Statistical Methods for Psychology

448 Chapter 13 Factorial Analysis of Variance

Table 13.14 Illustration of calculations for 2 333 2 factorial design

(a) Data

B 1 B 2 B 3 B 1 B 2 B 3

A 1 42316212532

18 15 27 14 33 42

82123193046

10 13 14 26 20 40

A 2 6 2 20 11 23 17

4 6 15 7 14 16

13 8 8 6 13 25

71217161212

Cell Means

B 1 B 2 B 3 B 1 B 2 B 3 Means

A 1 10.000 18.000 20.000 20.000 27.000 40.000 22.500

A 2 7.500 7.000 15.000 10.000 15.500 17.500 12.083

Means 8.750 12.500 17.500 15.000 21.250 28.750 17.292

More Cell Means

B 1 B 2 B 3 Means C 1 C 2 Means

A 1 15.000 22.500 30.000 22.500 A 1 16.000 29.000 22.500

A 2 8.750 11.250 16.250 12.083 A 2 9.833 14.333 12.083

Means 11.875 16.875 23.125 17.292 Means 12.917 21.667 17.292

B 1 B 2 B 3 Means

C 1 8.750 12.500 17.500 12.917

C 2 15.000 21.250 28.750 21.667

Means 11.875 16.875 23.125 17.292

(b) Calculations

C 1 C 2

C 1 C 2

ABCells ACCells

BCCells

=918.75

SSC=naba(X..k 2 X...)^2 = 4323 3[(12.917 2 17.292)^21 (21.667 2 17.292)^2 ]

1 (23.125 2 17.292)^2 ]=1016.67

SSB=naca(X.j. 2 X ...)^2 = 4323 2[(11.875 2 17.292)^2 1 Á

= 1302.08

SSA=nbca(Xi.. 2 X ... )^2 = 4333 2[(22.50 2 17.292)^21 (12.083 2 17.292)^2 ]

SStotal=a(X 2 X ...)^2 =(4 2 17.292)^21 Á 1 (12 2 17.292)^2 =4727.92

(continues)