Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

DEMONSTRATION 14.1 477
STEP 2
STAGE 1
The two-factor analysis Rather than compute the df values and look up critical values for
F at this time, we will proceed directly to the ANOVA.
The first stage of the analysis is identical to the independent-measures ANOVA presented in
Chapter 13, where each cell in the data matrix is considered a separate treatment condition.
SS total
5 SX 2 2 G2
N
5 31,836 2 14402
80 5 5916
SS within treatments
= ΣSS inside each treatment
= 1540 + 1270 + 1320 + 1266 = 5396
SS between treatments 5S T2
n 2 G2
N
The corresponding degrees of freedom are
5 4402
20 1 3002
20 1 3402
20 1 3602
20 2 14402
80
5 520
df total
= N – 1 = 79
df within treatments
= Σdf = 19 + 19 + 19 + 19 = 76
df between treatments
= number of treatments – 1 = 3
STAGE 2
The second stage of the analysis partitions the between-treatments variability into three components:
the main effect for factor A, the main effect for factor B, and the A × B interaction.
For factor A (normal/obese),
SS A
5 S T2 ROWS
n ROWS
2 G2
N
5 7402
40 1 7002
40 2 14402
80
5 20
For factor B (full/empty),
SS B
5 S T2 COLS
n COLS
2 G2
N
5 7802
40 1 6602
40 2 14402
80
5 180
For the A × B interaction,
SS A×B
= SS between treatments
– SS A
– SS B
= 520 – 20 – 180
= 320
The corresponding degrees of freedom are
df A
= number of rows – 1 = 1
df B
= number of columns – 1 = 1
df A × B
= df between treatments
– df A
– df B
= 3 – 1 – 1
= 1