Using randomization techniques to analyse behavioural data

Data from behavioural studies are frequently non-normally distributed and cannot be analysed with traditional parametric statistics. Instead, behaviourists must rely on rank-transformation tests, which lose potentially valuable information present in the data. Recently, however, biologists in other disciplines have resolved similar statistical difficulties by using resampling methods. Results from Kruskal–Wallis non-parametric ANOVA and randomization tests were compared for two behavioural data sets. It was found that randomization tests were more powerful than Kruskal–Wallis, and could thus detect smaller effect sizes present in the data. In addition, the variance was calculated around the P-value at eight levels of replication ranging from 500 to 10 000, to determine the optimal number of replications for the randomization test. The variance around the P-value decreased as the number of replications increased. The P-value stabilized at 5000 replications, and thus it is recommended that at least 5000 replications be used for randomization tests on behavioural data. ? 1996 The Association for the Study of Animal Behaviour Animal behaviourists frequently use nonparametric statistical methods when their data are not normally distributed (Martin & Bateson 1986). Most of these methods involve ranking the data sequentially and performing statistics on the ranks (Sokal & Rohlf 1995). Although nonparametric approaches do not require data to be normally distributed, they usually assume that the distributions being compared are symmetrical (Day & Quinn 1989). One drawback of these methods, however, is that some information is invariably lost in the rank-transformation stage, thus making non-parametric approaches less powerful and less desirable than traditional parametric statistics. In recent years, alternative tests have become available which are based on resampling methods. These tests do not make distributional assumptions, and are often more powerful than other non-parametric approaches (Manly 1991). Here we briefly describe resampling approaches and apply randomization tests and non-parametric analysis of variance (Kruskal– Wallis) to two behavioural data sets for comparison. Resampling statistical techniques are computerintensive methods that take many samples from the original data and analyse the data based on these samples (Crowley 1992). They can be used to determine confidence intervals for a given statistic (e.g. bootstrap, jackknife and permutation tests), for determining the effect of a stochastic process (Monte Carlo) or even for hypothesis testing (permutation and Monte Carlo). As microcomputers have become faster and less expensive, resampling techniques have been used more and more frequently in biology (for a complete review, see Crowley 1992). All of these techniques can be used by running simple computer programs, many of which have routines that are readily available (see Manly 1991). For biologists, probably the most widely known of the resampling methods is the bootstrap, which generates a confidence interval for a given statistic by taking N samples (of size N) with replacement from a data set, and calculates an estimate of the statistic. This procedure allows for the possibility that some values will be sampled more than once, but that others are not Correspondence: D. C. Adams, Department of Ecology and Evolution, SUNY at Stony Brook, Stony Brook, NY 11794-5245, U.S.A. (email: [email protected]. SUNYSB.EDU). C. D. Anthony is at the Department of Biology, University of Southwestern Louisiana, Lafayette, U.S.A. 0003–3472/96/040733+06 $18.00/0 ? 1996 The Association for the Study of Animal Behaviour