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Estimating Power to Detect Trends in Count Data

Brian R. Gray 1 and Michele M. Burlew 2

1 Upper Midwest Environmental Sciences Center, U.S. Geological Survey (USGS), La Crosse, Wisconsin
2 Episystems, Inc., St. Paul, Minnesota

Environmental monitoring programs typically aim to describe trends in selected environmental or ecological metrics. However, little attention may be paid to whether such programs attain adequate power to detect future trends that are scientifically meaningful within a reasonable temporal period. The estimation of power to detect trends in monitoring data is particularly challenging when those data comprise counts. Potential approaches include the use of variance estimates derived from design-based and error variance-weighted design-based means, and simulations from models that ostensibly represent the design from which the observed data arose. We used the latter approach to assess power to detect trends in macroinvertebrate, fish and vegetation counts on approximately 50 km reaches of the Upper Mississippi River. Counts were assumed to derive from Poisson-gamma mixture processes, local variance (for a given mean) was allowed to vary by spatially-defined strata, and strata effects were themselves allowed to vary randomly by sampling event. Multiple simulated datasets from this model, with imposed trends of varying magnitudes, were then analyzed for trend effects. This approach suggests that, at a = 0.05, power to detect future decreases of 5% per year in mayfly relative abundance, for example, of 80% after approximately 12 years. Changes of 3% per year would be detected at the same power after approximately 17 years. Doubling sample size per sampling event decreases these detection periods by approximately four years. An advantage of the described approach is that the characteristics of the models used to analyze the observed data, to generate the simulated data, and to analyze the simulated data were equivalent.

Keywords: Long Term Resource Monitoring Program (LTRMP), Mississippi River, models, statistical power, trends

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