Higher Order full factorial designs, Part 1

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I really appreciate this excellent material. One question: at @6:34 you show that if your treatment groups do not have the same number of samples (i.e. number of replicates can be different across treatments) then you use the formula (SSE/(2^k)*(n-1)) to compute the pooled variance. However, isn't that the formula you use to compute the pooled variance when the number of samples is identical across all treatment groups? I say this because you divide by (n-1) which assumes that each treatment has n samples.

s