Division of Biostatistics and Bioinformatics, National Jewish Health, University of Colorado Denver, Denver, Colorado, USA.
Adv Physiol Educ. 2010 Dec;34(4):186-91. doi: 10.1152/advan.00068.2010.
Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This sixth installment of Explorations in Statistics explores correlation, a familiar technique that estimates the magnitude of a straight-line relationship between two variables. Correlation is meaningful only when the two variables are true random variables: for example, if we restrict in some way the variability of one variable, then the magnitude of the correlation will decrease. Correlation cannot help us decide if changes in one variable result in changes in the second variable, if changes in the second variable result in changes in the first variable, or if changes in a third variable result in concurrent changes in the first two variables. Correlation can help provide us with evidence that study of the nature of the relationship between x and y may be warranted in an actual experiment in which one of them is controlled.
如果能够积极探索，学习就会更有意义。本统计学探索系列的第六部分探讨了相关性，这是一种常用的技术，用于估计两个变量之间直线关系的强度。只有当两个变量都是真正的随机变量时，相关性才有意义：例如，如果我们以某种方式限制一个变量的可变性，那么相关性的强度就会降低。相关性不能帮助我们确定一个变量的变化是否导致第二个变量的变化，或者第二个变量的变化是否导致第一个变量的变化，或者第三个变量的变化是否导致前两个变量的同时变化。相关性可以帮助我们提供证据，表明在实际实验中，当其中一个变量受到控制时，研究 x 和 y 之间关系的性质可能是合理的。
