Bayesian Analysis of a 2 × 2 Contingency Table with Both Completely and Partially Cross-Classified Data

Philip J. Smith, Sung C Choi and Erdogan Gunel

Journal of Educational and Behavioral Statistics, 1985, vol. 10, issue 1, 31-43

Abstract: A frequently used experimental design is one in which the experimental units are measured twice (e.g., under different test conditions). When the response variable is dichotomous, the equality of the two proportions is usually assessed by a test due to McNemar (1947) . However, in addition to obtaining this complete data where two responses are available for each unit, incomplete data may be available also: In this case observations are available on the first response alone for some units and additional observations are available on the second response alone for other units. In this paper Bayesian methods are presented for estimating and testing hypotheses regarding the two success probabilities in light of both the complete and incomplete data. A method by which the prior distribution may be assessed is sketched and a numerical example to illustrate the method is presented.

Keywords: AIC criterion; Bayesian statistics; EM algorithm; highest posterior density region; incomplete data; method of moments; posterior probability; 2×2 table (search for similar items in EconPapers)
Date: 1985
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Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:10:y:1985:i:1:p:31-43

DOI: 10.3102/10769986010001031

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