Small-Sample Comparisons of Exact Levels for Chi-Squared Goodness-of-Fit Statistics
Small-Sample Comparisons of Exact Levels for Chi-Squared Goodness-of-Fit Statistics
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DOI：
10.1080/01621459.1978.10481567
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发表时间：
1978-06
影响因子：
3.7
通讯作者：
K. Larntz
中科院分区：
文献类型：
--
作者：
K. Larntz
摘要本文研究了三种用于分类数据分析的拟合优度统计量的小样本性质及其渐近卡方逼近的充分性。基于似然比和Freeman-Tukey统计的近似检验产生的精确水平通常超过中等预期值的标称水平。相比之下，Pearson统计量达到了非常接近名义值的精确水平。似然比和Freeman-Tukey统计量被大量拒绝的原因与它们对小观测计数的处理有关。
Abstract The small-sample properties of three goodness-of-fit statistics for the analysis of categorical data are examined with respect to the adequacy of the asymptotic chi-squared approximation. The approximate tests based on the likelihood ratio and Freeman-Tukey statistics yield exact levels that are typically in excess of the nominal levels for moderate expected values. In contrast, the Pearson statistic attains exact levels that are quite close to the nominal values. The reason for the large number of rejections for the likelihood ratio and Freeman-Tukey statistics is related to their handling of small observed counts.