Statistical Methods for Psychology

Magnitude of Effect

We can calculate^2 for these data as SStreat SStotal 5 3497.60 4617.60 5 .76, indicating

that treatment differences account for 76% of the variation in the study. A nearly unbiased

estimate would be v^2 , which would be

Both estimates indicate that group differences account for a very substantial proportion

of the variation in this study.

12.3 A Priori Comparisons

There are two reasons for starting our discussion with a priori comparisons and t tests. In

the first place, standard t tests between pairs of means can be a perfectly legitimate method

of comparison. Second, the basic formula for t, and minor modifications on it, are applica-

ble to a large number of procedures, and a review at this time is useful.

As we have seen, a priori comparisons (also called contrasts) are planned before the

data have been collected. There are several different kinds of a priori comparison proce-

dures, and we will discuss them in turn.

Multiple tTests

One of the simplest methods of running preplanned comparisons is to use individual t tests be-

tween pairs of groups. In running individual t tests, if the assumption of homogeneity of vari-

ance is tenable, we usually replace the individual variances, or the pooled variance estimate,

v^2 =

SStreat 2 (k 2 1)MSerror

SStotal 1 MSerror

=

3497.60 2 4(32)

4617.60 132

=

3369.6

4649.6

=0.72

h > >

12.3 A Priori Comparisons 369

Table 12.1 Data and analysis on morphine tolerance

(a) Data

M-S M-M S-S S-M Mc-M

3 2 14 29 24

5 12 6 20 26

1131236 40

8642132

1101925 20

1731833

4 11 9 26 27

9192117 30

Mean 4.00 10.00 11.00 24.00 29.00

St. Dev 3.16 5.13 6.72 6.37 6.16

(b) Summary Table

Source df SS MS F

Treatment 4 3497.60 874.40 27.33*

Error 35 1120.00 32.00

Total 39 4617.60

*p,.05

contrasts