Comments on the Neyman-Fisher Controversy and Its Consequences
Comments on the Neyman-Fisher Controversy and Its Consequences
复制标题
对内曼-费舍尔争议及其后果的评论
DOI：
10.1214/13-sts454
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
D. Rubin
中科院分区：
文献类型：
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作者：
Arman Sabbaghi;D. Rubin
在这里考虑的奈曼-费舍尔争议起源于1935年介绍耶日奈曼的统计问题，在农业试验的皇家统计学会。Neyman断言，用于随机化完全区组设计的标准ANOVA F检验是有效的，而用于拉丁方的类似检验在检测处理之间的差异的意义上是无效的，当平均不存在时，比期望的更频繁（即，具有比广告的更高的I型错误）。然而，对于两种设计，Neyman的期望均值残差平方和表达式通常是不正确的。此外，Neyman认为I型错误（当检验零平均治疗效应的零假设时）高于预期，只要预期平均治疗平方和大于预期平均残差平方和，通常是不正确的。简单的例子表明，如果没有对潜在结果的进一步假设，就不能从期望的平方和确定F检验的I型误差。最终，我们认为，奈曼-费舍尔争议对统计学的发展产生了有害的影响，其主要后果是，潜在的结果被忽视，而倾向于线性模型和经典的统计程序，这些模型和程序在没有应用背景的情况下是不精确的。
The Neyman-Fisher controversy considered here originated with the 1935 presentation of Jerzy Neyman's Statistical Problems in Agricultural Experimentation to the Royal Statistical Society. Neyman asserted that the standard ANOVA F-test for randomized complete block designs is valid, whereas the analogous test for Latin squares is invalid in the sense of detecting differentiation among the treatments, when none existed on average, more often than desired (i.e., having a higher Type I error than advertised). However, Neyman's expressions for the expected mean residual sum of squares, for both designs, are generally incorrect. Furthermore, Neyman's belief that the Type I error (when testing the null hypothesis of zero average treatment effects) is higher than desired, whenever the expected mean treatment sum of squares is greater than the expected mean residual sum of squares, is generally incorrect. Simple examples show that, without further assumptions on the potential outcomes, one cannot determine the Type I error of the F-test from expected sums of squares. Ultimately, we believe that the Neyman-Fisher controversy had a deleterious impact on the development of statistics, with a major consequence being that potential outcomes were ignored in favor of linear models and classical statistical procedures that are imprecise without applied contexts.