The Myth of Continuity-Corrected Sample Size Formulae

SUMMARY In this paper, we consider methods for determining sample sizes when inference on two proportions is required. It is assumed that the proportions are from independent samples. Fisher's exact test is regarded as the relevant test for sample size determination in this case. However, the computation involved is extremely laborious, and so good approximations are extremely useful. One of the best-accepted approximations is due to Casagrande, Pike, and Srmith (1978, Biometrics 34, 483-486). This approximation is supposed to be derived from applying the correction for continuity when a normal distribution is used to approximate a discrete distribution. However, a consistent application of the correction for continuity does not give the Casagrande, Pike, and Smith approximation. Nevertheless, it is shown that this approximation gives an upper bound for the required sample size based on the normal approximation to the binomial distribution. As such,

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