Point estimation of the treatment means: μ ?_i=y ?_i=(∑_j?y_ij )/n
Example treatment 1 (j=1…4): μ ?_1=y ?_1=(∑_j?y_1j )/n
Point estimation of treatment effect (with sum to zero condition): τ ?_i=y ?_i-y ?
Example treatment 1: τ ?_1=y ?_1-y ?
Common variance σ^2 is estimated by a weighted mean of separate sample variances, or equivalently, by the within- or the mean square error (MSE): σ ?^2=s^2=((n_1-1) s_1^2+…+(n_t-1) s_t^2)/(n_1+…+n_t-1)=SSE/(N-t )=MSE
Standard error of treatment means: ?se(y ??_i)=σ ?/√(n_t )