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Stats: TwoWay ANOVA
The twoway analysis of variance is an extension to the oneway analysis of variance. There are two
independent variables (hence the name twoway).
Assumptions
•
The populations from which the samples were obtained must be normally or approximately normally
distributed.
•
The samples must be independent.
•
The variances of the populations must be equal.
•
The groups must have the same sample size.
Hypotheses
There are three sets of hypothesis with the twoway ANOVA.
The null hypotheses for each of the sets are given below.
1. The population means of the first factor are equal. This is like the oneway ANOVA for the row
factor.
2. The population means of the second factor are equal. This is like the oneway ANOVA for the
column factor.
3. There is no interaction between the two factors. This is similar to performing a test for independence
with contingency tables.
Factors
The two independent variables in a twoway ANOVA are called factors. The idea is that there are two
variables, factors, which affect the dependent variable. Each factor will have two or more levels within it, and
the degrees of freedom for each factor is one less than the number of levels.
Treatment Groups
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 Spring '07
 Bagwhandee
 Variance

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