A simple test for the difference of means in meta-analysis when study-specific variances are unreported

Standard meta-analysis requires the quantity of interest and its estimated varianceto be reported for each study. Datasets that lack such variance information pose im-portant challenges to meta-analytic inference. In a study with continuous outcomes,only sample means and sample sizes may be reported in the treatment arm. Classicalmeta-analytical technique is unable to apply statistical inference to such datasets. Inthis paper, we propose a statistical tool for testing equal means between two groupsin meta-analysis when the variances of the constituent studies are unreported, usingpivot inference based on the exact t-distribution and the generalized likelihood ratio.These are considered under a fixed effect model. In simulations, the type I errorsand power probabilities of the proposed tests are investigated as metrics of theirperformance. The t-test statistic provides type I errors very close to the nominalsignificance level in all cases, and has large power. The generalized likelihood ratiotest statistic performs well when the number of studies is moderate-to-large. Theperformance of our tests surpasses that of the conventional test, which is based onthe normal distribution. The difference is especially pronounced when the numberof studies is small. The distribution given by our tests is also shown to closely followthe theoretical distribution