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A note on Cochran test for homogeneity in one-way ANOVA and meta-analysis

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Abstract

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.

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Authors and Affiliations

  1. Department of Epidemiology and Biostatistics, School of Public Health, Indiana University Bloomington, 1025 E. 7th Street, Bloomington, IN, 47405-7109, USA

    Zhongxue Chen

  2. Department of Statistical Science, Southern Methodist University, 3225 Daniel Avenue, PO Box 750332, Dallas, TX, 75275-0332, USA

    Hon Keung Tony Ng

  3. School of Mathematics, University of Manchester, Alan Turing 2.223, Oxford Road, Manchester, M13 9PL, UK

    Saralees Nadarajah

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  1. Zhongxue Chen
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  2. Hon Keung Tony Ng
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  3. Saralees Nadarajah
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Correspondence to Zhongxue Chen.

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Chen, Z., Ng, H.K.T. & Nadarajah, S. A note on Cochran test for homogeneity in one-way ANOVA and meta-analysis. Stat Papers 55, 301–310 (2014). https://doi.org/10.1007/s00362-012-0475-9

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  • DOI: https://doi.org/10.1007/s00362-012-0475-9

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