Two studies, opposite results: Am I allowed to compute an overall mean using random-effect model? I am performing a meta-analysis. I have a subgroup made only of 2 studies and they show opposite results. The 1st has excellent outcomes the 2nd very bad ones.
Is it true that I am not allowed to compute the data from these two (different) studies under a random-effect model? I have been told that it is methodologically not correct to perform a meta-analysis of 2 studies with such opposite results.
They suggested me to report the raw data from these studies separately (without an overall outcome calculated by a random-effect model). Any suggestion? Or any place where I can find the explanation about this point?
 A: try to find the confounding variable.. see if you get any interactions or mabe run another test with different methodology (and more variables that may give you a clearer picture.
A: I am not an expert, but I think it is common sense to not merge two studies if they have strongly opposite outcomes. For the sake of the example, say they measure a variable $X$ (glucose in the blood etc.) in identical conditions.
Since the outcome is different, you can imagine that there is "something" unknown, so that one of the team measures actually $X + a$. Now does that make sense to merge the records? You end up with a mixture model which is much more difficult to analyze. To give you an example, the mean is meaningless because it will depend mostly on the ratio between the sample sizes.
Addition: Thank you @Michael Chernick for this fantastic quote in the comments below:

Man puts one foot in a bucket on fire and the other in a ice bucket. On average the temperature is normal. You wouldn't want to describe this with the sample mean

A: Generally, there can not be bimodal findings. The theoretical underpinnings must be considered. Moreover, two sets of outcomes can not be combined in this way. If you are keen to apply meta-analysis, the outcomes showing excellent results and outcomes showing bad results may be meta-anlysed separately. Be sure that number of outcomes (effect-sizes for a group of excellent (or bad) results is more than say, 15. If the effect-sizes are in d-form, you may follow one of the several available random-effects formulas (Hedges and Olkin 1985) for checking the variablity in effect-sizes of r (see Davar 2006).
