Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/66266
Authors: 
Borkowf, Craig B.
Gail, Mitchell H.
Carroll, Raymond J.
Gill, Richard D.
Year of Publication: 
1997
Series/Report no.: 
Discussion Papers, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 1997,15
Abstract: 
Epidemiologists sometimes study the association between two measures of exposure on the same subjects by grouping the data into categories that are defined by sample quantiles of the two marginal distributions. Although such grouped data are presented in a twoway contingency table, the cell counts in this table do not have a multinomial distribution. We use the term bivariate quantile distribution (BQD) to describe the joint distribution of counts in such a table. Blomqvist (1950) gave an exact BQD theory for the case of only 4 categories based on division at the sample medians. The asymptotic theory he presented was not valid, however, except in special cases. We present a valid asymptotic theory for arbitrary numbers of categories and apply this theory to construct confidence intervals for the kappa statistic. We show by simulations that the confidence interval procedures we propose have near nominal coverage for sample sizes exceeding 90, both for 2 x 2 and 3 x 3 tables. These simulations also illustrate that the asymptotic theory of Blomqvist (1950) and the methods given by Fleiss, Cohen and Everitt (1969) for multinomial sampling can yield subnominal coverage for BQD data, although in some cases the coverage for these procedures is near nominal levels.
Subjects: 
Agreement
bivariate sample quantile distribution
contingency table
kappa statistic
sample quantile
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

Files in This Item:
File
Size
189.4 kB





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.