Is this the answer?

http://handbook.cochrane.org/chapter_7/7_7_3_3_obtaining_standard_deviations_from_standard_errors.htm

Dear Azeem,

I'm not sure whether this is possible. It is nearly always better to work with raw data rather than summary statistics.

If you have the change scores, why not just compute the standard deviation of those change scores.  Most often when this question is asked, the person asking really wants to conduct a t-test for the differences between means.  Most all general statistics programs have a paired sample (dependent sample) t-test available.  The output will usually give you the pooled standard error of the differences between means, and the other information you are looking for.  Of course, you will most likely need raw data coded as separate variables (pre and post) to run this analysis. 

Alternatively, if you know the correlation between the paired samples or the covariance between the paired samples, you can use the following formula to calculate the variance.

Var(X - Y) = var(X) + var(Y) - 2 * cov (X,Y)

or

var(X - Y) = var(X) + var(Y) - sd(X) * sd(Y) * corr(X,Y)

where var = variance, cov = covariance, sd = standard deviation, corr = correlation.  The standard deviation is just the square root of the variance.  Without knowing the relationship (correlation or covariance) between the samples, you may be unable to analytically derive the variance of the change scores.  

I hope this is helpful.  If you need further help, please ask; someone here can probably assist you with your analysis or computations. 

David Drehmer

I am conducting a meta-analysis and at least from what I gather from Cochrane the method you offer Mr. Drehemer would be inappropriate. Apparently, I need to use a combination of ES, CI, and P-value when appropriate.

Are you saying you have repeated measures on the same case (Raw scores for pre and post measure on the same subject)?

If your question here is part of the questions you have also posted on ResearchGate, then it sounds like you have a very difficult analysis to do.  With only 8 studies, 5 of which report change scores and three report only post scores and the instruments are not the same across studies, you may have very little power to answer the questions you wish to ask of your analysis.  Your reference to Cochrane is indeed a good one, but what you've quoted here does not capture the complexity with which you must deal.  Basically this chapter is little more than the definition of a confidence interval, and solving for a pooled standard deviation under the assumption of independence of the samples.  While Cochrane's chapter and my prior answer to your question are not inconsistent with each other, I am at a loss about what you are really trying to do and what data you have to do it. 

What, specifically, are you attempting to learn.  It would be helpful to understand the substantive problem before offering further opinions on statistical methods.  What specific data do you have and why is that data appropriate to your study.  Can you meaningfully combine it through summary statistics or even in its raw form, if you have it.  Can you get the authors of the original studies to share their relevant data with you to do your analysis?  Combining data that comes from different sources with different scales may present its own set of major problems.  Can you identify those problems and find a way to effectively deal with them?  Stated differently, two people and 24 bottles of beer do not produce the same results as 2 bottles of beer and 24 people.  It is always good to know what you want to do before you assess how well you have done it. 

It sounds like you have many design issues as well as statistical issues to be overcome.  I think this is a very difficult problem under the best of circumstances, and yours presents many challenges.  Let me take this opportunity to applaud you for your struggle with this situation.  I'm guessing that your tolerance for frustration is pretty high.  My own prognosis for this study is guarded to poor, though I am often surprised by the creative application of old tools.

First, this situation calls for someone who is a well seasoned statistician, and preferably someone who has been steeped in the traditions of meta analysis.  Perhaps you an find a statistician or an epidemiologist at your university who would be willing and able to work through this issue with you.  Second, you might benefit from reading and studying an additional text on meta analysis such as:

Borenstein, Michael, Larry V. Hedges, Julian P. T. Higgins, and Hannah R. Rothstein. 2011. Introduction to Meta-Analysis. Somerset: Wiley.

Third, continue to reach out to people on ResearchGate, knowing that there are experts that can offer informed opinions when they have enough background to do so.  Please let me know if I can be of further help.

Best wishes,

David Drehmer

David E. Drehmer's explanation and calculations for the variance are correct except he left out a 2 multiplier in the second equation. It should be:

var(X - Y) = var(X) + var(Y) - sd(X) * sd(Y) * 2 * corr(X,Y)

So, How can I get corr(X,Y)

Note that mean of the difference is the same as the difference between the means.Therefore, if you have the change score then go ahead and compute the SD.

Note that Sd for pre -post test is

SQRT(((N*SUMof the D*D) - (sum of d)*(sum of d)) / (n-1))

Hi Azeem, I am having the same issue. If you found a solution can you please help me how to do it. I actually tested the formula which Dr. Drehmer' suggested but something doesn't look right. I am getting change in STD in hundreds (which is not possible). Thanks in advance.

Hi everyone,

This situation and potential solutions are discussed with enough detail in section 6.5.2.8 (Imputing standard deviations for changes from baseline) of the Cochrane Handbook for Systematic Reviews of Interventions (Version 6, 2019).

SD change = √(SD2baseline + SD2final - (2 x Corr x SDbaseline x SDfinal))

Where Corr is the correlation coefficient.

Here the link: https://training.cochrane.org/handbook/current/chapter-06#section-6-5-2-8

Diego A Bonilla the problem is that to calculate the "SD change" you need the correlation coefficient, and to calculate the correlation coefficient you the "SD change"...

Any ideas on how to solve this?

Dear Daniel Gomes da Silva Machado ,

Yes. That's when you might impute the average of the Corr calculated from a study reported in considerable detail (as the Cochrane handbook states in their section https://training.cochrane.org/handbook/current/chapter-06#section-6-5-2-8), as loog as methods, reported variable, subjects and intervention are similar.

I also have solved this problem in a current meta-analysis I'm working on with the personal communication to the author of a given RCT. In this case, I received promt response and authors were so kind delivering the necessary information.

Hope this help!