Does the P Value Have a Future in Plant Pathology?
Madden, L. V. | Shah, D. A. | Esker, P. D.
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, H₀. 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 H₀ being true. However, P is often mistakenly equated with the posterior probability that H₀ 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 H₀ can be approximated using P and the prior probability that H₀ is true. When one is completely uncertain about the truth of H₀ before an experiment (i.e., when the prior probability of H₀ is 0.5), the posterior probability of H₀ 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).
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