A Test Procedure for Ordered Hypothesis of Population Proportions Against a Control
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Date
2016
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Publisher
Turkish Clinical publications, Turkey
Abstract
Objective: This paper aims to present a novel procedure for testing a set of population proportions
against an ordered alternative with a control. Material and Methods: The distribution of the test statistic for the
proposed test was determined theoretically and through Monte-Carlo experiments. The efficiency of the proposed test method was compared with the classical Chi-square test of homogeneity of population proportions
using their empirical Type I error rates and powers at various sample sizes. Results: The new test statistic that
was developed for testing a set of population proportions against an ordered alternative with a control was
found to have a Chi-square distribution with non-integer values degrees of freedom v that depend on the number of population groups k being compared. Table of values of v for comparing up to 26 population groups was
constructed while an expression was developed to determine v for cases where k > 26. Further results showed
that the new test method is capable of detecting the superiority of a treatment, for instance a new drug type,
over some of the existing ones in situations where only the qualitative data on users’ preferences of all the available treatments (drug types) are available. The new test method was found to be relatively more powerful and
consistent at estimating the nominal Type I error rates (α), especially at smaller sample sizes than the classical
Chi-square test of homogeneity of population proportions. Conclusion: The new test method proposed here
could find applications in pharmacology where a newly developed drug might be expected to be more preferred
by users than some of the existing ones. This kind of test problem can equally exist in medicine, engineering
and humanities in situations where only the qualitative data on users’ preferences of a set of treatments or systems are available.
Description
Keywords
Ordered hypothesis, test of population proportions, Chi-square test of homogeneity of population proportions, Gaussian density, Chi-square distribution, non-inter values degrees of freedom