The chi-square goodness-of-fit test is commonly used for testing if resources (e.g., habitats) are used by animals in proportion to availability. This method assumes that an animal's resource selection is independent of the selection made by other animals. We define and estimate a parameter to model dependent behavior as evidenced by sightings of animals in pairs or groups with respect to time and location. The estimated dependency parameter is used to characterize a multivariate chi-square distribution from which we devise a test of resource selection. Our method, based on the maximum of the multivariate chi-square distribution, incorporates information about dependent observations. We illustrate our method with data from a study of the ecology of sharp-tailed grouse in eastern Washington. We compare our method with the univariate chi-square goodness-of-fit test by theory, by simulation, and by analysis of real data.

Key Words
Chi-square analysis; Dependent observations; Preference; Selection; Sharp-tailed grouse; Use versus availability.

Nairanjana Dasgupta is Assistant Professor, and J. Richard Alldredge is Professor, Program in Statistics, Washington State University, Pullman, WA 99164-3144.