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