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| This model can be fit by [[Statistics/OrdinaryLeastSquares|OLS]] by [[Statistics/Parameterization#Reference_Parameterization|dummy coding]] the group variable. The intercept term is the group mean for the reference group. Each coefficient is the difference between the corresponding group's mean and the reference group; the second group's mean is the sum of the intercept and the first coefficient. | This model can be re-expressed in the general linear model (by [[Statistics/Parameterization#Reference_Parameterization|dummy coding]] the group variable), and can therefore be fit by [[Statistics/OrdinaryLeastSquares|OLS]]. The intercept term is the group mean for the reference group. Each coefficient is the difference between the corresponding group's mean and the reference group; the second group's mean is the sum of the intercept and the first coefficient. |
Analysis of Variance
Analysis of variance (ANOVA) is a methodology for breaking down total variance into components.
Contents
Description
Total variance can be broken into between-group variance and within-group variance. By comparing the two components, it is possible to infer whether groups are different. That is to say, between-group variance being much larger than within-group variance suggests that the groups have differing means.
One-way ANOVA
The one-way ANOVA model is specified as:
where i indexes groups and j indexes the observations within group i.
This model can be re-expressed in the general linear model (by dummy coding the group variable), and can therefore be fit by OLS. The intercept term is the group mean for the reference group. Each coefficient is the difference between the corresponding group's mean and the reference group; the second group's mean is the sum of the intercept and the first coefficient.