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

Y1 - 2011/1

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

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U2 - 10.1080/03610921003714154

DO - 10.1080/03610921003714154

M3 - Article

AN - SCOPUS:79952995993

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 -