While median splits simplify analysis, they compromise validity. Meta-analyses benefit more from continuous data approaches or advanced modeling to avoid Type II errors and false-positive conclusions

I agree with Suraj Kapoor . You usually don't want to do a median split on a variable that can be treated as a continuous variable. That being said, sometimes there are reasons to do so. Maybe one of the best is that the reviewer said you have to. (Actually, not really a good reason, but sometimes you just do what you have to...)

But, to the question, a median split just splits the values by the median value, creating two levels for a new categorical variable. For example, if A is (1,2,3,4,5,6,7,8). The median is 4.5. The new variable B is just Group1 if A < 4.5 and Group2 if A > 4.5.

If A is exactly equal to the median ? I don't know what people usually do....

I agree with Suraj Kapoor and Sal Mangiafico - for literature on this see:

MacCallum, R. C., Zhang, S., Preacher, K. J., & Rucker, D. D. (2002). On the practice of dichotomization of quantitative variables. Psychological Methods, 7(1), 19–40. https://doi.org/10.1037/1082-989X.7.1.19

http://www.quantpsy.org/pubs/maccallum_zhang_preacher_rucker_2002.pdf

This applies generally to any regression (including meta-analysis with moderators as that's also a type of regression model).

I hope this message finds you well. I am writing to express my sincere gratitude for the invaluable information you provided regarding median distribution. Your insights have significantly enhanced my understanding of the subject, and I am truly appreciative of the time and effort you invested in sharing your expertise.

Thank you once again for your support and guidance. I look forward to applying this knowledge in my work.