Statistical Methods for Psychology

Section 14.8 Two Between-Subjects Variables and One Within-Subjects Variable 485

Table 14.7 (continued)

(c) Summary Table

Source df SS MS F

Between subjects 39 21,490.344
Group (Condition) 1 107.256 107.256 0.21
Sex 1 3358.056 3358.056 6.73
G 3 S 1 63.757 63.757 0.13
Ss win groups 36 17,961.275 498.924
Within subjects 120 13,914.250
Time 3 274.069 91.356 0.90
T 3 G 3 1377.819 459.273 4.51
T 3 S 3 779.919 259.973 2.55
T 3 G 3 S 3 476.419 158.806 1.56
T 3 Ss w/in groups** 108 11,006.025 101.908

Total 159 35,404.594

*p,.05
** Obtained by subtraction

=6437.294 2 107.256 2 274.069 2 3358.056 2 1377.819 2 63.757 2 779.919=476.419

SSGTS=SScells GTS 2 SSG 2 SST 2 SSS 2 SSGT 2 SSGS 2 SSTS

SScells GTS=na(Xcells GTS 2 X)^2 = 103 (19.7–14.594)^2 1 Á 1 (9.50–14.594)^24 =6437.294

SSTS=SScells TS 2 SST 2 SSS=4412.044 2 274.069 2 3358.056=779.919

SScells TS=nga(Xcells TS 2 X)^2 = 10323 (24.60 2 14.594)^2 1 Á 1 (9.85 2 14.594)^24 =4412.044

SSTG=SScells TG 2 SST 2 SSG=1759.144 2 274.069 2 107.256=1377.819

SScells TG=nsa(Xcells TG 2 X)^2 = 10323 (13.45 2 14.594)^2 1 Á 1 (12.300 2 14.594)^24 =1759.144

SStime=ngsa(XT 2 X)^2 = 1032323 (16.625 2 14.594)^2 1 Á 1 (13.225 2 14.594)^24 =274.069

SSGS=SScells GS 2 SSG 2 SSS=3529.069 2 107.256 2 3358.056=63.757

SScells GS=nta(Xcells GS 2 X)^2 = 10343 (20.625 2 14.594)^2 1 Á 1 (9.825 2 14.594)^24 =3529.069

The summary table for the analysis of variance is presented in Table 14.7c. In this table,

the ** indicate terms that were obtained by subtraction. Specifically,

These last two terms are the error terms for between-subjects and within-subjects effects,

respectively. That these error terms are appropriate is shown by examining the expected

mean squares presented in Table 14.8 on page 486.^5 For the expected mean squares of ran-

dom and mixed models, see Kirk (1968) or Winer (1971).

SST 3 Ss w/in groups=SSw/in subj 2 SST 2 SSTG 2 SSTS 2 SSTGS

SSSs w/in groups=SSbetween subj 2 SSG 2 SSS 2 SSGS

SSw/in subj=SStotal 2 SSbetween subj

(^5) As in earlier tables of expected mean squares, we use the to refer to the variance of random terms and to
refer to the variability of fixed terms. Subjects are always treated as random, whereas in this study the two main
independent variables are fixed.
s^2 u^2