Statistical Methods for Psychology

Thus

We can now estimate for each effect:

Partial Effects

Both and represent the size of an effect (SSeffect) relative to the total variability in

the experiment (SStotal). Often it makes more sense just to consider one factor separately

from the others. For example, in the Spilich et al. (1992) study of the effects of smok-

ing under different kinds of tasks, the task differences were huge and of limited interest

in themselves. If we want a measure of the effect of smoking, we probably don’t want

to dilute that measure with irrelevant variance. Thus we might want to estimate the

effect of smoking relative to a total variability based only on smoking and error. This

can be written

We then simply calculate the necessary terms and divide. For example, in the case of the

partial effectof the smoking by task interaction, treating both variables as fixed, we

would have

This is a reasonable sized effect.

d-Family Measures

The r-family measures ( and ) make some sense when we are speaking about an om-

nibus Ftest involving several levels of one of the independent variables, but when we are

looking closely at differences among individual groups or sets of groups, the d-family of

measures often is more useful and interpretable. Effect sizes (d) are a bit more complicated

h^2 v^2

v^2 ST(partial)=

sNST

sNST1sNerror

=

38.26

38.26 1108

=0.26

sN^ e=MSerror=^108

=(3 2 1)(3 2 1)(682 2 108)>(15)(3)(3)=

5166

135

=38.26

sNSxT^2 =(s 2 1)(t 2 1)(MSST 2 MSe)>nst

partial v^2 =

sN^2 effect

sN^2 effect1sN^2 e

h^2 v^2

vNCase^23 Letter=

sNab^2

sNtotal^2

=

1.977

19.344

=0.10

vNLetter^2 =

sNb^2

sNtotal^2

=

7.414

19.344

=0.38

vNCase^2 =

sNa^2

sNtotal^2

=

1.927

19.344

=0.10

v^2

sN^2 total=sN^2 a1sN^2 b1sN^2 ab1sN^2 e

=1.927 1 7.414 1 1.977 1 8.026=19.344

sN^2 e=MSerror=8.026

sN^2 ab=(a 2 1)(MSAB 2 MSerror)>na

=(2 2 1)(47.575 2 8.026)>(10 3 2)=1.977

440 Chapter 13 Factorial Analysis of Variance

partial effect