AVOIDING ERRONEOUSLY HIGH-LEVELS OF DETECTION IN COMBINATIONS OF SEMI-INDEPENDENT TESTS - AN APPLICATION TO TESTING FOR DENSITY-DEPENDENCE

A randomization procedure is proposed which allows statistical tests t o be combined into a single test to maintain specified and acceptable levels of false detection. This method was applied to the problem of d etecting density dependence in 135 unpublished time-series (of greater -than-or-equal-to 10 generations) from insect populations, and to simu lated density-dependent and density-independent data, so that the corr ectness of observed levels of detection from the published data could be verified. To allow the application of the randomization procedure t o Bulmer's (1975) tests and Varley and Gradwell's (1960) test, these w ere recast as randomization tests. The randomization procedure was tes ted with 39 combinations of tests for density dependence (and limitati on/attraction); it generally produced combined tests with levels of de tection that were intermediate between detection levels of the constit uent tests (and hence was limited by these). The specified rate of fal se detection (5%) was never exceeded (by more than 1%) when combined t ests were applied to time-series from a random-walk model. Two differe nt combinations of tests produced levels of detection from the publish ed time-series which were slightly greater than their constituent test s 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 B ulmer's second test. The combination of Bulmer's first and Pollard et al.'s test produced a greater level of detection (21.5%) than any othe r single test or combination of tests. These results were confirmed by the analysis of modelled density dependent data. Although the increas e in power of combinations of tests over single tests is small with th e data we used, the combined tests (listed above) had rates of detecti on that were less influenced by the form of data (of two forms of dens ity-dependent data) than were their constituent tests. Hence, it appea rs that the combined tests are of greater generality than single test statistics. The method presented here for combining several statistica l tests into a single randomization test is applicable in many other a reas of ecology where we wish to apply several tests and take the most probable result of these; and if the tests being conducted are, or ca n be expressed as, randomization tests.