• Arc-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


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. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)