Cautionary Note about Estimating Mean Length at Age with Subsampled Data

Abstract

Subsampling fixed or random numbers of fish per length category to estimate mean length at age is commonplace. However, biologists often ignore the fact that those data are collected in a stratified manner and do not represent a simple random sample of the population. We demonstrate that failure to consider the stratified nature of data and use the correct formulae to calculate means and standard errors will usually result in biased estimates of mean length at age and will always inflate standard error estimates. If the distribution of lengths within a particular age is highly skewed, estimates will be severely biased if the data are not treated in a stratified manner. Subsampling in proportion to the number of fish in each length category may be superior from a statistical standpoint; however, the more commonplace sampling of a fixed number of fish per length category is superior from the standpoints of logistics and the frequent need to accurately estimate age proportions in the largest length categories.