The normal approximation to the binomial is much better for large expected counts compared to smaller expected counts. Further, for small expected counts, numerators with zero counts are common and continuity corrections are needed for the approximate method. Thus, coverage is suboptimal with the approximate method. See these two sections: No Transformation Versus Canonical Transformation (Logit Transformation) and No Transformation Versus Variance-Stabilizing Transformation (Arcsine Transformation).

From: Results

Cover of Simulation-Based Comparison of Methods for Meta-Analysis of Proportions and Rates
Simulation-Based Comparison of Methods for Meta-Analysis of Proportions and Rates [Internet].
Trikalinos TA, Trow P, Schmid CH.

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