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Avoiding erroneously high levels of detection in combinations of semi-independent tests : An application to testing for density dependence

Holyoak M, Crowley PH

Oecologia, 1993

Abstract

A randomization procedure is proposed which allows statistical tests to be combined into a single test to maintain specified and acceptable levels of false detection. This method was applied to the problem of detecting density dependence in 135 unpublished time-series (of ≥10 generations) from insect populations, and to simulated density-dependent and density-independent data, so that the correctness of observed levels of detection from the published data could be verified. To allow the application of the randomization procedure to Bulmer's (1975) tests and Varley and Gradwell's (1960) test, these were recast as randomization tests. The randomization procedure was tested with 39 combinations of tests for density dependence (and limitation/attraction); it generally producedcombined tests with levels of detection that were intermediate between detection levels of the constituent tests (and hence was limite by these). The specified rate of false detection (5%) was never exceeded (by more than 1%) when combined tests were applied to time-series from a random-walk model. Two different combinations of tests produced levels of detection from the published time-series which were slightly greater than their constituent tests when they were combined into single tests. These were the randomized form of Bulmer's (1975) first test with the tests of Pollard et al. (1987) and Reddingius and den Boer (1989) with the randomized form of Bulmer's second test. The combination of Bulmer's first…

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