The Chi-Square Test: Often Used and More Often Misinterpreted
The Chi-Square Test: Often Used and More Often Misinterpreted
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DOI：
10.1177/1098214011426594
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发表时间：
2012-09-01
影响因子：
1.7
通讯作者：
Christie, Christina A.
中科院分区：
文献类型：
--
作者：
Franke, Todd Michael;Ho, Timothy;Christie, Christina A.
交叉分类类别数据的检查在评估和研究中很常见，卡尔·皮尔逊卡方检验家族代表了回答有关分类变量之间的关联或差异的问题的最常用的统计分析之一。不幸的是，这些测试也是该领域中最常被误解的统计测试。问题不在于研究人员和评估人员误用卡方检验的结果，而是他们倾向于过度解释或错误解释结果，导致基于分析的陈述可能具有有限的统计支持或没有统计支持。本文试图澄清关于Pearson开发的卡方检验家族的使用和解释的任何混淆，主要侧重于独立性和方差齐性（分布的同一性）的卡方检验。最近的评价文献的简要调查，以说明卡方检验的流行，并提供这些测试是如何被误解的例子。虽然卡方检验的卡尔·皮尔森家族中的所有三种检验的综合形式-独立性，同质性和拟合优度-基本上使用相同的公式，但这三种检验中的每一种实际上都具有特定的假设，抽样方法，解释和拒绝零假设后的选项。最后，一个鲜为人知的选择，使用和解释事后比较的基础上古德曼的程序（古德曼，1963年）拒绝卡方检验的同质性，详细描述。
The examination of cross-classified category data is common in evaluation and research, with Karl Pearson's family of chi-square tests representing one of the most utilized statistical analyses for answering questions about the association or difference between categorical variables. Unfortunately, these tests are also among the more commonly misinterpreted statistical tests in the field. The problem is not that researchers and evaluators misapply the results of chi-square tests, but rather they tend to over interpret or incorrectly interpret the results, leading to statements that may have limited or no statistical support based on the analyses preformed.This paper attempts to clarify any confusion about the uses and interpretations of the family of chi-square tests developed by Pearson, focusing primarily on the chi-square tests of independence and homogeneity of variance (identity of distributions). A brief survey of the recent evaluation literature is presented to illustrate the prevalence of the chi-square test and to offer examples of how these tests are misinterpreted. While the omnibus form of all three tests in the Karl Pearson family of chi-square tests-independence, homogeneity, and goodness-of-fit,-use essentially the same formula, each of these three tests is, in fact, distinct with specific hypotheses, sampling approaches, interpretations, and options following rejection of the null hypothesis. Finally, a little known option, the use and interpretation of post hoc comparisons based on Goodman's procedure (Goodman, 1963) following the rejection of the chi-square test of homogeneity, is described in detail.