# How to estimate the covariance matrix for repeated measures data given summary statistics?

I've been working on a power analysis for an RCT study for a psychological intervention. And I've been wondering how one would estimate the covariance matrix (or rho) for repeated measures data? This is more of an academic question, since I have data from previous studies that I can use. But I'm curious what one would do if one only had access to journal articles, where most of the time only means and standard deviations are reported?

Say I wanted to calculate power for a mixed design ANOVA with 2 groups and 4 time points. I only have F-values, means and standard deviations from journal articles and no access to pilot data. Can I use this to estimate the covariance?

Here's some data generated in R, which corresponds to the summary statistics that can be found in studies.

# M
Initial  3 months 6 months  12 months
Treatment  12.58    6.34     6.61      5.79
Control    12.39    8.78     9.34      9.20

# SD
Initial  3 months 6 months  12 months
Treatment  9.17     6.36     8.44      7.74
Control    10.38    8.88     9.27      9.19

# F-statistic from mixed design ANOVA
df    F value  Pr(>F)
group       1     7.059    0.00842 **
time        3     26.874   <2e-16 ***
time:group  3     2.867    0.0358 *
residuals   714

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@user603 The OP is not trying to reconstruct the entire data set, just the correlation structure of the repeated measures. Even so, I think the answer is no. I say this assuming that you are talking about the group means and group standard deviations. –  Michael Chernick Jul 24 '12 at 13:49
thanks Michael: i didn't understood it that way at first. –  user603 Jul 24 '12 at 14:04
@Kris My thinking was that with six unknowns you couldn't construct enough equations to solve for all the correlations. But I forgot to consider the F statistics. How many F values do you have and which tests are they being used for? –  Michael Chernick Jul 24 '12 at 14:06
@MichaelChernick I've added some example data to my post, to try to clarify which statistics I assume can be found in published articles. –  Kris Jul 25 '12 at 7:40
@Kris So from this I see that you have the 3 tests for the coefficients for the interaction and two main effects in this case along with 8 treatment means and standard deviations and the same for the control. I will give this some more thought. –  Michael Chernick Jul 25 '12 at 11:08
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