SPSS - Calculation of confidence intervals in estimated marginal means of repeated measures ANOVA

Question

I used SPSS to do a repeated measures ANOVA including one within- and one between subject factor. Let's say the between-subject factor is treatment group with levels treatment and control, and the within-subject factor is time, with levels pre-treatment and post-treatment. I asked SPSS to also give me the Estimated Marginal Means and descriptive statistics.

In the ouput, when I look at the Estimated Marginal Means for the interaction of group and time, I get four means, one for each cell of these two crossed factors. These means are the same as those I get in the descriptive statistics, which is what I expected. However, in the Estimated Marginal Means I also get standard errors of the means and 95% confidence intervals for the four means. I cannot figure out how these were computed, because they do not match the standard deviations for these 4 cells that are reported in the descriptive statistics. Sometimes the standard errors and CIs in the Marginal Means are larger than expected based on the standard deviations of the cells, and sometimes they are smaller.

Do the Marginal Means make some kind of adjustment, or compute the standard deviation of the cells in some different way than would be expected?

Thanks for your help.

Answer 1

After a little more manual calculation, I found the answer to my question. It seems that when a between-subjects factor is included in the repeated measures ANOVA, SPSS bases its estimate of the standard error of the condition mean for a group not on the standard deviation of the dependent measure within that group, but on the pooled standard deviations of the dependent measure within both groups. They are pooled by taking the square root of the summed squared standard deviations of both groups. The standard error is computed by using the pooled N.