Analysis of Variance
Chapter 12
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
,Learning Objectives
LO12-1 Apply the F distribution to test a hypothesis that
two population variances are equal.
LO12-2 Use ANOVA to test a hypothesis that three or
more population means are equal.
LO12-3 Use confidence intervals to test and interpret
differences between pairs of population means.
LO12-4 Use a blocking variable in a two-way ANOVA to
test a hypothesis that three or more population
means are equal.
LO12-5 Perform a two-way ANOVA with interaction and
describe the results.
12-2
, LO12-1 Apply the F distribution to test a hypothesis
that two population variances are equal.
Testing the Hypothesis of Two Equal
Population Variances: The F Distribution
The distribution is named to honor Sir Ronald Fisher, one of the
founders of modern-day statistics.
The distribution is:
Used to test a hypothesis of equal population variances.
Used to simultaneously test a hypothesis that several population means
are equal. The simultaneous comparison of several population means is
called analysis of variance (ANOVA).
12-3
, LO12-1
Characteristics of a F-
Distribution
There is a “family” of F- distributions.
A particular member of the family is
determined by two parameters: the
degrees of freedom in the numerator
and the degrees of freedom in the
denominator.
The F-distribution is continuous.
A F-value cannot be negative.
The F-distribution is positively
skewed.
It is asymptotic. As F , the curve
approaches the X-axis but never
touches it.
12-4
Chapter 12
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
,Learning Objectives
LO12-1 Apply the F distribution to test a hypothesis that
two population variances are equal.
LO12-2 Use ANOVA to test a hypothesis that three or
more population means are equal.
LO12-3 Use confidence intervals to test and interpret
differences between pairs of population means.
LO12-4 Use a blocking variable in a two-way ANOVA to
test a hypothesis that three or more population
means are equal.
LO12-5 Perform a two-way ANOVA with interaction and
describe the results.
12-2
, LO12-1 Apply the F distribution to test a hypothesis
that two population variances are equal.
Testing the Hypothesis of Two Equal
Population Variances: The F Distribution
The distribution is named to honor Sir Ronald Fisher, one of the
founders of modern-day statistics.
The distribution is:
Used to test a hypothesis of equal population variances.
Used to simultaneously test a hypothesis that several population means
are equal. The simultaneous comparison of several population means is
called analysis of variance (ANOVA).
12-3
, LO12-1
Characteristics of a F-
Distribution
There is a “family” of F- distributions.
A particular member of the family is
determined by two parameters: the
degrees of freedom in the numerator
and the degrees of freedom in the
denominator.
The F-distribution is continuous.
A F-value cannot be negative.
The F-distribution is positively
skewed.
It is asymptotic. As F , the curve
approaches the X-axis but never
touches it.
12-4
