Hypothesis tests for and against a simple order among proportions estimated by pooled testing

Joshua M. Tebbs, Christopher R. Bilder

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


The use of pooled testing as a means of estimating the prevalence of rare traits has received considerable attention in recent years, particularly in the areas of public health, genetics, animal-disease assessment, and plant pathology. In pooled-testing applications, observations are made on pools of individuals amalgamated together. In this paper, we examine order-restricted hypothesis tests involving k > 2 binomial proportions estimated by pooled testing, extending the earlier work of Tebbs and Swallow (2003, Biometrika, 90, 471-477 and Biometrical Journal, 45, 618-630). In particular, we focus on (i) testing the equality of proportions versus an isotonic alternative and (ii) testing for a violation of isotonicity. We propose new tests for each scenario and provide results which characterize the small-sample performance of our procedures. We illustrate our methods using two data sets; one from an observational HIV study and one from an agricultural experiment.

Original languageEnglish (US)
Pages (from-to)792-804
Number of pages13
JournalBiometrical Journal
Issue number5
StatePublished - Aug 2006


  • Are-sin square-root transformation
  • Erwinia stewartii
  • Group testing
  • HIV prevalence
  • Isotonic regression
  • Likelihood ratio test
  • Order-restricted inference
  • Stewart's wilt rating
  • Vector-transfer design

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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