### Abstract

The P value (significance level) is possibly the mostly widely used, and also misused, quantity in data analysis. P has been heavily criticized on philosophical and theoretical grounds, especially from a Bayesian perspective. In contrast, a properly interpreted P has been strongly defended as a measure of evidence against the null hypothesis, H_{0}. We discuss the meaning of P and null-hypothesis statistical testing, and present some key arguments concerning their use. P is the probability of observing data as extreme as, or more extreme than, the data actually observed, conditional on H_{0} being true. However, P is often mistakenly equated with the posterior probability that H_{0} is true conditional on the data, which can lead to exaggerated claims about the effect of a treatment, experimental factor or interaction. Fortunately, a lower bound for the posterior probability of H_{0} can be approximated using P and the prior probability that H_{0} is true. When one is completely uncertain about the truth of H_{0} before an experiment (i.e., when the prior probability of H_{0} is 0.5), the posterior probability of H_{0} is much higher than P, which means that one needs P values lower than typically accepted for statistical significance (e.g., P = 0.05) for strong evidence against H0. When properly interpreted, we support the continued use of P as one component of a data analysis that emphasizes data visualization and estimation of effect sizes (treatment effects).

Original language | English (US) |
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Pages (from-to) | 1400-1407 |

Number of pages | 8 |

Journal | PHYTOPATHOLOGY |

Volume | 105 |

Issue number | 11 |

DOIs | |

State | Published - Nov 1 2015 |

### All Science Journal Classification (ASJC) codes

- Agronomy and Crop Science
- Plant Science

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## Cite this

*PHYTOPATHOLOGY*,

*105*(11), 1400-1407. https://doi.org/10.1094/PHYTO-07-15-0165-LE