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Abstract:
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Hypothesis testing and decision rules are in the news as never before. The reproducibility of experiments, one of the touchstones of the scientific method, is uncertain, while some warn that most scientific results are wrong. At the heart of the controversy is the significance of statistical significance: specifically, the significance of p-values. Poorly crafted decision rules have led to a loss of confidence in p-values, with some proposing to ban this incredibly useful tool altogether. We reject this over-reaction. We will discuss three aspects of p-values: 1) improving model specification, thereby reducing the probability of a type II error (false negative), by introducing new families of transformations to remove skewness and excess kurtosis; 2) setting significance level as a decreasing function of sample size, thereby reducing the probability of a type I error (false positive), compromising between a fixed significance level and a fixed meaningful effect size; 3) continuous decision rules that assign plausibility levels to the null hypothesis and alternative hypothesis.
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