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

408 CHAPTER 12 | Introduction to Analysis of Variance
Compute the F-Ratio Finally, we can compute F.
F 5 MS between
MS within
5 35
3.83 5 9.14
STEP 4
Make a decision about H 0
, and state a conclusion The obtained F of 9.14 exceeds the
critical value of 3.88. Therefore, we can reject the null hypothesis. The type of keyboard used
has a significant effect on the number of errors committed, F(2, 12) = 9.14, p < .05. The
following table summarizes the results of the analysis:
Source SS df MS
Between treatments 70 2 35 F = 9.14
Within treatments 46 12 3.83
Total 116 14
DEMONSTRATION 12.2
COMPUTING EFFECT SIZE FOR ANALYSIS OF VARIANCE
We will compute eta squared (η 2 ), the percentage of variance explained, for the data that
were analyzed in Demonstration 12.1. The data produced a between-treatments SS of
70 and a total SS of 116. Thus,
2 5 SS between
5 70 5 0.60 sor 60%d
SS total
116
PROBLEMS
1. Explain why the F-ratio is expected to be near 1.00
when the null hypothesis is true.
2. Describe the similarities between an F-ratio and a
t statistic.
3. Why should you use ANOVA instead of several t tests
to evaluate mean differences when an experiment
consists of three or more treatment conditions?
4. Calculate SS total
, SS between
, and SS within
for the following
set of data:
Treatment 1 Treatment 2 Treatment 3
n = 10 n = 10 n = 10 N = 30
T = 10 T = 20 T = 30 G = 60
SS = 27 SS = 16 SS = 23 ΣX 2 = 206
5. A researcher uses an ANOVA to compare three treatment
conditions with a sample of n = 8 in each treatment.
For this analysis, find df total
, df between
, and df within
.
6. A researcher reports an F-ratio with df between
= 2
and df within
= 30 for an independent-measures
ANOVA.
a. How many treatment conditions were compared in
the experiment?
b. How many subjects participated in the experiment?
7. A researcher reports an F-ratio with df = 2, 27 from
an independent-measures research study.
a. How many treatment conditions were compared in
the study?
b. What was the total number of participants in the
study?
8. A research report from an independent-measures study
states that there are significant differences between
treatments, F(3, 48) = 2.95, p < .05.
a. How many treatment conditions were compared in
the study?
b. What was the total number of participants in the
study?