Statistical Methods for Psychology

If we temporarily ignore intervals entirely (e.g., we simply collect our data over the en-

tire session rather than breaking it down into 5-minute intervals), we can think of the study

as producing the following data:

474 Chapter 14 Repeated-Measures Designs

Control Same Different

88.333 211.500 197.500

211.500 233.500 148.167

100.667 186.000 161.000

137.333 116.333 152.500

62.333 236.333 159.167

207.000 244.000 63.500

154.833 299.833 103.167

85.000 324.667 172.333

130.875 231.521 144.667

where the “raw scores” in this table are the subject means from Table 14.4. Because each sub-

ject is represented only once in these totals, the analysis we will apply here is the same as a

one-way analysis of variance on independent groups. Indeed, except for a constant represent-

ing the number of scores per subject (which cancels out in the end), the sums of squares for

the simple one-way on these data would be the same as those in the actual analysis. The Fthat

tests the main effect of Groups if this were a simple one-way on subject totals would be equal

to the one that we will obtain from the full analysis. Thus, the between-subjects partition of

the total variation can be seen as essentially a separate analysis of variance, with its own error

term (sometimes referred to as errorbetween) independent of the within-subjects effects.

Partitioning the Within-Subjects Effects

Next consider the within-subjects element of the partition of. As we have already seen,

this is itself partitioned into three terms. A comparison of the six intervals involves compar-

isons of scores from the same subject, and thus Intervals is a within-subjects term—it depends

on differences within each subject. Since Intervals is a within-subjects term, the interaction of

Intervals with Groups is also a within-subjects effect. The third term (Intervals 3 Ss within

groups) is sometimes referred to as since it is the error term for the within-subjects

effects. The term is actually the sum of the sums of squares for the

I 3 Sinteractions calculated separately for each group. Thus, it can be seen as logically equiv-

alent to the error term used in the previous design.

The Analysis

Before considering the analysis in detail, it is instructive to look at the general pattern of re-

sults. Although there are not enough observations in each cell to examine the distributions

in any serious way, it is apparent that on any given interval there is substantial variability

within groups. For example, for the second interval in the control group, scores range from

0 to 270. There do not appear to be any extreme outliers, however, as often happens in this

kind of research, and the variances within cells, although large, are approximately equal.

You can also see that there are large individual differences, with some of the animals consis-

tently showing relatively little ambulatory behavior and some showing a great deal. These

are the kinds of differences that will be partialled out by our analysis. Looking at the Interval

means, you will see that, as expected, behavior decreased substantially after the first

5-minute interval and then increased slightly during the rest of the session. Finally, looking

at the difference between the means for the Control and Same groups, you will see the

SSIntervals 3 Ss w/in groups

errorwithin

SStotal

errorbetween

errorwithin