Let's say that I'm conducting a meta-analysis, looking at the performance of group A and group B with respect to a certain construct. Now, some of the studies that I'll come across will report that no statistical differences could be found between the two groups but no exact test statistics and/or raw data will be presented. In a meta-analysis, how should I handle such studies?
Basically, I see three different alternatives here:
- Include them all and assign to each one of them an effect size of 0.
- Throw them all out.
- Do some kind of power analysis for each one of them or set a threshold at a certain number of participants. Include all which should have been able to reach statistical significance and assign to each one of them an effect size of 0. Throw the rest out.
I can see merits with all the different options. Option one is fairly conservative and you'll only risk making a type II error. Option two raises the risk for making a type I error, but it also avoids having your results ruined because of a bunch of underpowered studies. Option three seems like the middle road between option one and option two, but a lot of assumptions and/or pure guesses will have to be made (What effect size should you base your power analyses on? What number of participants should you demand from each study for it to pass?), probably making the final result less reliable and more subjective.