Notes on the ANOVA formulas

1. In computing the SSE, if we summed only the squares for a fixed g and divided by n_g, we would have the variance, i.e., the square of the SD, of the sample from group g. So we can begin to see where the term "analysis of variance" comes from. Also, it follows from what we have just said that, if we have already computed the variances, or the SDs, of the samples, then we could use them to compute the SSE: If Var_g and SD_g denote the variance and standard deviation of the sample from group g, then the SSE is the sum of the products n_g(Var_g) = n_g(SD_g²)

2. Provided that we interpret n_g(AV_g-AV)² as the sum of n_g copies of (AV_g-AV)², there are the same total number of terms in finding SSE and SSG, namely the total number of data points N.