Anirban,

You are into something interesting yet, intricate. I agree with Ahmed that we need to know what your goal is with the analysis/ research. The intricacy of your problem since you are dealing with Meta-analysis of technical efficiency (TE) studies, is that you need to know how representative those individual studies were in terms of representing all the DMU’s in the sectors they addressed. Good scientific papers will always address the representativity of their data sets and, they are normally representative such that Mean TE’s (MTE) can be considered as representative. This is the reason that Thiam and Bravo-Ureta (2005); Odeck and Bråthen (2012); Kiadaliri et. al (2013) Fall et. al (2018)) use the mean technical efficiency (MTE) as a measure of effect size without further consideration of sampling bias. Therefore, and in the first instance, you could proceed by using the reported MTE’s as well.

Next and given that you want to consider sampling bias as something new which has not been considered in the literature of meta-analyses of MTE’s, the only option left for you is to go through the abundant literature and ask the individual authors how representative their data were with regards to the total population of their DMUs. If their studies were not all that representative, you may use the information they provide to correct for sampling bias and then produce a paper that goes further to pinpoint the sampling issue. This may be a cumbersome process that may take time to accomplish since a meta-analysis normally includes many studies.

Finally, if you feel that the TE data should be normally distributed and you have good arguments for it, you could apply e.g., the Fisher transformation; but please explain why. Note now that SFA-based-TE’s for instance, apply non-normal distributions built on real observations!

I hope this helped.