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

434 CHAPTER 13 | Repeated-Measures Analysis of Variance
Treatment
Participant I II D
A 3 5 2
B 4 14 10
C 5 7 2
D 4 6 2
M D
= 4
SS D
= 48
The Repeated-Measures t Test The null hypothesis for the t test states that for the
general population there is no mean difference between the two treatment conditions.
H 0
: μ D
= 0
With n = 4 participants, the test has df = 3 and the critical boundaries for a two-tailed test
with α = .05 are t = ±3.182.
For these data, the sample mean difference is M D
= 4, the variance for the difference
scores is s 2 = 16, and the standard error is S
MD
= 2 points. These values produce a t statistic of
t 5 M D 2m D
S MD
5 4 2 0
2
5 2.00
The t value is not in the critical region so we fail to reject H 0
and conclude that there is no
significant difference between the two treatments.
The Repeated-Measures ANOVA Now we will reorganize the data into a format
that is compatible with a repeated-measures ANOVA. Notice that the ANOVA
uses the original scores (not the difference scores) and requires the P totals for each
participant.
Treatment
Participant I II P
A 3 5 8 G = 48
B 4 14 18 ΣX 2 = 372
C 5 7 12 N = 8
D 4 6 10
Again, the null hypothesis states that for the general population there is no mean difference
between the two treatment conditions.
H 0
: μ 1
– μ 2
= 0
For this study, df between treatments
= 1, df within treatments
= 6, df between subjects
= 3, which produce
df error
= (6 – 3) = 3. Thus, the F-ratio has df = 1, 3 and the critical value for α = .05 is
F = 10.13. Note that the denominator of the F-ratio has the same df value as the t statistic
(df = 3) and that the critical value for F is equal to the squared critical value for
t (10.13 = 3.182 2 ).