ANOVA
2
What is Analysis of Variance (ANOVA)?
• A Hypothesis Test to compare means
• How: Compares means or other estimates of variance for
each source of variation
• The underlying test used in many Designed Experiments
• Superior to regression because inputs do not have to be
continuous variables
3
Method
• Uses sums of squares, just like a standard
deviation, to evaluate the total variability of the
system
• Calculates “standard deviations” for each source
and subtracts the variability from the total
4
ANOVA Within vs Between
Within subgroup variation
Between subgroup variation
5
The F-Distribution
• Variance = Sum of Squared deviations/df
• There are two variances (Within and Between), the F statistic is the
ratio of the two variances. The ratio forms an F-distribution.
• The F-distribution depends on two sets of degrees of freedom – the
df from each variance: df1
for the Between and df2
for the Within
Error
Factor
MS
MS F =
2
Within
2
Between
df ,df
s
s
F
1 2
=
One Way ANOVA
Identical to a t-test if there are only two levels
One Way ANOVA Example
Donald P. Lynch, Ph.D. 8
Assumptions of ANOVA
1. Normality (not important)
2. Homogeneity of Variance (not important)
3. Sample is random (extremely important)
4. For multi-factor ANOVA input factors must be
independent (extremely important)
1. Verify with correlation
2. This will be demonstrated with regression
TW0-Way ANOVA
Multi-Factor ANOVA Example
Inputs Output
