A Holistic View of Finite Populations for Determining an Appropriate Sample Size

Abstract

This study presents practical and easy-to-implement approaches for determining appropriate, or “safe”, sample sizes for routinely conducted statistical surveys. Finite populations are considered holistically and independently of whether they are continuous, categorical, or dichotomous. It is proposed that in routinely conducted sampling surveys variance-ordered categories of populations should be the basis for calculating the safe sample size given that the variance within a target population is a primary factor in determining sample size a priori. Several theoretical and operational justifications are presented for this thesis. Dichotomous populations are often assumed to have higher variances than continuous populations when the latter have been standardized and have all values in the interval [0 1]. Herein, it is shown that this is not a valid assumption; a significant proportion of dichotomous populations have lower variances than continuous populations. Conversely, many continuous populations have variances that exceed the limits that are broadly assumed in literature for determining a safe sample size. Finite populations should thus be viewed holistically. A simple first step is to partition finite populations into just two categories: convex and concave. These two categories are relative to a flat population with a known variance as the threshold between them. This variance is used to determine a safe sample size for any continuous population with a flat or positive curvature, including approximately 20% of dichotomous populations. For all other populations the value of 0.25 is recommended for approximating the actual population variance as the primary parameter for sample size determination. The suggested approaches have been successfully implemented in fisheries statistical monitoring programmes but it is believed that they are equally applicable to other applications sectors.