### 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) |
---|---|

Pages (from-to) | 1866-1878 |

Number of pages | 13 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 40 |

Issue number | 10 |

DOIs | |

State | Published - Jan 1 2011 |

### Fingerprint

### 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

**Application of anbar's approach to hypothesis testing to detect the difference between two proportions.** / Soulakova, Julia N; Roy, Ananya.

Research output: Contribution to journal › Article

*Communications in Statistics - Theory and Methods*, vol. 40, no. 10, pp. 1866-1878. https://doi.org/10.1080/03610921003714154

}

TY - JOUR

T1 - Application of anbar's approach to hypothesis testing to detect the difference between two proportions

AU - Soulakova, Julia N

AU - Roy, Ananya

PY - 2011/1/1

Y1 - 2011/1/1

N2 - 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.

AB - 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.

KW - Binomial distribution

KW - Large sample

KW - Normal approximation

UR - http://www.scopus.com/inward/record.url?scp=79952995993&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952995993&partnerID=8YFLogxK

U2 - 10.1080/03610921003714154

DO - 10.1080/03610921003714154

M3 - Article

VL - 40

SP - 1866

EP - 1878

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

IS - 10

ER -