TY - JOUR

T1 - Extending the Barnard’s test to non-inferiority

AU - Almendra-Arao, Félix

AU - Sotres-Ramos, David

AU - Zuñiga-Estrada, Magin

PY - 2017/7/3

Y1 - 2017/7/3

N2 - © 2016 Taylor & Francis Group, LLC. In 1945, George Alfred Barnard presented an unconditional exact test to compare two independent proportions. Critical regions for this test, by construction accomplish the very useful property of being Barnard convex sets. Besides, there are empirical findings suggesting that Barnard’s test is the most generally powerful. For Barnard’s test, calculation of critical regions is complicated due that they are constructed in an iterative form until is obtained a test size, as close as possible to the nominal significance level and less than or equal to it. In this article we present an extension to non-inferiority of this very leading test. This extension was contructed for any dissimilarity measure and tables were constructed for the difference between proportions. Also we calculate the critical regions for this extended test for sample sizes less or equal than 30, nominal significance level 0.01, 0.025, 0.05, and 0.10 and for non-inferiority margins 0.05, 0.10, 0.15, and 0.20. Additionally, we computed test sizes for the mentioned configurations. To do this calculations, we have written a program in the R environment.

AB - © 2016 Taylor & Francis Group, LLC. In 1945, George Alfred Barnard presented an unconditional exact test to compare two independent proportions. Critical regions for this test, by construction accomplish the very useful property of being Barnard convex sets. Besides, there are empirical findings suggesting that Barnard’s test is the most generally powerful. For Barnard’s test, calculation of critical regions is complicated due that they are constructed in an iterative form until is obtained a test size, as close as possible to the nominal significance level and less than or equal to it. In this article we present an extension to non-inferiority of this very leading test. This extension was contructed for any dissimilarity measure and tables were constructed for the difference between proportions. Also we calculate the critical regions for this extended test for sample sizes less or equal than 30, nominal significance level 0.01, 0.025, 0.05, and 0.10 and for non-inferiority margins 0.05, 0.10, 0.15, and 0.20. Additionally, we computed test sizes for the mentioned configurations. To do this calculations, we have written a program in the R environment.

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U2 - 10.1080/03610926.2013.875577

DO - 10.1080/03610926.2013.875577

M3 - Article

SP - 6293

EP - 6302

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

ER -