How SPSS works our standard errors for simple effects in a WW design
Suppose we have a repeated measures ANOVA with two two level repeated measures factors, W1 and W2. Supppose further that we are interested in comparing the difference between the two levels of W2 at each level of W1.
/EMMEANS does this for us but what does it do? There are two ways we can do the equivalent test. Either by computing the difference between the two columns being compared, W12 and W11, in the difference comprising the simple effect, W12 - W11, where Wij is the combination of factors with W2=i and W1=j.
If we then perform one sample t-test on this difference (ie a paired t-test) the standard error of the mean will correspond to the standard error of the simple effect and the mean will be the difference being tested by the simple effect so the confidence interval for the W12-W11 difference would be the mean difference +/- t( on n-1 df) se of the mean difference for n subjects.
Another way to do this test of a simple effect test is to perform a repeated measures ANOVA in SPSS on the two columns, W11 and W12. Then the standard error of the difference W12-W11 equals sqrt(2 MSE/n) where MSE is the Mean Square Error in the repeated measures ANOVA only containing the two columns W11 and W12.
Other simple effects for repeated measures factors may be obtained similarly. In using this approach SPSS is using the standard errors only associated with the particular combinations of factors being differenced to comprise the simple effect.