Testing a Point Null Hypothesis: The Irreconcilability of P Values and Evidence: Comment

1987 ◽  
Vol 82 (397) ◽  
pp. 129
Author(s):  
James M. Dickey
Keyword(s):  
Null Hypothesis ◽  
P Values ◽  
Point Null Hypothesis

scholarly journals Three Insights from a Bayesian Interpretation of the One-Sided P Value

2016 ◽  
Vol 77 (3) ◽  
pp. 529-539 ◽  
Author(s):  
Maarten Marsman ◽  
Eric-Jan Wagenmakers
Keyword(s):  
Statistical Models ◽  
Null Hypothesis ◽  
Posterior Probability ◽  
P Value ◽  
P Values ◽  
Inferential Method ◽  
Point Null Hypothesis ◽  
Probability Mass ◽  
The One ◽  
Size Variable

P values have been critiqued on several grounds but remain entrenched as the dominant inferential method in the empirical sciences. In this article, we elaborate on the fact that in many statistical models, the one-sided P value has a direct Bayesian interpretation as the approximate posterior mass for values lower than zero. The connection between the one-sided P value and posterior probability mass reveals three insights: (1) P values can be interpreted as Bayesian tests of direction, to be used only when the null hypothesis is known from the outset to be false; (2) as a measure of evidence, P values are biased against a point null hypothesis; and (3) with N fixed and effect size variable, there is an approximately linear relation between P values and Bayesian point null hypothesis tests.

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