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

468 CHAPTER 14 | Two-Factor Analysis of Variance (Independent Measures)
comparing only two treatment conditions. Therefore, the analysis is essentially a singlefactor
ANOVA duplicating the procedure presented in Chapter 12. To facilitate the change
from a two-factor to a single-factor analysis, the data for the self-regulated condition (first
row of the matrix) are reproduced as follows using the notation for a single-factor study.
Paper
Self-regulated time
Computer screen
n = 5 n = 5 N = 10
M = 9 M = 5 G = 70
T = 45 T = 25
STEP 1
State the hypothesis. For this restricted set of the data, the null hypothesis would state that
there is no difference between the mean for the paper condition and the mean for the computer
screen condition. In symbols,
H 0
: μ paper
= μ screen
for self-regulated study time
STEP 2
To evaluate this hypothesis, we use an F-ratio for which the numerator, MS between treatments
, is
determined by the mean differences between these two groups and the denominator consists
of MS within treatments
from the original ANOVA. Thus, the F-ratio has the structure
F 5
variance (differences) for the means in row 1
variance (differences) expected if there are no treatment effects
5 MS for the two treatments in row 1
between treatments
MS within treatments
from the original ANOVA
To compute the MS between treatments
, we begin with the two treatment totals T = 45 and
T = 25. Each of these totals is based on n = 5 scores, and the two totals add up to a grand
total of G = 70. The SS between treatments
for the two treatments is
SS between treatments
5S T2
n 2 G2
N
5 452
5 1 252
5 2 702
10
5 405 1 125 2 490
5 40
Because this SS value is based on only two treatments, it has df = 1. Therefore,
MS between treatments
5 40 1 5 40
Using MS within treatments
= 3 with df = 16 from the original two-factor analysis, the final
F-ratio is
F 5 MS between treatments
MS within treatments
5 40 3 5 13.33