Correcting Bias in Sample Size Estimation

The estimation of the sample size of an experiment on the basis of a pilot sample is considered. Pilot samples provide estimates of the unknown parameters of the population, which are used for estimating the sample size. Consequently, the computed sample size is viewed here as a random variable. Then, the actual power of the experiment is a random variable, whose mean, namely conditional power (CP), is often different from the power to achieve, giving a bias. In this paper, we propose a calibrated correction to the estimator of the population parameter in order to obtain a CP closer to the power to achieve than the CPs provided by classical pointwise and conservative estimators. A simulation study shows that this calibrated sample size estimator performs well, with the Z test and with the t test.