Geiger and Zhang, 2002

Geiger, H. J., and X. Zhang. 2002. A simple proceedure to evaluate escapement trends over time that emphasizes biological meaning over statistical significace. Alaska Fishery Research Bulletin 9(2):128-134.

Statistical hypothesis testing for a "significant" decline is poorly suited for the analysis of salmon stock trends. Unfortunately, when statistical hypothesis-test machinery is applied to an escapement series, biologically unimportant, small downward fluctuations can be considered "significant," especially in long series. Alternatively, often very steep declines in escapement levels are found to be "not significant," especially in short series. The hypothesis test may tell more about the length of the series than the magnitude of the decline or the stock dynamics. We propose a simple and robust method of estimating the magnitude of stock decline (or increase), and propose a way to reference stock decline in terms of an underlying escapement level at the beginning of the series, so the decline can be judged in some kind of context. We regressed escapement on time using a resistant regression line. We propose using the back-cast estimate of what the escapement was in year zero of the series as a nonparametric escapement benchmark, and we call this benchmarkthe year zero-reference point. This back-cast estimate is just the estimated y-intercept of the regression line. In several 15 year series that we examined, we concluded that an escapement decline was biologically meaningful whe the estimated underlying annual decline was more than 5% of the year-zero reference point, as that decline will result in the underlying escapement level dropping by half over a 10-year period.