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

402 CHAPTER 12 | Introduction to Analysis of Variance
95 %
–2.101 0 2.101
FIGURE 12.10
The distribution of t statistics
with df = 18 and the
corresponding distribution
of F-ratios with df = 1, 18.
Notice that the critical values
for α = .05 are t = ±2.101
and F = 2.101 2 = 4.41.
95 %
0 1 2 3 4 5
4.41
(2.101 2 )
b. For α = .05, the critical region for t is determined by values greater than
+2.101 or less than –2.101. When these boundaries are squared, you get
±2.1012 = 4.41
Notice that 4.41 is the critical value for α = .05 in the F distribution. Any value that is in
the critical region for t will end up in the critical region for F-ratios after it is squared.
LEARNING CHECK
1. If an analysis of variance is used for the following data, what would be the effect of
changing the value of SS 2
to 100?
a. increase SS within
and increase the size of the F-ratio
Sample Data
b. increase SS within
and decrease the size of the F-ratio
c. decrease SS within
and increase the size of the F-ratio
d. decrease SS within
and decrease the size of the F-ratio
M 1
= 15
SS 1
= 90
M 2
= 25
SS 2
= 70
2. For an ANOVA, how does an increase in the sample sizes influence the likelihood of
rejecting the null hypothesis and measures of effect size?
a. both will increase.
b. both will decrease
c. the likelihood of rejecting H 0
will increase but there will be little or no effect on
measures of effect size.
d. the likelihood of rejecting H 0
will decrease but there will be little or no effect on
measures of effect size.