Journal of Statistical Theory and Applications

Volume 12, Issue 3, September 2013, Pages 208 - 224

On a Comparison of Tests of Homogeneity of Binomial Proportions

Authors
Martin Klein, Peter Linton
Corresponding Author
Martin Klein
Available Online 1 September 2013.
DOI
https://doi.org/10.2991/jsta.2013.12.3.1How to use a DOI?
Keywords
Chi-squared approximation; Edgeworth series; Exact test; Moment-matching approximation; Nuisance parameter; Power study
Abstract
There are multiple tests of homogeneity of binomial proportions in the statistics literature. However, when working with sparse data, most test procedures may fail to perform well. In this article we review nine classical and recent testing procedures, including the standard Pearson and likelihood ratio tests; exact conditional and unconditional tests; tests based on moment matching chi-squared approximations; a recently proposed test based on a normal approximation in an asymptotic framework for sparse data; and a recent test based on higher order moment corrections using an Edgeworth approximation. For each test we review its theoretical underpinning, and show how to calculate the P-value. Most of the P-values can be readily calculated in a statistical computing software package such as R. We compare type I error probability and power via simulation. As expected, none of the procedures uniformly outperforms the others in terms of type I error probability and power, but we can make some recommendations based on our empirical results. In particular, we indicate scenarios in which certain otherwise reasonable test procedures can perform inadequately.
Open Access
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Journal
Journal of Statistical Theory and Applications
Volume-Issue
12 - 3
Pages
208 - 224
Publication Date
2013/09
ISSN (Online)
2214-1766
ISSN (Print)
1538-7887
DOI
https://doi.org/10.2991/jsta.2013.12.3.1How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Martin Klein
AU  - Peter Linton
PY  - 2013
DA  - 2013/09
TI  - On a Comparison of Tests of Homogeneity of Binomial Proportions
JO  - Journal of Statistical Theory and Applications
SP  - 208
EP  - 224
VL  - 12
IS  - 3
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.2013.12.3.1
DO  - https://doi.org/10.2991/jsta.2013.12.3.1
ID  - Klein2013
ER  -