I'm not sure that one simply "accepts" heterogeneity or not, on a conceptual level. Practically speaking one can do a chi-square test, but this can have low power. Making a binary yes/no decision on whether heterogeneity exists is, in my opinion, a bit oversimplistic. I prefer to see the group level variance in a mixed-effects meta analysis computed using a well reasoned estimation approach for the problem (Veroniki et al. have a nice summary of different estimators) +/- representation in terms of I^2, and then have a careful discussion of why these values do or do not make sense, and how they change the interpretation of the main findings.

Veroniki, A. A., Jackson, D., Viechtbauer, W., Bender, R., Bowden, J., Knapp, G., Kuss, O., Higgins, J. P., Langan, D., & Salanti, G. (2016). Methods to estimate the between-study variance and its uncertainty in meta-analysis. Research Synthesis Methods, 7(1), 55–79. https://doi.org/10.1002/jrsm.1164

There are several tests to quantify the heterogeneity such as Cochrane Q and I square. These should be reported. There is no "acceptable" heterogeneity. Heterogeneity should be explained by different methods such as subgroup analysis or meta-regression, etc.

Thank you for your opinion and suggestions@ Abraham Nunes , and Ramin Sadeghi

Heterogenity can be measures by i square value .If the i square value is more that 50 percent then there is a lot of hetrogenity in data and the same should then follow random effect model. Pls mail at [email protected] for further queries if any

Dear Jaspreet, thanks for your reply. This I know.

Yes