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Activity Number: 107 - SPEED: Statistical Methods, Computing, and Applications Part 1
Type: Contributed
Date/Time: Monday, August 8, 2022 : 8:30 AM to 10:20 PM
Sponsor: Section on Statistical Computing
Abstract #323131
Title: The Role of Berkson Paradox in Significance Testing
Author(s): Miodrag Lovric*
Companies: Radford University
Keywords: Berkson paradox; Zero-probability theorem; Point null hypothesis
Abstract:

The dominant paradigm in traditional statistical testing that is based on point null hypotheses is unsatisfactory and for decades it was exposed to innumerable disapprovals and recently it even caused a methodological crisis in some fields of science. It has triggered serious damages to the image of Statistical science and statisticians. One of the unresolved problems in this area is the so-called large sample paradox which results in rejecting almost all point null hypotheses when the sample size increases. This paradox was initially noticed by Berkson in 1936 in the case of the chi-square test application. He concluded that essentially Chi-square test is no test at all since prior to testing we know that the null hypothesis would be rejected with sufficiently large sample. We generalize his original observations to the case of point null hypothesis of the normal mean. We recommend that point null hypotheses of a normal mean should be abandoned and replaced by interval null hypotheses accompanied by the practically meaningful alternative hypotheses. This proposal is established on the consequences of the Zero probability theorem proved by C.R. Rao and Lovric in 2016.


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