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

Julia N. Soulakova, Ananya Roy

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 languageEnglish (US)
Pages (from-to)1866-1878
Number of pages13
JournalCommunications in Statistics - Theory and Methods
Issue number10
StatePublished - Jan 2011


  • Binomial distribution
  • Large sample
  • Normal approximation

ASJC Scopus subject areas

  • Statistics and Probability

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