Estimating means and variances: The comparative efficiency of composite and grab samples

Abstract

This paper compares the efficiencies of two sampling techniques for estimating a population mean and variance. One procedure, called grab sampling, consists of collecting and analyzing one sample per period. The second procedure, called composite sampling, collectsn samples per period which are then pooled and analyzed as a single sample. We review the well known fact that composite sampling provides a superior estimate of the mean. However, it is somewhat surprising that composite sampling does not always generate a more efficient estimate of the variance. For populations with platykurtic distributions, grab sampling gives a more efficient estimate of the variance, whereas composite sampling is better for leptokurtic distributions. These conditions on kurtosis can be related to peakedness and skewness. For example, a necessary condition for composite sampling to provide a more efficient estimate of the variance is that the population density function evaluated at the mean (i.e.f(μ)) be greater than$1/\sigma \sqrt {2\pi }$. If$f(\mu )< 1/\sigma \sqrt {2\pi }$, then a grab sample is more efficient. In spite of this result, however, composite sampling does provide a smaller estimate of standard error than does grab sampling in the context of estimating population means.