestimate what

would be the proper denominator for F, playing havoc with the probability of a Type I error.

For that reason we are going to adopt a different, and in some ways simpler, approach.

The approach we will take follows the advice of Boik that a separate error term be de-

rived for each tested effect. Thus, when we look at the simple effect of Intervals for the

Control condition, for example, the error term will speak specifically to that effect and will

MSI 3 Ss w/in groups

~ ́

́N

Marginal Means of Activity

Interval

1 2 3 4 5 6

Estimated Marginal Means

400

300

200

100

0

Group

1.00

2.00

3.00

Figure 14.2 Interval 3 Group interaction for data from Table 14.4