Statistical Methods for Psychology

difference is only a matter of degree. Here we first obtain the for the three-

dimensional matrix. This sum of squares represents all of the variation among the cell

means in the full-factorial design. From this, we must subtract all of the variation that

can be accounted for by the main effects andby the first-order interactions. What

remains is the variation that can be accounted for by only the joint effect of all three vari-

ables, namely.

The final sum of squares is. This is most easily obtained by subtracting

from. Since represents all of the variation that can be attributa-

ble to differences among cells (

), subtracting it from will leave us with only that variation within the

cells themselves.

SSBC 1 SSABC SStotal

SScellsABC=SSA 1 SSB 1 SSC 1 SSAB 1 SSAC 1

SScellsABC SStotal SScellsABC

SSerror

SSABC

SScells

Section 13.12 Higher-Order Factorial Designs 449

Table 13.14 (continued)

(c) Summary table

Source df SS MS F

A(Experience) 1 1302.08 1302.08 48.78
B(Road) 2 1016.67 508.33 19.04
C(Conditions) 1 918.75 918.75 34.42
AB 2 116.67 58.33 2.19
AC 1 216.75 216.75 8.12
BC 2 50.00 25.00 , 1
ABC 2 146.00 73.00 2.73
Error 36 961.00 26.69

Total 47 4727.92

*p, .05

SSerror=SStotal 2 SSCell ABC=4727.92 2 3766.92=961.00

=146.00

=3766.92 2 1302.08 2 1016.67 2 918.75 2 116.67 2 216.75 2 50.00

SSABC=SSCell ABC 2 SSA 2 SSB 2 SSC 2 SSAB 2 SSAC 2 SSBC

=3766.92

SSCell ABC=na(Xijk 2 X ... )^2 =4[(10.00 2 17.292)^21 Á 1 (17.50 2 17.292)^2 ]

=50.00

SSBC=SSCell BC 2 SSB 2 SSC=1985.42 2 1016.67 2 918.75

=1985.42

SSCell BC=naa(X.jk 2 X ... )^2 = 43 2[(8.75 2 17.292)^2 1 Á 1 (28.75 2 17.292)^2 ]

=216.75

SSAC=SSCell AC 2 SSA 2 SSC=2437.58 2 1302.08 2 918.75

=2437.58

SSCell AC=nba(Xi.k 2 X ... )^2 = 43 3[(16.00 2 17.292)^2 1 Á 1 (14.333 2 17.292)^2 ]

SSAB=SSCell AB 2 SSA 2 SSB=2435.42 2 1302.08 2 1016.67=116.67

=2435.42

SSCell AB=nca(Xij. 2 X ... )^2 = 43 2[(15.00 2 17.292)^2 1 Á 1 (16.25 2 17.292)^2