Statistical Methods for Psychology

For this example we will examine the simple effects of Group at Interval 1 and Group
at Interval 6. The original data can be found in Table 14.4 on page 472. The sums of
squares for these effects are

Testing the simple effects of between-subjects terms is a little trickier. Consider for a
moment the simple effect of Group at Interval 1. This is essentially a one-way analysis of
variance with no repeated measures, since the Group means now represent the average of
single—rather than repeated—observations on subjects. Thus, subject differences are con-
founded with experimental error. In this case, the appropriate error sum of squares is
, where, from Table 14.4,

and

It may be easier for you to understand why we need this special error term if
you think about what it really represents. If you were presented with only the data for In-
terval 1 in Table 14.4 and wished to test the differences among the three groups, you would
run a standard one-way analysis of variance, and the would be the average of the
variances within each of the three groups. Similarly, if you had only the data from Interval 2,
Interval 3, and so on, you would again average the variances within the three treatment
groups. The that we have just finished calculating is in reality the average of the
error terms for these six different sets (Intervals) of data. As such, it is the average of the
variance within each of the 18 cells.
We can now proceed to form our Fratios.

A further difficulty arises in the evaluation of F. Since also represents the
sum of two heterogeneoussources of error [as can be seen by examination of the E(MS)
for Ss w/in groups and I 3 Ss w/in groups], our Fwill not be distributed on 2 and 126 df.
We will get ourselves out of this difficulty in the same way we did when we faced a simi-
lar problem concerning t in Chapter 7. We will simply calculate the relevant dfagainst
which to evaluate F—more precisely; we will calculate a statistic denoted as and evaluatef¿

MSw/in cell

FG at Int. 6=

MSG at Int. 6

MSw/in cell

=

10,732> 2

5285.09

=1.02

FG at Int. 1=

MSG at Int. 1

MSw/in cell

=

79,426.33> 2

5285.09

=7.51

MSw/in cell

MSerror

MSw/in cell

=

665,921.37

211105

=5285.09

MSw/in cell=

SSw/in cell

dfSs w/in group 1 dfI 3 Ss w/in group

=384,722.03 1 281,199.34=665,921.37

SSw/in cell=SSSs w/in group 1 SSI 3 Ss w/in groups

SSw/in cell

=10,732.00

1 (138.625 2 149.125)^24

SSG at Int. 6= 83 (130.125 2 149.125)^21 (178.625 2 149.125)^2

=79,426.33

1 (290.125 2 286.208)^24

SSG at Int. 1= 83 (213.875 2 286.208)^21 (354.625 2 286.208)^2

Section 14.7 One Between-Subjects Variable and One Within-Subjects Variable 481