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 389
straightforward. Specifically, we determine how much of the total SS is accounted for by
the SS between treatments
.
The percentage of variance accounted for 5 SS between treatments
SS total
(12.14)
For the data in Example 12.2, we obtain
The percentage of variance accounted for = 84 = 0.488 (or 48.8%)
172
In published reports of ANOVA results, the percentage of variance accounted for by the
treatment effect is usually called η 2 (the Greek letter eta squared) instead of using r 2 . Thus,
for the study in Example 12.2, η 2 = 0.488.
The following example is an opportunity for you to test your understanding of computing
η 2 to measure effect size in ANOVA.
EXAMPLE 12.3
The ANOVA from an independent-measures study is summarized in the following table.
Source SS df MS
Between treatments 84 2 42 F(2, 12) = 7.00
Within treatments 72 12 6
Total 156 14
Compute η 2 to measure effect size for this study. You should find that η 2 = 0.538.
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IN THE LITERATURE
Reporting the Results of Analysis of Variance
The APA format for reporting the results of ANOVA begins with a presentation of
the treatment means and standard deviations in the narrative of the article, a table, or
a graph. These descriptive statistics are not needed in the calculations of the actual
ANOVA, but you can easily determine the treatment means from n and T (M = T/n) and
the standard deviations from the SS values for each treatment [s 5 ÏSS/(n21)]. Next,
report the results of the ANOVA. For the study described in Example 12.1, the report
might state the following:
The means and standard deviations are presented in Table 1. The analysis of variance
indicates that there are significant differences among the three strategies for studying,
F(2, 15) = 7.16, p < .05, η 2 = 0.488.
TABLE 1
Quiz scores following three different strategies for studying.
Simply reread
Answer prepared
questions
Create and answer
your own questions
M 5.00 9.00 10.00
SD 2.19 2.61 2.45