Estimating the population variance, standard deviation, and coefficient of variation: Sample size and accuracy

Small sample sizes are often used in human and primate evolutionary research to estimate population parameters such as the mean, variance, and standard deviation, as well as statistical measures such as the coefficient of variation. Determining how well sample estimates represent population parameters is essential for establishing confidence in the inferences made using those samples. We present methods for determining a priori the probability, based on Cochran's theorem, that the sample variance and sample standard deviation are within a specified fraction of the population parameters. We validate these methods using random resampling with replacement of a single variable from a commonly used large craniometric data set comprising modern human population samples from around the world. Results based on Cochran's theorem, which we validate, indicate that large random samples comprising hundreds of observations, rather than tens of observations, are needed to be confident that the sample estimate is a reasonably accurate approximation of the true population variance. Smaller sample sizes on the order of tens of observations, however, are sufficient for estimating the population standard deviation. We extend our method of validation to show that the coefficient of variation mirrors closely the results for the standard deviation.