I have conducted a mixed-design ANOVA with a between-subjects factor (Group: Control Group [0] vs. Intervention Group [1]) and a within-subjects factor (Time: Baseline [0], Follow-up 1 [1], and Follow-up 2 [2]). To further investigate a significant interaction (Time Point * Group), I performed pairwise comparisons in SPSS. I now receive a table with the mean and a Standard Error for each group at each time point.
In the 'Estimates' table, I now find the means of the respective groups at each time point (for example, the mean of the control group at Time Point 1 [Baseline]). This mean corresponds to the 'ordinary' mean that I could calculate descriptively.
However, in addition, I now find a Standard Error in the table, rather than a Standard Deviation. Since the formula for the Standard Error (SE) is SD/sqrt(n), I thought that multiplying SE by sqrt(n) would lead me to the original Standard Deviation. However, this is not the case. The Standard Deviation that I find, for instance, in the 'Descriptive Statistics' table is different from when I attempt to calculate it from the provided Standard Error (SE) (using: SE * sqrt(n)).
Can someone tell me why this is the case and why SPSS, in the output of the Follow-Up Tests (Pairwise Comparisons), provides the same means, but the Standard Error (SE) does not match the value I get when I divide the SD by the square root of n (SD/sqrt(n)) [or the other way around: I don't get the same Standard Deviation (SD) when I multiply the SE with the sqrt(n)]?
Thank you in advance."
I tried to multiply the SE with the sqrt(n) to get the SD, but it didn't match the "actual" SD which I can calculate descriptively (or which I can find in the "Descriptive statistics" table)