How Small Is Big: Sample Size and Skewness

Abstract

Sample sizes of 50 have been cited as sufficient to obtain stable means and standard deviations in normative test data. The influence of skewness on this minimum number, however, has not been evaluated. Normative test data with varying levels of skewness were compiled for 12 measures from 7 tests collected as part of ongoing normative studies in Brisbane, Australia. Means and standard deviations were computed from sample sizes of 10 to 100 drawn with replacement from larger samples of 272 to 973 cases. The minimum sample size was determined by the number at which both mean and standard deviation estimates remained within the 90% confidence intervals surrounding the population estimates. Sample sizes of greater than 85 were found to generate stable means and standard deviations regardless of the level of skewness, with smaller samples required in skewed distributions. A formula was derived to compute recommended sample size at differing levels of skewness.

Keywords: minimum sample sizes; normative data; psychological assessment; psychometrics; skewness.