Statistical Methods for Psychology

be subdivided into three components—the main effect of Intervals (the repeated measure)

and its interactions with the two partitions of the between-subject variation. You will see this

partitioning represented in the summary table when we come to it.

Partitioning the Between-Subjects Effects

Let us first consider the partition of the between-subjects term in more detail. From the de-

sign of the experiment, we know that this term can be partitioned into two parts. One of

these parts is the main effect of Groups (G), since the treatments (Control, Same, and Dif-

ferent) involve different groups of subjects. This is not the only source of differences

among subjects, however. We have eight different subjects within the control group, and

differences among them are certainly between-subjects differences. The same holds for the

subjects within the other groups. Here we are speaking of differences among subjects in

the same group—that is, Ss within groups.

Section 14.7 One Between-Subjects Variable and One Within-Subjects Variable 473

Table 14.4 (continued)

Interval

123456 Mean

292 139 104 184 193 122 172.333

Mean 290.125 98.250 108.500 109.000 123.500 138.625 144.667

Interval 286.208 152.583 142.000 135.875 148.333 149.125 169.021

mean

(b) Calculations

(c) Summary Table

Source df SS MS F

Between subjects 23 670,537.1
Groups 2 285,815.0 142,907.5 7.80
Ss w/in groups 21 384,722.0 18,320.1
Within subjects 120 761,755.8
Intervals 5 399,736.5 79,947.3 29.85
I 3 G 10 80,820.0 8,082.0 3.02*
I 3 Ss w/in groups** 105 281,199.3 2,678.1

Total 143 1,432,292.9

*p,.05
**Calculated by subtraction

SSI 3 G=SScells 2 SSinterval 2 SSgroups=766,371.5 2 285,815.0 2 399.736.5=80,820.0

SScells=na(XGI 2 X...)^2 = 83 (213.875 2 169.021)^2 1 Á 1 (138.625 2 169.021)^24 =766,371.5

SSintervals=nga(XI 2 X...)^2 = 8333 (286.208 2 169.021)^2 1 Á 1 (149.125 2 169.021)^24 =399,736.5

SSgroups=nia(XG 2 X...)^2 = 8363 (130.875 2 169.021)^2 1 Á 1 (144.667 2 169.021)^24 =285,815.0

SSsubj=ia(XS 2 X...)^2 =6[(88.333 2 169.021)^2 1 Á 1 (172.333 2 169.021)^2 ]=670,537.1

SStotal=a(X 2 X...)^2 =(150 2 169.021)^2 1 Á 1 (122 2 169.021)^2 =1,432,292.9