Garthwaite, Paul H. and Crawford, John R.
|DOI (Digital Object Identifier) Link:||http://dx.doi.org/10.1080/02664763.2010.537649|
|Google Scholar:||Look up in Google Scholar|
We suppose a case is to be compared with controls on the basis of a test that gives a single discrete score. The score of the case may tie with the scores of one or more controls. However, scores relate to an underlying quantity of interest that is continuous and so an observed score can be treated as the rounded value of an underlying continuous score. This makes it reasonable to break ties. This paper addresses the problem of forming a confidence interval for the proportion of controls that have a lower underlying score than the case. In the absence of ties, this is the standard task of making inferences about a binomial proportion and many methods for forming confidence intervals have been proposed. We give a general procedure to extend these methods to handle ties, under the assumption that ties may be broken at random. Properties of the procedure are given and an example examines its performance when it is used to extend several methods. A real example shows that an estimated confidence interval can be much too small if the uncertainty associated with ties is not taken into account. Software implementing the procedure is freely available.
|Item Type:||Journal Article|
|Copyright Holders:||2011 Taylor & Francis|
|Keywords:||Coverage; Clopper–Pearson interval; credible interval; discrete distribution; multiple ties; Wald interval|
|Academic Unit/Department:||Mathematics, Computing and Technology > Mathematics and Statistics
Mathematics, Computing and Technology
|Depositing User:||Emma Howard|
|Date Deposited:||06 Mar 2012 09:55|
|Last Modified:||18 Jan 2016 13:58|
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