Statistical Methods for Psychology

the Games-Howell procedure using those separate covariance matrices. In other words, to

compare Intervals 3 and 4 for the Control group, you would generate your error term using

only the Intervals 3 and 4 data from just the Control group.

Myers (1979) has suggested making post hoc tests on a repeated measure using paired

t-tests and a Bonferroni correction. (This is essentially what I did for the migraine exam-

ple, though a Bonferroni correction was not necessary because I ran only one contrast.)

Maxwell (1980) showed that this approach does a good job of controlling the familywise

error rate, and Baker and Lew (1987) showed that it generally compared well against

Tukey’s test in terms of power. Baker proposed a simple modification of the Bonferroni

(roughly in line with that of Holm) that had even greater power.

14.8 Two Between-Subjects Variables and One Within-Subjects Variable

The basic theory of repeated-measures analysis of variance has already been described in

the discussion of the previous designs. However, experimenters commonly plan experi-

ments with three or more variables, some or all of which represent repeated measures on

the same subjects. We will briefly discuss the analysis of these designs. The calculations

are straight forward, because the sums of squares for main effects and interactions are ob-

tained in the usual way and the error terms are obtained by subtraction.

We will not consider the theory behind these designs at any length. Essentially, it

amounts to the extrapolation of what has already been said about the two-variable case. For

an excellent discussion of the underlying statistical theory see Winer (1971) or Maxwell

and Delaney (2004).

I will take as an example a study by St. Lawrence, Brasfield, Shirley, Jefferson, Alleyne,

and O’Bannon (1995) on an intervention program to reduce the risk of HIV infection among

African-American adolescents. The study involved a comparison of two approaches, one of

which was a standard 2-hour educational program used as a control condition (EC) and the

other was an 8-week behavioral skills training program (BST). Subjects were Male and

Female adolescents, and measures were taken at Pretest, Posttest, and 6 and 12 months

follow-up (FU6 and FU12). There were multiple dependent variables in the study, but the

one that we will consider is log(freq 1 1), where freq is the frequency of condom-protected

intercourse.^4 This is a 2 32 3 4 repeated-measures design, with Intervention and Sex as

between-subjects factors and Time as the within-subjects factor. This design may be dia-

grammed as follows, where represents the ith group of subjects.

Behavioral Skills Training Educational Control

Pretest Posttest FU6 FU12 Pretest Posttest FU6 FU12

Male

Female

The raw data and the necessary summary tables of cell totals are presented in Table 14.7a.

(These data have been generated to closely mimic the data reported by St. Lawrence et al.,

though they had many more subjects. Decimal points have been omitted.) In Table 14.7b are

the calculations for the main effects and interactions. Here, as elsewhere, the calculations are

carried out exactly as they are for any main effects and interactions.

G 3 G 3 G 3 G 3 G 4 G 4 G 4 G 4

G 1 G 1 G 1 G 1 G 2 G 2 G 2 G 2

Gi

Section 14.8 Two Between-Subjects Variables and One Within-Subjects Variable 483

(^4) The authors used a logarithmic transformation here because the original data were very positively skewed. They
took the log of (X 1 1) instead of Xbecause log(0) is not defined.