Section 10.4
Analysis of Variance
Section 10.4 Objectives
• Use one-way analysis of variance to test claims
involving three or more means
• Introduce (mention very briefly) two-way analysis of
variance
One-Way ANOVA
One-way analysis of variance
Analysis of variance is usually abbreviated
ANOVA.
One-Way ANOVA
One-way analysis of variance
A hypothesis-testing technique that is used
to compare means from three or more
populations.
One-Way ANOVA
One-way analysis of variance
Hypotheses:
 H0: μ1 = μ2 = μ3 =…= μk (all population
means are equal)
 Ha: At least one of the means is different
from the others.
One-Way ANOVA
In a one-way ANOVA test, the following must be true.
1. Each sample must be randomly selected from a
normal, or approximately normal, population.
2. The samples must be independent of each other.
3. Each population must have the same variance.
Two-Way ANOVA
Two-way analysis of variance
• A hypothesis-testing technique that is used to test the
effect of two independent variables, or factors, on
one dependent variable.
Section 10.4 Summary
• Discussed (briefly) one-way analysis of variance to
test claims involving three or more means
• Introduced (barely) two-way analysis of variance