Bates B T, Zhang S, Dufek J S, Chen F C
Department of Exercise and Movement Science, University of Oregon, Eugene, USA.
Med Sci Sports Exerc. 1996 Mar;28(3):386-91. doi: 10.1097/00005768-199603000-00015.
The purpose of the study was to investigate the effects of variability as a function of sample size on the Pearson product-moment correlation coefficient (PCC) under the assumption of a perfect relationship between two variables. The effects of sample size (subjects/trials) and variability on the PCC were demonstrated using a computer model. The model was also used to evaluate selected examples taken from the literature. The results indicated that variability in excess of 10% of the range for each variable resulted in a mean reduction of the shared variance by 50% or greater. Although sample size did not affect the mean PCC, it did have a dramatic effect on extreme percentile values producing unreliable results. These results indicate that a small PCC value can be an artifact of variability. It is suggested, therefore, that one should be cautious when stating conclusions regarding the relationship between two variables without having knowledge of the associated variabilities.
本研究的目的是在两个变量之间存在完美关系的假设下，研究作为样本量函数的变异性对皮尔逊积矩相关系数（PCC）的影响。使用计算机模型展示了样本量（受试者/试验次数）和变异性对PCC的影响。该模型还用于评估从文献中选取的特定示例。结果表明，每个变量超过范围10%的变异性导致共享方差平均降低50%或更多。虽然样本量不影响平均PCC，但它对极端百分位数有显著影响，会产生不可靠的结果。这些结果表明，较小的PCC值可能是变异性的假象。因此，建议在不了解相关变异性的情况下对两个变量之间的关系进行结论陈述时应谨慎。
