Volume 12, Issue 3, September 2013, Pages 208 - 224
On a Comparison of Tests of Homogeneity of Binomial Proportions
Martin Klein, Peter Linton
Received 17 March 2012, Accepted 25 March 2013, Available Online 1 September 2013.
- https://doi.org/10.2991/jsta.2013.12.3.1How to use a DOI?
- Chi-squared approximation; Edgeworth series; Exact test; Moment-matching approximation; Nuisance parameter; Power study
- 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
- 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 -