I'm am currently assisting on a Meta-Analysis and we are currently faced with correlating variables without the raw scores. The question has 2 parts, however I feel like the answer to one will likely relate to the other.

I want to know how to calculate the correlation coefficient between two variables when only the MEAN and STANDARD DEVIATION is available. For example, for a sample of 20 people:

MEAN(SD)

Var 1 time 1: 2.3 (1)

Var 1 time 2: 3.4 (2)

Var 1 time 3: 3 (1.4)

Var 2 time 1: 4.5 (.4)

Var 2 time 2: 3.5 (.5)

Var 2 time 3: 3.4 (.7)

I also would like to know if It is possible to calculate the correlation between two variables with only one time point across a MULTITUDE OF STUDIES. For example:

Study 1 n=20

Var 1: 2.3 (2)

Var 2: 3.4 (1)

Study 2 n=20

Var 1: 4.5 (1.5)

Var 2: 6.4 (.5)

Study 3 n=20

Var 1: 1.4 (.5)

Var 2: 3.4 (.5)

Thanks in advance for any help