A systematic review with data synthesis is being conducted. The data synthesis aims to assess if there are correlations between changes in two pair of variables (e.g., disability and pain).

From each included study, only mean and SD (no more data available) have been extracted in different follow-up periods (1-month, 3-months, 6-months, 12-months).

Doubt/question:

I would like to run a correlation analysis of two pairs of Hedges'g effect size values to assess a correlation between variables' changes. What I would like to know is if it is possible to run spearman correlation weighted by sample size and number of follow-ups between Hedges'g values. And if yes, how it could be reported or justified.

I have already calculated repeated Hedges'g values for the same group in different follow-up times (1-month, 3-month, 6-month, 12-month) in different variables (i.e., variable1 and variable2).

An example of the Hedges'g matrix is:

----------------------- Var1 Var2

g1 (3-months) -0.5 -0.9 ---> n=12

g1 (6-months) -0.4 -1.6 ---> n=12

g2 (3-months) +0.1 +0.0 --> n=12

g3 (1-months) -0.7 -0.3 ---> n=40

g3 (3-months) -0.6 -0.3 ---> n=40

g3 (6-months) -0.8 -0.4 ---> n=40

g3 (12-month) -1.0 -0.5 ---> n=40

g4 (1-months) -0.7 -0.2 ---> n=40

g4 (3-months) -0.5 -0.3 ---> n=40

g4 (6-months) -0.4 -0.3 ---> n=40

g4 (12-month) -0.6 -0.2 ---> n=40

- If I run spearman correlation only with Hedges'g values (without taking into account sample size), it would be wrong because sample size is not taking into account.

- If I run spearman correlation creating n cases (12 with the first pair of values, 12 with the second pair of values, 12 with the third pair of values, 40 with the fourth pair of values, 40 with the fifht pair of values, etc), it would be wrong because for the same sample/group I am creating more cases than participants.

- Then, my question is if I weight the Hedges'g values according sample size and number of measurements (6 cases for the first pair, 6 cases for the second pair, 12 for the third pair, 10 for the fourth pair, 10 for the fifth pair, etc.) and then calculate spearman correlation, would it be correct?

Thanks in advance for your time.