Biostatistics Series Module 4: Comparing Groups - Categorical Variables.
Biostatistics Series Module 4: Comparing Groups - Categorical Variables.
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DOI：
10.4103/0019-5154.185700
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发表时间：
2016-07
影响因子：
1.7
通讯作者：
Gogtay N
中科院分区：
文献类型：
--
作者：
Hazra A;Gogtay N
分类变量通常表示为计数或频率。为了便于分析，这些数据被方便地排列在联想表中。通常，这样的表被指定为r×c个表，其中r表示行数，c表示列数。卡方(χ2)概率分布在分析分类变量时特别有用。许多测试产生的测试统计数据至少近似符合χ2分布，因此被称为χ2测试。例子包括皮尔逊的χ2测试(或简称χ2测试)、麦克内马尔的χ2测试、曼特尔-汉泽尔χ2测试等。皮尔逊的χ2检验是评估两个或多个独立群体之间分类变量分布差异的最常用检验。如果以某种方式对组进行排序，则应使用趋势的χ2测试。费雪精确概率检验是对两个二分范畴变量之间独立性的检验。它提供了一种比χ2统计量更好的替代方法，可以在数字较小时评估两个独立比例之间的差异，但不能应用于大于二维的列联表。麦克内马尔的χ2测试评估了配对比例之间的差异。当2×2表中的频率表示成对样本或观测值时，使用它。科克伦的Q检验是麦克内马尔检验的推广，它比较了两个以上相关的比例。来自χ2测试或其对应测试的P值并不表明所涉及的类别变量之间的差异或联系的强度。这一信息可以从相对风险或优势比统计量中获得，该统计量是从2×2表中获得的二分关联的度量。
Categorical variables are commonly represented as counts or frequencies. For analysis, such data are conveniently arranged in contingency tables. Conventionally, such tables are designated as r × c tables, with r denoting number of rows and c denoting number of columns. The Chi-square (χ2) probability distribution is particularly useful in analyzing categorical variables. A number of tests yield test statistics that fit, at least approximately, a χ2 distribution and hence are referred to as χ2 tests. Examples include Pearson's χ2 test (or simply the χ2 test), McNemar's χ2 test, Mantel–Haenszel χ2 test and others. The Pearson's χ2 test is the most commonly used test for assessing difference in distribution of a categorical variable between two or more independent groups. If the groups are ordered in some manner, the χ2 test for trend should be used. The Fisher's exact probability test is a test of the independence between two dichotomous categorical variables. It provides a better alternative to the χ2 statistic to assess the difference between two independent proportions when numbers are small, but cannot be applied to a contingency table larger than a two-dimensional one. The McNemar's χ2 test assesses the difference between paired proportions. It is used when the frequencies in a 2 × 2 table represent paired samples or observations. The Cochran's Q test is a generalization of the McNemar's test that compares more than two related proportions. The P value from the χ2 test or its counterparts does not indicate the strength of the difference or association between the categorical variables involved. This information can be obtained from the relative risk or the odds ratio statistic which is measures of dichotomous association obtained from 2 × 2 tables.