The Effect of Two-Stage Sampling on the F Statistic
两阶段抽样对 F 统计量的影响AI 解读 ↓
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两阶段抽样对 F 统计量的影响
- 研究问题
- 两阶段调查抽样中的簇内相关会怎样扭曲常规 F 统计量，以及如何诊断并修正由此产生的检验问题？
- 方法与思路
- 作者提出簇内相关影响的诊断指标，按各回归变量及其交叉乘积分解，并据此构造无需迭代的 F 检验修正。
- 材料陈述的贡献
- 摘要称理论与数值分析支持诊断指标的有效性；在所报告模拟中，修正检验的表现至少不逊于 GLS。
- 阅读关注点
- 核对诊断指标的定义、分解方式与修正所需条件，尤其关注簇内相关未知时如何计算，以及模拟比较的设计。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明；OLS 无偏性和修正有效性的具体条件未说明，模拟比较不能推广到所有设计。
原文摘要
The assumption of iid observations that underlies many statistical procedures is called into question when analyzing complex survey data. The population structure-particularly the existence of clusters in two-stage samples that usually exhibit positive intracluster correlation-invalidates the independence assumption. Kish and Frankel (1974) investigated the impact of this fact on regression analysis by using the standard sample-survey-theory framework; Campbell (1977) and Scott and Holt (1982) used the linear model framework. In general, although ordinary least squares (OLS) procedures are unbiased but not fully efficient for estimation of the regression coefficients, serious difficulties can arise when using OLS estimators for second-order terms. Variances of the OLS estimators for the regression coefficients can be larger (sometimes much larger) than the usual OLS variance expression would indicate. Failure to consider this possibility leads to underestimation of variances, with consequences for confidence intervals. This article follows this effect through to the F statistic, because of its importance to hypothesis tests and confidence ellipsoids. Our major aim is to investigate the effect of intracluster correlation on the F statistic. We propose a diagnostic measure identifying when the ordinary F statistic is likely to be affected and give decomposition in terms of the contributions of the individual regressors and their cross-products, based on a similar decomposition for the projection matrix in Appendix A. We establish numerically and theoretically the effectiveness of this measure in understanding the degree of distortion of F by intracluster correlation. The measure leads to a correction for the F test for unknown intracluster correlation. This is a slightly simpler numerical procedure than the generalized least squares (GLS), since it does not require iteration. The correction is shown to perform at least as well as the GLS in a simulation study.