Abstract #302023

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JSM 2003 Abstract #302023
Activity Number: 217
Type: Contributed
Date/Time: Tuesday, August 5, 2003 : 8:30 AM to 10:20 AM
Sponsor: Biometrics Section
Abstract - #302023
Title: Exact Distributions of Extreme Values for Occupancy Models and Their Application: Alternatives to the Standard Chi-Square Test of the Hypothesis of Equal Cell Frequencies
Author(s): Chih-Chieh Wu*+ and Roger C. Grimson and Sanjay Shete and Christopher I. Amos
Companies: University of Texas, MD Anderson Cancer Center and Clinical Statistics and University of Texas M.D. Anderson Cancer Center and
Address: Department of Epidemiology, Houston, TX, 77030,
Keywords: disease clustering ; combinatorics ; maximum ; minimum
Abstract:

The probability distributions of extreme values are fundamentally required for either practical applications or theoretical interests. This paper presents the exact distributions of maximum and minimum cell frequencies for the classical occupancy models which are based on symmetric multinomial distributions and suggests the use of these two novel exact test statistics for testing the null hypothesis of equal cell frequencies of multinomial distributions. We constrast the Type I error rate and power with the most commonly used test: the standard chi-square test. Our investigation showed that the maximum and the minimum cell frequencies have more power than the standard chi-square test over feasible regions. The distributions of extreme values for various occupancy models are also presented. These methods are applicable to characterize disease incidence patterns over time or particular types of spatial units.

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