One-Way ANOVA Model Y ij denotes the ith observation within the jth of m groups. n j is the number of observations in the jth group. n =  n j is the total number of observations. μ j ≡ E(Y ij ) represents the population mean in group j (as before). One-way ANOVA model: Y ij = μ i + ε ij Y ij = μ + α j + ε ij μ represents general level of response in the population. α j represents effect on response variable of membership in jth group. ε ij is an error variable that follows the usual linear-model assumptions

Least squares.  ( Y ij - μ j ) 2 Y ij = μ + α j + ε ij

 ( Y ij - μ - α j ) 2 Overparametrized α 1 = 0 or  α j = 0 or  n j α j = 0 or... R commands factor() contrasts() Residuals ANOVA

logit(P) = log(P/(1-P))