Biological Examples of Small Expected Frequencies and the Chi-Square Test

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Abstract
The present paper is meant to report the analysis of some biological data on the host-commensal relationship between host animals [bay scallops (Aequipecten) and penshells (Atrina)] and crabs (Pinnotheres) using Nass''s approximation, to reanalyze the data using the exact distribution of the chi-square measure and to gain an understanding of the situations in which Nass''s approximation is close to the exact distribution. It is found that in the tail part of the distribution, the part which is usually used in taking hypotheses and setting up confidence intervals, Nass'' approximation is fairly close to the exact distribution even for such small observed frequencies as 1 and 2 and much closer to the exact distribution than the usual approximation in which we take the chi-square measure as being distributed as Pearson''s chi-square with modified degrees of freedom.

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