Is it appropriate to estimate the mean difference from a Wilcoxon p-value? I am conducting a meta-analysis involving paired data (two instruments measuring the same thing). Original papers do not provide the standard deviation of the mean difference. One paper provides a p-value (<0.001) for a "Wilcoxon" test. I am assuming this is a Wilcoxon signed rank test (presumably two-tailed). I have the median difference and the mean difference. Can I generate a reasonable estimate of the mean difference? The sample size is reasonably large n=569.
I have edited a typo. I have the mean difference, not the standard deviation of the mean difference.
 A: If you have the mean difference then all you are lacking is the standard error. If you are prepared to make some fairly big assumptions then you might be able to proceed.
The first and biggest leap is to assume that if the authors had done a $t$-test they would have got a similar $p$. In practice this usually is the case but it is an assumption. Given you have the $p$-value you can back-calculate what value of $t$ they would have got. In your case you only have the upper bound n $p$ so you need to form the $p$ which is the largest value which if rounded would still be less than 0.001 so 0.0005. Then assuming you have the sample size you can work out the degreees of freedom and then $t$. In R which I use

qt(0.0005, 200, lower.tail = FALSE)
  [1] 3.339835

where I assumed you had 200 degrees of freedom.
Since you know that $t = \bar{X}/se$ and you now know two terms in that equation you can retrieve the standard error which is what you needed for meta-analysis. This is conservative since if the actual $p$ was even smaller your value for $t$ would be larger and the standard error smaller. If you had the exact $p$ that would not apply.
It would be vital when you write up your study to clarify what you have done and what assumptions it rests on for transparency.
