Astivia Oscar L Olvera, Zumbo Bruno D
University of British Columbia, Vancouver, British Columbia, Canada.
Br J Math Stat Psychol. 2017 Nov;70(3):347-367. doi: 10.1111/bmsp.12085. Epub 2017 Jan 31.
The purpose of this paper is to highlight the importance of a population model in guiding the design and interpretation of simulation studies used to investigate the Spearman rank correlation. The Spearman rank correlation has been known for over a hundred years to applied researchers and methodologists alike and is one of the most widely used non-parametric statistics. Still, certain misconceptions can be found, either explicitly or implicitly, in the published literature because a population definition for this statistic is rarely discussed within the social and behavioural sciences. By relying on copula distribution theory, a population model is presented for the Spearman rank correlation, and its properties are explored both theoretically and in a simulation study. Through the use of the Iman-Conover algorithm (which allows the user to specify the rank correlation as a population parameter), simulation studies from previously published articles are explored, and it is found that many of the conclusions purported in them regarding the nature of the Spearman correlation would change if the data-generation mechanism better matched the simulation design. More specifically, issues such as small sample bias and lack of power of the t-test and r-to-z Fisher transformation disappear when the rank correlation is calculated from data sampled where the rank correlation is the population parameter. A proof for the consistency of the sample estimate of the rank correlation is shown as well as the flexibility of the copula model to encompass results previously published in the mathematical literature.
本文的目的是强调总体模型在指导用于研究斯皮尔曼等级相关的模拟研究的设计和解释方面的重要性。斯皮尔曼等级相关已为应用研究人员和方法学家所熟知达一百多年之久，并且是使用最广泛的非参数统计量之一。然而，在已发表的文献中，仍然可以明确或隐含地发现某些误解，因为在社会和行为科学领域，很少讨论该统计量的总体定义。通过依赖 copula 分布理论，本文提出了斯皮尔曼等级相关的总体模型，并从理论和模拟研究两方面对其性质进行了探索。通过使用伊曼 - 康诺弗算法（该算法允许用户将等级相关指定为总体参数），对先前发表文章中的模拟研究进行了探讨，结果发现，如果数据生成机制能更好地匹配模拟设计，那么其中许多关于斯皮尔曼相关性性质的结论将会改变。更具体地说，当从等级相关为总体参数的样本数据中计算等级相关时，诸如小样本偏差以及 t 检验和 r 到 z 费舍尔变换的功效不足等问题就会消失。文中还给出了等级相关样本估计一致性的证明，以及 copula 模型包含先前数学文献中已发表结果的灵活性。
