= Analysis of Variance = '''Analysis of variance''' ('''ANOVA''') is a methodology for breaking down total variance into components. <> ---- == 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: {{attachment:one.svg}} where ''i'' indexes groups and ''j'' indexes the observations within group ''i''. 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. ---- CategoryRicottone