Bias in linear model power and sample size calculation due to estimating noncentrality

Data analysts frequently calculate power and sample size for a planned study using mean and variance estimates from an initial trial. Hence power, or the sample size needed to achieve a fixed power, varies randomly. Such calculations can be very inaccurate in the General Linear Univariate Model (GLUM). Biased noncentrality estimators and censored power calculations create inaccuracy. Censoring occurs if only certain outcomes of an initial trial lead to a power calculation. For example, a confirmatory study may be planned (and a sample size estimated) only following a significant result in the initial trial. Computing accurate point estimates or confidence bounds of GLUM noncentrality, power, or sample size in the presence of censoring involves truncated noncentral F distributions. We recommend confidence bounds, whether or not censoring occurs. A power analysis of data from humans exposed to carbon monoxide demonstrates the substantial impact on sample size that may occur. The results highlight potential biases and should aid study planning and interpretation.