Using Variance Components to Estimate Power in a Hierarchically Nested Sampling Design: Improving Monitoring of Larval Devils Hole Pupfish

Authors: Maria C. Dzul, Philip M. Dixon, Michael C. Quist, Stephen J. Dinsmore, Michael R. Bower

Year: 2010 (xlii)

Abstract

Hierarchically nested sampling designs, or designs which include one or more levels of sub-samples, are common in fisheries and wildlife monitoring where replication of samples can be expensive. Variance components estimation can be used to determine how variance is partitioned among different levels of sampling, thereby helping estimate statistical power under various sampling design structures. We use the monitoring of larval Devils Hole pupfish, Cyprinodon diabolis, as an example to illustrate how power can be evaluated in sampling designs with multiple levels. Surveys for larval Devils Hole pupfish include three levels of sampling: surveys (2 samples per month), events (3 samples per survey), and plots (9 samples per event). The goal of this study was to determine how changing the sample size at each level (survey, event, and plot) affected the ability to detect a defined change in abundance at some level of statistical power. Using a linear mixed model, variance components were estimated for all three sampling levels (i.e., survey, event, and plot). Next, sample sizes across all levels were allowed to vary, as to represent different combinations of surveys, events, and plots. Variance was recalculated and used to calculate statistical power. Increasing sample size at the level of survey had the greatest influence on statistical power, followed by plot and event. However, since surveys are more difficult to implement, increasing the number of plots per event represents a more efficient method to increase power.