A Gentle Introduction to the Comparison Between Null Hypothesis Testing and Bayesian Analysis: Reanalysis of Two Randomized Controlled Trials

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Abstract

The debate on the use and misuse of P values has risen and fallen throughout their almost century-long existence in scientific discovery. Over the past few years, the debate has again received front-page attention, particularly through the public reminder by the American Statistical Association on how P values should be used and interpreted. At the core of the issue lies a fault in the way that scientific evidence is dichotomized and research is subsequently reported, and this fault is exacerbated by researchers giving license to statistical models to do scientific inference. This paper highlights a different approach to handling the evidence collected during a randomized controlled trial, one that does not dichotomize, but rather reports the evidence collected. Through the use of a coin flipping experiment and reanalysis of real-world data, the traditional approach of testing null hypothesis significance is contrasted with a Bayesian approach. This paper is meant to be understood by those who rely on statistical models to draw conclusions from data, but are not statisticians and may therefore not be able to grasp the debate that is primarily led by statisticians.

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