A Note on Cochran Test for Homogeneity in Two Ways ANOVA and Meta-Analysis

Pamphile Mezui-Mbeng

doi:10.4236/ojs.2015.57078

Home > Journals > Physics & Mathematics > OJS

Open Journal of Statistics > Vol.5 No.7, December 2015

A Note on Cochran Test for Homogeneity in Two Ways ANOVA and Meta-Analysis ()

Pamphile Mezui-Mbeng

CIREGED, Department of Economics, Omar Bongo University, Libreville, Gabon.

DOI: 10.4236/ojs.2015.57078 PDF HTML XML 3,517 Downloads 4,168 Views

Abstract

In this paper, we generalize the proof of the Cochran statistic in the case of an ANOVA two ways structure that asymptotically follows a Chi-2. While construction of homogeneity statistics test usually resorts to the determination of the covariance matrix and its inverse, the Moore-Penrose matrix, our approach, avoids this step. We also show that the Cochran statistic in ANOVA two ways is equivalent to conventional homogeneity statistics test. In particular, we show that it satisfies the invariance property. Finally, we conduct empirical verification from a meta-analysis that confirms our theoretical results.

Keywords

Cochran Homogeneity Test, Chi-Square Distribution, Desimonian-Laird Test, Invariant, Two Ways ANOVA

Share and Cite:

Mezui-Mbeng, P. (2015) A Note on Cochran Test for Homogeneity in Two Ways ANOVA and Meta-Analysis. Open Journal of Statistics, 5, 787-796. doi: 10.4236/ojs.2015.57078.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Hartung, J., Makambi, K. and Argaç, D. (2001) An Extended ANOVA F Test with Applications to the Heterogeneity Problem in Meta-Analysis. Biometrical Journal, 43, 135-146. http://dx.doi.org/10.1002/1521-4036(200105)43:2<135::AID-BIMJ135>3.0.CO;2-H
[2]	Hartung, J., Argaç, D. and Makambi, K. (2002) Small Sample Properties of Tests on Homogeneity in One-Way ANOVA and Meta-Analysis. Stat Pap, 43, 197-235. http://dx.doi.org/10.1007/s00362-002-0097-8
[3]	Hartung, J., Knapp, G. and Sinha, B. (2008) Statistical Meta-Analysis with Applications. Vol. 738, Wiley, New York. http://dx.doi.org/10.1002/9780470386347
[4]	Asiribo, O. and Gurland, J. (1990) Coping with Variance Heterogeneity. Communications in Statistics—Theory and Methods, 19, 4029-4048. http://dx.doi.org/10.1080/03610929008830427
[5]	De Beuckelaer, A. (1996) A Closer Examination on Some Parametric Alternatives to the ANOVA F Test. Stat Pap, 37, 291-305. http://dx.doi.org/10.1007/BF02926110
[6]	Cochran, W. (1937) Problems Arising in the Analysis of a Series of Similar Experiments. Journal of the Royal Statistical Society, 4, 102-118. http://dx.doi.org/10.2307/2984123
[7]	Der Simonian, R. and Laird, N. (1986) Meta-Analysis in Clinical Trials. Controlled Clinical Trials, 7, 177-188. http://dx.doi.org/10.1016/0197-2456(86)90046-2
[8]	Biggerstaff, B. and Jackson, D. (2008) The Exact Distribution of Cochran’s Heterogeneity Statistic in One-Way Random Effects Meta-Analysis. Statistics in Medicine, 27, 6093-6110. http://dx.doi.org/10.1002/sim.3428
[9]	James, G. (1951) The Comparison of Several Groups of Observations When the Ratios of the Population Variances Are Unknown. Biometrika, 38, 324-329. http://dx.doi.org/10.1093/biomet/38.3-4.324
[10]	Kulinskaya, E., Morgenthaler, S. and Staudte, R. (2008) Meta-Analysis: A Guide to Calibrating and Combining Statistical Evidence. Vol. 757, Wiley, New York.
[11]	Welch, B. (1951) On the Comparison of Several Mean Values: An Alternative Approach. Biometrika, 38, 330-336. http://dx.doi.org/10.1093/biomet/38.3-4.330
[12]	Chen, Z., Ng, H.T. and Nadarajah, S. (2014) A Note on Cochran Test Homogeneity in One-Way ANOVA and Meta-Analysis. Stat Pap, 55, 301-310. http://dx.doi.org/10.1007/s00362-012-0475-9
[13]	Schott, J. (1997) Matrix Analysis for Statistics. Wiley, New York.
[14]	Seber, G. (2008) A Matrix Handbook for Statisticians. Vol. 746, Wiley, New York.