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I have found that

SSerror = SStotal - SStreatment

which makes sense to me alongside an example of a one-way ANOVA, however, how does this apply to a factorial ANOVA?

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If you have equal n and a full factorial, you can subtract all the effect sums of squares from sum of squares total. If you have unequal n, you can compute the sum of squared deviations of values from their mean in each cell and then summing. Or, simply, analyze it as a one-way to get SSE.

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  • $\begingroup$ Thank you. I have two within-subjects variables, and therefore more than one SSE value to find. So the SStotal should equal all of the SSeffect (variables and interactions) plus the SSEs. If I suctract all the effect SS from SStotal, I will end up with the sum of SSEs - how do I separate this? $\endgroup$
    – Lkb
    Commented Oct 19, 2017 at 12:07
  • $\begingroup$ In that case, an SSE is not a residual but the sum of squares for a Treatment x Subjects interaction. Therefore, you can compute each one directly but you can also compute the Subjects x A x B interaction by subtraction (SST - all other effects including “Subjects” and interactions. $\endgroup$
    – David Lane
    Commented Oct 20, 2017 at 3:35

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