9/29/2015
1
ANALYSIS OF
VARIANCE
Analysis of Variance
Used to compare two or more means to see if there are
any reliable differences among them
Types:
One-way ANOVA
Factorial ANOVA
Within subjects ANOVA
ANCOVA / MANOVA
Assumptions of ANOVA
•DV utilizes interval or ratio level of measurement
•Groups are relatively equal in size
•Normality (DV has a normal distribution for each value
category)
•Homogeneity of variance (groups have similar variances
on DV)
Research Problem
Goal DV IV Statistic
Description Continuous Mean, Median, Mode
Range, Std. Deviation
Discrete Frequency/Percentage
Group
Differences Discrete Discrete Chi Square & Non-
parametric statistics
Continuous Discrete T-test, ANOVA
Association/
Prediction Continuous Continuous Correlation, Regression
Structure Continuous Factor Analysis
Note: Discrete data – NOMINAL Continuous data – INTERVAL
ORDINAL RATIO
Testing Homogeneity of variances
•Levene’s test of homogeneity of variance (if
significant, assumption not met)
•However, F test is robust to violations of
homogeneity of variance if:
1. Equal number of observations
2. Populations are normal
3. Ratio of largest variance to smallest variance
does not exceed 3
Population 1:
MALES
Population 2:
FEMALES
Is there a significant difference between males and
females in neuroticism levels?
≠
Review: Testing Differences Between
Means Using the T Test
9/29/2015
One way ANOVA – nondirectional procedure that
tests equality among 2 or more means using
independent groups
When applied to only 2 groups, the one-way
ANOVA is exactly identical to the two-tailed t test
for independent samples
One way ANOVA = extended t-test
ANOVA (Analysis of Variance)
Problem: Is there a significant difference in levels of
achievement motivation among individuals from
the high, middle, and low socioeconomic status?
Population 1:
High SES
Population 2:
Middle SES
Population 3:
Low SES
ANOVA (Analysis of Variance)
ANOVA allows us to evaluate if there is a
significant difference among more than 2 means or
treatments!
ANOVA (Analysis of Variance)
Why not conduct multiple t-tests?
1)High SES versus Middle SES
2)Middle SES versus Low SES
3)High SES versus Low SES
ANOVA (Analysis of Variance)
