Using the Sample Range as a Basis for Calculating Sample Size in Power Calculations

Lacking a sample standard deviation to use as an estimate of σ in sample size computations, consultants often divide a sample range (R) by a constant to estimate σ. To avoid underpowered studies, the estimate must have a high probability of being greater than or equal to σ. The probability of being greater than or equal to σ is estimated for R/6, R/4, and R/(standardized mean range) for various parent distributions and a range of sample sizes. Those probabilities are found to be quite low for many distributions and sample sizes. Alternative divisors (K) are found for which the probability of R/K being greater than or equal to σ is at least 95%.