# Within subject effect size when no correlation available

I am doing a research project on the topic of replicability in psychology. To do this, I did a set of 10 meta-analysis on different studies.

My problem is the following : some of those studies were between subject but most were within subject. To calculate the effect sizes in those studies, I believe I need to know the correlation between the two measures. However, most studies do not report any correlation, and since I do not have access to the original datasets (some studies are more than 15 years old), it is not possible for me to retrieve them. When looking for a solution on the Internet, I have been finding conflicting answers : - should I just ignore the correlation, as this article seems to suggest it ? (http://jakewestfall.org/blog/index.php/2016/03/25/five-different-cohens-d-statistics-for-within-subject-designs/) - should I use a random correlation ? - Or try to find a median correlation in the field ? (If so, how ?) - Should I do something else ?

I am hoping that I am not the first one to be in such a predicament and that some one more well-versed in statistics than me (a Philosophy major) might be able to provide some insight on this issue. In any case, I am very grateful to any one reading and commenting on this post !

You have a number of options. If you can find information about the likely correlation then you can impute a value of $r$ from them. As a sensitivity analysis you can try a range of values and see how they affect the answer. If the authors have published the means and standard deviations from the post condition you can just treat the study as a between groups design and ignore the pre- readings. This loses precision in general but there may be o viable alternative.