For an 2 way ANOVA test, we have in population terms: , where $g$ is the number of levels of factor 1, and $b$ is the number of levels for factor 2. We can write the sample analogue as where the last term is the residual. How does one deduce this representation for the interaction term betwe...

When we're in the presence of two populations, for the same assumptions (random samples, multivariate distribution, same covariance matrix), and we want to test the mean vectors, we have two options: $T^2$ statistic (a Mahalanobis distance function) A statistic,function of the Wilk's lambda (MA...