Curran-Everett Douglas
Division of Biostatistics and Bioinformatics, National Jewish Health, Denver, Colorado; and Department of Biostatistics and Informatics, Colorado School of Public Health, University of Colorado Denver, Denver, Colorado
Adv Physiol Educ. 2017 Sep 1;41(3):449-453. doi: 10.1152/advan.00064.2017.
Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This twelfth installment of explores the assumption of normality, an assumption essential to the meaningful interpretation of a test. Although the data themselves can be consistent with a normal distribution, they need not be. Instead, it is the theoretical distribution of the sample mean or the theoretical distribution of the difference between sample means that must be roughly normal. The most versatile approach to assess normality is to bootstrap the sample mean, the difference between sample means, or itself. We can then assess whether the distributions of these bootstrap statistics are consistent with a normal distribution by studying their normal quantile plots. If we suspect that an inference we make from a test may not be justified-if we suspect that the theoretical distribution of the sample mean or the theoretical distribution of the difference between sample means is not normal-then we can use a permutation method to analyze our data.
如果你能积极探索，学习会更有意义。本系列的第十二部分探讨正态性假设，这是对检验进行有意义解释所必需的假设。虽然数据本身可能与正态分布一致，但不一定非得如此。相反，必须是样本均值的理论分布或样本均值之差的理论分布大致呈正态。评估正态性最通用的方法是对样本均值、样本均值之差或其本身进行自抽样。然后，我们可以通过研究它们的正态分位数图来评估这些自抽样统计量的分布是否与正态分布一致。如果我们怀疑从检验中得出的推断可能不合理——如果我们怀疑样本均值的理论分布或样本均值之差的理论分布不正常——那么我们可以使用置换方法来分析我们的数据。
