Statistical Methods for Psychology

Calculation

In Table 13.4b you can see that is calculated in the same way as any sum of

squares. We simply calculate using only the data for the older participants. If we con-

sider only those data, the five Condition means are 7.0, 6.9, 11.0, 13.4, and 12.0. Thus, the

sum of squares will be

The other simple effects are calculated in the same way, by ignoring all data in which you

are not at the moment interested. Notice that the sum of squares for the simple effect of

Condition for older participants (351.52) is the same value as that we obtained in Chapter 11

when we ran a one-way analysis of variance on only the data from older participants.

The degrees of freedom for the simple effects are calculated in the same way as for the

corresponding main effects. This makes sense because the number of means we are com-

paring remains the same. Whether we use all of the participants or only some of them, we

are still comparing five conditions and have 5 2 1 54 dffor Condition.

To test the simple effects, we generally use the error term from the overall analysis

( ). The expected mean squares are presented in Table 13.5, and they make it clear

why this is the appropriate error term. The expected mean square for each simple effect

contains only one effect other than error (e.g., ), whereas is an estimate of

error variance ( ). In fact, the only difference between what I have done in Table 13.4 and

what I would do if I ran a standard one-way analysis of variance on the Old participants’

data (which is the way I usually calculate sums of squares for simple effects when I use

computer software) is the error term. continues to be based on all the data because

it is a better estimate with more degrees of freedom.

Interpretation

From the column labeled Fin the bottom table in Table 13.4c, it is evident that differences

due to Conditions occur for both ages although the sum of squares for the older participants

is only about one-quarter of what it is for the younger ones. With regard to the Age effects,

however, no differences occur on the lower-level tasks of counting and rhyming, but differ-

ences do occur on the higher-level tasks. In other words, differences between age groups

MSerror

s^2 e

ns^2 a at bj MSerror

MSerror

= 103 [(7 2 10.06)^21 (6.9 2 10.06)^21... 1 (12 2 10.06)^2 ]=351.52

SSC at Old=na(X 1 j 2 X1.)^2

SSC

SSC at Old

Section 13.4 Simple Effects 425

Table 13.5 Expected mean squares for simple effects

Source E(MS)

Simple Effects of A

Aat B 1

Aat B 2

Aat B 3

Simple Effect of B

Bat A 1

Bat A 2

Error s^2 e

s^2 e 1 nu^2 b at a 1

s^2 e 1 nu^2 b at a 2

s^2 e 1 nu^2 a at b 1

s^2 e 1 nu^2 a at b 2

s^2 e 1 nu^2 a at b 3