### Abstract

In this paper, Anbar's (1983) approach for estimating a difference between two binomial proportions is discussed with respect to a hypothesis testing problem. Such an approach results in two possible testing strategies. While the results of the tests are expected to agree for a large sample size when two proportions are equal, the tests are shown to perform quite differently in terms of their probabilities of a Type I error for selected sample sizes. Moreover, the tests can lead to different conclusions, which is illustrated via a simple example; and the probability of such cases can be relatively large. In an attempt to improve the tests while preserving their relative simplicity feature, a modified test is proposed. The performance of this test and a conventional test based on normal approximation is assessed. It is shown that the modified Anbar's test better controls the probability of a Type I error for moderate sample sizes.

Original language | English (US) |
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Pages (from-to) | 1866-1878 |

Number of pages | 13 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 40 |

Issue number | 10 |

DOIs | |

Publication status | Published - Jan 1 2011 |

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### Keywords

- Binomial distribution
- Large sample
- Normal approximation

### ASJC Scopus subject areas

- Statistics and Probability

### Cite this

*Communications in Statistics - Theory and Methods*,

*40*(10), 1866-1878. https://doi.org/10.1080/03610921003714154