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
MSF =
2
Within
2
Betweendf,df
s
sF
21=
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 ExampleInputs Output
