Advances and Applications in Statistics
Volume 49, Issue 1, Pages 67 - 86
(July 2016) http://dx.doi.org/10.17654/AS049010067 |
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ADJUSTING NOMINAL SIGNIFICANCE LEVELS AND TEST SIZES WHEN USING AN ASYMPTOTIC NON-INFERIORITY TEST
Félix Almendra-Arao, Hortensia Reyes-Cervantes and José Juan Castro-Alva
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Abstract: In a recent article, Almendra-Arao et al. [5] shown that the classical asymptotic non-inferiority test for two independent proportions behaves in a liberal form, that is, the type I error is inflated and this happens inclusively for sample sizes as large as 1000, moreover the inflation is severe. This problem is not an exception of this test, but it is a common weakness of asymptotic tests. Therefore, it is recommended to have a way of adjusting the nominal level to specify to apply the asymptotic statistical test. In this research, we use the binary search algorithm to adjust both, the nominal significance level and the test size of any asymptotical non-inferiority test in a conservative form, that is, to obtain an adjusted test size less than or equal to the nominal significance level. The method is motivated by using the classical asymptotic non-inferiority test for two independent proportions to conduct the presentation; however the scope for the application of this method is wide and includes any asymptotic non-inferiority or superiority test for two independent proportions. Calculations were carried out in a computational program in C++ written by the authors pursuing that objective. |
Keywords and phrases: non-inferiority test, Blackwelder test, significance level, binomial proportions, hypothesis test. |
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