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

SECTION 12.4 | Examples of Hypothesis Testing and Effect Size with ANOVA 391
The F-ratio for these data has df = 2, 17. With α = .05, the critical value for the F-ratio
is 3.59.
STEP 3
Compute the F-ratio. First, compute the three SS values. As usual, SS total
is the SS for
the total set of N = 20 scores, and SS within
combines the SS values from inside each of the
treatment conditions.
SS total
5SX 2 2 G2
N
5 3377 2 2502
20
SS within
= ΣSS inside each treatment
= 3377 – 3125 = 37 + 90 + 60
= 252 = 187
SS between
can be found by subtraction (Equation 12.5).
SS between
= SS total
– SS within
= 252 – 187
= 65
Or, SS between
can be calculated using the computation formula (Equation 12.7). If you use the
computational formula, be careful to match each treatment total (T) with the appropriate
sample size (n) as follows:
SS between
5 S T2
n 2 G2
N
Finally, compute the MS values and the F-ratio:
5 362
4 1 1302
10 1 842
6 2 2502
20
5 324 1 1690 1 1176 2 3125
5 65
MS between
5 SS
df 5 65 2 5 32.5
MS within
5 SS
df 5 187
17 5 11
F 5 MS between
MS within
5 32.5
11 5 2.95
STEP 4
Make a decision. Because the obtained F-ratio is not in the critical region, we fail to
reject the null hypothesis and conclude that there are no significant differences among the
three populations of students in terms of the average amount of homework each week. ■
■ Assumptions for the Independent-Measures ANOVA
The independent-measures ANOVA requires the same three assumptions that were necessary
for the independent-measures t hypothesis test:
1. The observations within each sample must be independent (see p. 244).
2. The populations from which the samples are selected must be normal.