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Explorations in statistics: hypothesis tests and P values

Division of Biostatistics and Bioinformatics, National Jewish Health, and Department of Biostatistics and Informatics and Department of Physiology and Biophysics, University of Colorado Denver, Denver, Colorado

Address for reprint requests and other correspondence: D. Curran-Everett, Div. of Biostatistics and Bioinformatics, M222, National Jewish Health, 1400 Jackson St., Denver, CO 80206 (e-mail: EverettD{at}NJHealth.org)

Abstract

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This second installment of Explorations in Statistics delves into test statistics and P values, two concepts fundamental to the test of a scientific null hypothesis. The essence of a test statistic is that it compares what we observe in the experiment to what we expect to see if the null hypothesis is true. The P value associated with the magnitude of that test statistic answers this question: if the null hypothesis is true, what proportion of possible values of the test statistic are at least as extreme as the one I got? Although statisticians continue to stress the limitations of hypothesis tests, there are two realities we must acknowledge: hypothesis tests are ingrained within science, and the simple test of a null hypothesis can be useful. As a result, it behooves us to explore the notions of hypothesis tests, test statistics, and P values.

Key words: power; R; significance test; software; test statistic

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