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that some of their most common interpretations have problems. The casual view of the P value as posterior probability of the truth of the null hypothesis is false and not even close to valid under any reasonable model, yet this misunderstanding persists even in high-stakes settings (as discussed, fo...
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| Format: | Text |
| Language: | English |
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| Online Access: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.261.3491 http://www.stat.columbia.edu/%7Egelman/research/published/pvalues3.pdf |
| Summary: | that some of their most common interpretations have problems. The casual view of the P value as posterior probability of the truth of the null hypothesis is false and not even close to valid under any reasonable model, yet this misunderstanding persists even in high-stakes settings (as discussed, for example, by Greenland in 2011). 2 The formal view of the P value as a probability conditional on the null is mathematically correct but typically irrelevant to research goals (hence, the popularity of alternative—if wrong—interpretations). A Bayesian interpretation based on a spike-and-slab model makes little sense in applied contexts in epidemiology, political science, and other fields in which true effects are typically nonzero and bounded (thus violating both the “spike ” and the “slab ” parts of the model). I find Greenland and Poole’s1 perspective to be valuable: it is important to go beyond criticism and to understand what information is actually contained in a P value. These authors discuss some connections between P values and Bayesian posterior probabilities. I am not so optimistic about the practical value of these connections. Conditional on the continuing omnipresence of P values in applications, however, these are important results that should be generally understood. |
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