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Analysis of Frequency Count Data Using the Negative Binomial Distribution
Author(s) -
White Gary C.,
Bennetts Robert E.
Publication year - 1996
Publication title -
ecology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.144
H-Index - 294
eISSN - 1939-9170
pISSN - 0012-9658
DOI - 10.2307/2265753
Subject(s) - overdispersion , negative binomial distribution , statistics , quasi likelihood , count data , poisson distribution , mathematics , binomial distribution , goodness of fit , zero inflated model , poisson regression , statistical hypothesis testing , regression analysis , likelihood ratio test , negative multinomial distribution , econometrics , beta binomial distribution , medicine , population , environmental health
The statistical distributions of the counts of organisms are generally skewed, and hence not normally distributed, nor are variances constant across treatments. We present a likelihood—ratio testing framework based on the negative binomial distribution that tests for the goodness of fit of this distribution to the observed counts, and then tests for differences in the mean and/or aggregation of the counts among treatments. Inferences about differences in means among treatments as well as the dispersion of the counts are possible. Simulations demonstrated that the statistical power of ANOVA is about the same as the likelihood—ratio testing procedure for testing equality of means, but our proposed testing procedure also provides information on dispersion. Type I error rates of Poisson regression exceeded the expected 5%, even when corrected for overdispersion. Count data on Orange—crowned Warblers (Vermivora celata) are used to demonstrate the procedure.