On a Comparison of Tests of Homogeneity of Binomial Proportions
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 r...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Springer
2013-09-01
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| Series: | Journal of Statistical Theory and Applications (JSTA) |
| Subjects: | |
| Online Access: | https://www.atlantis-press.com/article/9046.pdf |
| _version_ | 1818007298109341696 |
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| author | Martin Klein Peter Linton |
| author_facet | Martin Klein Peter Linton |
| author_sort | Martin Klein |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-14T05:13:21Z |
| format | Article |
| id | doaj.art-1915674689c84dcab7dc96ec01524df4 |
| institution | Directory Open Access Journal |
| issn | 1538-7887 |
| language | English |
| last_indexed | 2024-04-14T05:13:21Z |
| publishDate | 2013-09-01 |
| publisher | Springer |
| record_format | Article |
| series | Journal of Statistical Theory and Applications (JSTA) |
| spelling | doaj.art-1915674689c84dcab7dc96ec01524df42022-12-22T02:10:27ZengSpringerJournal of Statistical Theory and Applications (JSTA)1538-78872013-09-0112310.2991/jsta.2013.12.3.1On a Comparison of Tests of Homogeneity of Binomial ProportionsMartin KleinPeter LintonThere 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.https://www.atlantis-press.com/article/9046.pdfChi-squared approximation; Edgeworth series; Exact test; Moment-matching approximation; Nuisance parameter; Power study |
| spellingShingle | Martin Klein Peter Linton On a Comparison of Tests of Homogeneity of Binomial Proportions Journal of Statistical Theory and Applications (JSTA) Chi-squared approximation; Edgeworth series; Exact test; Moment-matching approximation; Nuisance parameter; Power study |
| title | On a Comparison of Tests of Homogeneity of Binomial Proportions |
| title_full | On a Comparison of Tests of Homogeneity of Binomial Proportions |
| title_fullStr | On a Comparison of Tests of Homogeneity of Binomial Proportions |
| title_full_unstemmed | On a Comparison of Tests of Homogeneity of Binomial Proportions |
| title_short | On a Comparison of Tests of Homogeneity of Binomial Proportions |
| title_sort | on a comparison of tests of homogeneity of binomial proportions |
| topic | Chi-squared approximation; Edgeworth series; Exact test; Moment-matching approximation; Nuisance parameter; Power study |
| url | https://www.atlantis-press.com/article/9046.pdf |
| work_keys_str_mv | AT martinklein onacomparisonoftestsofhomogeneityofbinomialproportions AT peterlinton onacomparisonoftestsofhomogeneityofbinomialproportions |