A Power Analysis for Detecting Trends

TLDR

A power analysis estimates the probability of detecting upward or downward trends in abundance using linear regression, based on sample size, variability, and rate of change, and can also compute the minimum number or precision of samples needed for a given confidence. The study investigates how linear and exponential changes, and abundance‑dependent sample variability, affect trend detection. The authors use linear regression on regularly spaced samples to model trends, considering both linear and exponential change and abundance‑dependent variability. Graphical summaries illustrate the power analysis, and the method is demonstrated by monitoring California sea otter populations via aerial surveys.

Abstract

A power analysis allows estimation of the probability of detecting upward or downward trends in abundance using linear regression, given number of samples and estimates of sample variability and rate of change. Alternatively, the minimum number or precision of samples required to detect trends with a given degree of confidence can be computed. The results are applicable to an experimental situation in which samples are taken at regular intervals in time or space. The effects of linear and exponential change and of having sample variability be a function of abundance are investigated. Results are summarized graphically and, as an example, applied to the monitoring of the California sea otter population with aerial surveys.