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To combine the proportions from different studies for meta-analysis, Freemanand Tukey double arcsine tranformation can be useful for normalization andvariance stabilization. The inverse function of the double arcsinetransformation has been also derived in the literature to recover the originalscale of the proportion after aggregation. In this brief note, we present thedomain and range of the inverse double arcsine transformation both analyticallyand graphically. We notice an erratic behavior in the mathematical formula forthe inverse double arcsine tranformation at both limits of its domain, andpropose approximation methods for both small and large samples. We also proposea simple accuracy measure, the maximum percent error (MPE), of the large sampleapproximation, which can be used to determine the sample size that wouldprovide a certain accuracy level, and conversely to determine the accuracylevel of the approximation given a sample size.

Domain of Inverse Double Arcsine Transformation