In its basic form, the Will Rogers phenomenon takes place when an increase in the average value of each of two sets is achieved by moving an element from one set to another. This leads to the conclusion that there has been an improvement, when in fact essentially nothing has changed. Extended versions of this phenomenon can occur in epidemiological studies, rendering their results unreliable. After describing epidemiological and clinical studies that have been affected by the Will Rogers phenomenon, this paper presents a simple method to correct for it. The method involves introducing a transition matrix between the two sets and taking probability weighted expectations. Two real-world biometrical examples, based on migration economics and breast cancer epidemiology, are given and improvements against a naïve analysis are demonstrated. In the cancer epidemiology example, we take account of estimation uncertainty. We also discuss briefly some limitations associated with our method.

中文翻译：

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一种通过生物识别应用校正威尔罗杰斯现象的简单方法

Will Rogers 现象的基本形式是通过将元素从一组移动到另一组来增加两组中每组的平均值。这导致了改进的结论，而实际上基本上没有任何改变。这种现象的扩展版本可能会出现在流行病学研究中，使其结果不可靠。在描述了受到威尔罗杰斯现象影响的流行病学和临床研究后，本文提出了一种简单的方法来纠正它。该方法包括在两个集合之间引入一个转移矩阵并采用概率加权期望。给出了两个基于移民经济学和乳腺癌流行病学的真实世界生物识别示例，并展示了针对幼稚分析的改进。在癌症流行病学示例中，我们考虑了估计的不确定性。我们还简要讨论了与我们的方法相关的一些限制。