The Effects of an Arcsin Square Root Transform on a Binomial Distributed Quantity.

Imaging Science and Biomedical Engineering Division

ABSTRACT This document provides proofs of the following: • The binomial distribution can be approximated with a Gaussian distribution at large values of N . • The arcsin square-root transform is the variance stabilising transform for the binomial distribution. • The Gaussian approximation for the binomial distribution is more accurate at smaller values of N after the variance stabilising transform has been applied. The conclusion contains some comments concerning the relationship between the variance stabilising transform and the improved accuracy of the Gaussian approximation, which holds for both the binomial and Poisson distributions.

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