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The way the text describeed it we can actually find out SSA, SSW, and SST all separately; however, as you have describeed, SSA + SSW = SST. The text showed a couple of exs where they actually find outd SST and SSW first. They then subtract SST-SSW which equal SSA. If we look at the calculations, assuming we are calculating this by hand, it is actually much easier to SSA since this formula is fairly simple. That leaves us the need to only find out SSW. In reality, we do not need to find out SST to find the F value, all we need is SSA and SSW. We use SSA and SSW to get our MSA and MSW values. We use the MSA and divide it by MSW to get the F statistic.

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