《BERNOULLIS FALLACY Statistical Illogioand the Crisis of Modern Science》PDF+mobi+epub高清完整电子版

奥布里·克莱顿（Aubrey Clayton）批判了对“频率统计”(frequentist statistics)方法的广泛依赖，并提出了基于贝叶斯推理(Bayesian reasoning) 的替代方法。“频率统计”框架高度依赖于“原假设显著性检验（NHST）”和用p值来判断统计显著性。p值是以原假设为条件的概率，即原假设为真却拒绝原假设而犯错的概率，但是它对原假设和备择假设本身的概率没有任何说明。 p值也不能衡量效应值（effect size）的大小：在大样本情况下，即使效应值很小，p值也可能很低。“频率统计”方法忽略了“先验知识”（prior knowledge）或情境在统计分析中的重要性，将概率视为数据纯粹的客观属性，而不是不确定性的主观度量。相反，贝叶斯方法（Bayesian methods）则能够融入“先验概率”（prior probabilities），例如疾病流行率、测试的敏感性和特异性，从而计算在获得阳性测试结果时果真患有该疾病的“后验概率”（posterior probability）。

Aubrey Clayton critiques the widespread reliance on frequentist statistics and proposes alternative approaches rooted in Bayesian reasoning. The frequentist framework relies heavily on “null hypothesis significance testing (NHST)” and p-values to determine statistical significance. The p-value is a conditional probability based on the null hypothesis, representing the probability of rejecting the null hypothesis and making an error when the null hypothesis is true. However, it provides no information about the probability of the null hypothesis or alternative hypothesis itself. It does not measure effect size：a small effect can produce a low p-value in large samples. Frequentist methods ignore the importance of “prior knowledge” or context in statistical analysis, treating probabilities purely as objective properties of data rather than subjective measures of uncertainty. Bayesian methods incorporate “prior probabilities”，e.g. disease prevalence，sensitivity and specificity of the test to calculate the “posterior probability” of having a disease after a positive test.

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