Statistical Methods for Psychology

424 Chapter 13 Factorial Analysis of Variance

Table 13.4 Illustration of calculation of simple effects (data taken from Table 13.2)

(a) Cell means (n=10)

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

(b) Calculations:

Conditions at Each Age

Age at Each Condition

(c) Summary Tables

Overall Analysis

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

Simple Effects

Source df SS MS F

Conditions

Cat Old 4 351.52 87.88 10.95*

Cat Young 4 1353.72 338.43 42.15*

Age

Aat Counting 1 1.25 1.25 < 1

Aat Rhyming 1 2.45 2.45 < 1

Aat Adjective 1 72.20 72.20 9.00*

Aat Imagery 1 88.20 88.20 10.99*

Aat Intentional 1 266.45 266.45 33.20*

Error 90 722.30 8.03

*p<.05

SSA at Counting= 103 [(7.0 2 6.75)^21 (6.5 2 6.75)^2 ]=1.25

SSA at Rhyming= 103 [(6.9 2 7.25)^21 (7.6 2 7.25)^2 ]=2.45

SSA at Adjective= 103 [(11.0 2 12.9)^21 (14.8 2 12.9)^2 ]=72.2

SSA at Imagery= 103 [(13.4 2 15.5)^21 (17.6 2 15.5)^2 ]=88.20

SSA at Intentional= 103 [(12.0 2 15.65)^21 (19.3 2 15.65)^2 ]=266.45

SSC at Old= 10 3 [(7.0 2 10.06)^21 (6.9 2 10.06)^21... 1 (12 2 10.06)^2 ]=351.52

SSC at Young= 10 3 [(6.5 2 13.16)^21 (7.6 2 13.16)^21... 1 (19.3 2 13.16)^2 ]=1353.72