A note on Cochran test for homogeneity in one-way ANOVA and meta-analysis
A note on Cochran test for homogeneity in one-way ANOVA and meta-analysis
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关于单向方差分析和荟萃分析中同质性 Cochran 检验的注释
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
S. Nadarajah
中科院分区：
文献类型：
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作者：
Zhongxue Chen;H. Ng;S. Nadarajah
本文给出了χ检验统计量的渐近Cochran 2分布的一个形式而简单直接的证明。然后，我们证明了这类检验统计量的一般形式对于权重的选择是不变的。这一事实很重要，因为在实践中，许多这样的测试统计量是用更复杂的形式构造的，这通常需要计算广义逆矩阵。基于我们的结果，我们可以简化检验统计量的构造。更重要的是，这类检验统计量的反保守性等性质可以从Cochran检验统计量中得到。此外，对于小样本量的情况，可以通过使用一些修正的统计量来改进测试的性能。
In this paper we provide a formal yet simple and straightforward proof of the asymptotic χ2 distribution for Cochran test statistic. Then, we show that the general form of this type of test statistics is invariant for the choice of weights. This fact is important since in practice many such test statistics are constructed with more complicated forms which usually require calculating generalized inverse matrices. Based on our results, we can simplify the construction of the test statistics. More importantly, properties such as anti-conservativeness of this type of test statistics can be drawn from Cochran test statistic. Furthermore, one can improve the performance of the tests by using some modified statistics with correction for small sample size situations.