Estimating Cell Entries in Contingency Tables - Distributional Assumptions vs Marginal Constraints (From Inferring Individual Behavior Grouped Data, 1981, by John Wanat - See NCJ-86079)

• NCJ Number: 86081
• Author(s): J Wanat
• Date Published: 1981
• Length: 17 pages
• Grant Number(s): 79-NI-AX-0058
• Sponsoring Agency: US Dept of Justice
• Corporate Author: University of Illinois at Chicago Circle
• Sale Source: National Institute of Justice/
• Language: English
• Country: United States of America
• Note: Available on microfiche as NCJ-86079

Annotation

This essay examines the expected values usually used in testing for independence in two-way contingency tables, which commonly involves using a chi-square test.

Abstract

The chi-square test usually involved in testing for independence in two-way contingency tables measures the goodness of fit between the observed data and the expected values. This study notes that the usually derived expected values in such analyses are based on assumptions about the distributional form and indistinguishability of the counted items, assumptions that may not always be reasonable. Then the paper presents an alternative method of estimating expected values, the most possible estimate approach, that does not rely on a priori assumptions about the distributional form or distinguishability of items being counted. Finally, by establishing that the most possible estimates approximate maximum likelihood estimates, the robustness of the standard ML estimator is demonstrated, and the researcher is thereby assured of safety in using it without attending to distributional assumptions. This analysis applies to 3x3 tables. Mathematical formulas, tabular data, and two bibliographic listings are provided. (Author abstract modified)