The Analysis of Categorical Data from Complex Sample Surveys: Chi-Squared Tests for Goodness of Fit and Independence in Two-Way Tables
The Analysis of Categorical Data from Complex Sample Surveys: Chi-Squared Tests for Goodness of Fit and Independence in Two-Way Tables
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DOI：
10.1080/01621459.1981.10477633
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发表时间：
1981-06
影响因子：
3.7
通讯作者：
J. Rao;A. Scott
中科院分区：
文献类型：
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作者：
J. Rao;A. Scott
摘要 研究了分层和聚类对双向列联表中拟合优度（简单假设）和独立性的标准 Pearson 卡方检验统计量渐近分布的影响（分别表示为 X 2 和 XI 2）。结果表明，X 2 和XI 2 均渐近分布为独立χ1 2 随机变量的加权和。然后，权重与调查抽样器使用的熟悉的设计效果 (deffs) 相关。提出了对 X 2 的简单校正，仅需要了解拟合优度问题中各个单元格的方差估计（或 defs），并提供了校正后的 X 2 性能的经验结果。 XI 2 的实证工作表明，XI 2 的名义显着性水平的失真比 X 2 小得多。还给出了简单聚类模型下的一些结果。
Abstract The effect of stratification and clustering on the asymptotic distributions of standard Pearson chi-squared test statistics for goodness of fit (simple hypothesis) and independence in a two-way contingency table, denoted as X 2 and XI 2, respectively, is investigated. It is shown that both X 2 and XI 2 are asymptotically distributed as weighted sums of independent χ1 2 random variables. The weights are then related to the familiar design effects (deffs) used by survey samplers. A simple correction to X 2, which requires only the knowledge of variance estimates (or deffs) for individual cells in the goodness-of-fit problem, is proposed and empirical results on the performance of corrected X 2 provided. Empirical work on XI 2 indicated that the distortion of nominal significance level is substantially smaller with XI 2 than with X 2. Some results under simple models for clustering are also given.