The chi-squared statistic in ethology: use and misuse

Abstract Pearson's chi-squared and related tests are not appropriate for all frequency-type data. Lack of independence between observations can invalidate traditional contingency table analysis because sampling distributions are no longer Poisson, multinomial or product multinominal. The usual consequence is that a true null hypothesis is rejected too often, making dubious a claim of significance. If possible, counts should be verified as coming from a Poisson or multinomial distribution before conducting tests. Assuming independence is not sufficient; chi-squared and related tests are shown not to be robust to the violation of this assumption. Frequency-type ethological data, such as the number of encounters between individuals or performances of a behaviour, are likely to violate the assumption of independence. A superior approach for the analysis of these data is demonstrated using parametric and non-parametric analysis of variance (ANOVA).

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