title: Hypothesis tests for and against a simple order among proportions estimated by pooled testing.
abstract: 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.
authors.affiliation: Department of Statistics, University of South Carolina, Columbia, SC 29208, USA. tebbs@stat.sc.edu
authors.forename: Joshua M
authors.initials: JM
authors.lastname: Tebbs
authors.forename: Christopher R
authors.initials: CR
authors.lastname: Bilder
mesh_terms: D000818:Animals; D001699:Biometry / Q000379:methods*; D001782:Blood Donors; D001517:Coleoptera / Q000382:microbiology; D003627:Data Interpretation, Statistical; D004522:Educational Status; D004885:Erwinia / Q000254:growth & development; D006678:HIV / Q000302:isolation & purification; D015658:HIV Infections / Q000097:blood / Q000453:epidemiology; D006801:Humans; D007303:Insect Vectors / Q000382:microbiology; D010935:Plant Diseases / Q000382:microbiology; D015995:Prevalence; D012107:Research Design; D013048:Specimen Handling / Q000379:methods*; D003313:Zea mays