Statistical Methods for Psychology

We will return to working with the example from Eysenck’s (1974) study. The means

and the analysis of variance summary table are presented below for easy reference.

Counting Rhyming Adjective Imagery Intention Mean

Older 7.0 6.9 11.0 13.4 12.0 10.06

Younger 6.5 7.6 14.8 17.6 19.3 13.16

Mean 6.75 7.25 12.90 15.50 15.65 11.61

Source df SS MS F

A(Age) 1 240.25 240.25 29.94*

C(Condition) 4 1514.94 378.735 47.19*

AC 4 190.30 47.575 5.93*

Error 90 722.30 8.026

Total 99 2667.79

*p,.05

One of the questions that would interest me is the contrast between the two lower lev-

els of processing (Counting and Rhyming) and the two higher levels (Adjective and

Imagery). I don’t have any particular thoughts about the Intentional group, so we will

ignore that. My coefficients for a standard linear contrast, then, are

Counting Rhyming Adjective Imagery Intention

−^1 ⁄ 2 −^1 ⁄ 2 1 ⁄ 2 1 ⁄ 2 0

The test on this contrast is

This tis clearly significant, showing that higher levels of processing lead to greater lev-

els of recall. But I want an effect size for this difference.

I am looking for an effect size on a difference between two sets of conditions, but

I need to consider the error term. Age is a normal variable in our world, and it leads to

variability in people’s responses. (If I had just designed this experiment as a one-way on

Conditions, and ignored the age of my participants, that age variability would have been a

normal part of MSerror). I need to have any Age effects contributing to error when it comes

to calculating an effect size. So I will add SSageand SSA 3 Cback into the error.

Having computed our error term for this effect, we find

dN=

°N

sN

=

7.20

3.48

=2.07

=

B

1152.85

95

= 2 12.135=3.48

Serror=

B

SSerror 1 SSAge 1 SSA 3 C

dferror 1 dfAge 1 dfA 3 C

=

B

722.30 1 240.25 1 190.30

901114

t=

°N

B

(©a^2 i)MSerror

n

=

7.20

B

(1)(8.026)

10

=

7.20

0.896

=8.04

cN= a 2

1

2

b(6.75) 1 a 2

1

2

b(7.25) 1 a

1

2

b(12.90) 1 a

1

2

b(15.50) 1 (0)(11.61)=7.20

442 Chapter 13 Factorial Analysis of Variance