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TESTING THE EQUALITY OF THE CORRELATION MATRICES WITH THE PERMUTATION TEST

Year 2010, Volume: 1 Issue: 1, 43 - 48, 29.07.2011

Ufuk Ekiz Meltem Ekiz

Abstract

In this study, the emprical rejection levels of the Shipley's test based on permutations are calculated by using the Monte Carlo procedure in order to test the hypothesis of the equality of correlation matrices of different populations, involving p variables. These values are obtained for normal and mixtures of normal distributed three population and are investigated when the expected rejection level is 0.05, 0.10 and 0.20 and the sample size differs from 3 to 10. In respect of the simulation results, the emprical rejection levels of the normal data seems to be very close to the expected rejection levels.
Separately, since all the results are smaller than a in case of mixtures of normal data, the test statistic appears to be robust for non-normal (mixtures of normal) data too.

Keywords

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References

  • Krzanowski, W.J. (1993). Permutational tests for correlation matrices. Statistics and Computing 3, 37- 44.
  • Manly, B.F., Rayner, J.C.W. (1987). The comparison of sample covariance matrices using likelihood ratio tests. Biometrika 74, 841-847.
  • Riska, B. (1985). Group size factors and geographic variation of morphometric correlation. Ecology 39, 792-803.
  • Sakaori, F. (2002). Permutation test for equality of correlation coefficients in two populations. Commun. Statist.- Simula. 31(4), 641-651.
  • Shipley, B. (2000). A Permutation procedure for testing the equality of pattern hypotheses across groups involving correlation or covariance matrices. Statistics and Compu- ting 10, 253-257.
  • Smith, H., Gnanadesikan, R., Hughes, J.B. (1962). Multivariate analysis of variance (MANOVA). Biometrics. 18(1), 22-41.

Year 2010, Volume: 1 Issue: 1, 43 - 48, 29.07.2011

Ufuk Ekiz Meltem Ekiz

Abstract

References

  • Krzanowski, W.J. (1993). Permutational tests for correlation matrices. Statistics and Computing 3, 37- 44.
  • Manly, B.F., Rayner, J.C.W. (1987). The comparison of sample covariance matrices using likelihood ratio tests. Biometrika 74, 841-847.
  • Riska, B. (1985). Group size factors and geographic variation of morphometric correlation. Ecology 39, 792-803.
  • Sakaori, F. (2002). Permutation test for equality of correlation coefficients in two populations. Commun. Statist.- Simula. 31(4), 641-651.
  • Shipley, B. (2000). A Permutation procedure for testing the equality of pattern hypotheses across groups involving correlation or covariance matrices. Statistics and Compu- ting 10, 253-257.
  • Smith, H., Gnanadesikan, R., Hughes, J.B. (1962). Multivariate analysis of variance (MANOVA). Biometrics. 18(1), 22-41.

KORELASYON MATRİSLERİNİN EŞİTLİĞİ TESTİNDE PERMÜTASYON TESTİ

Year 2010, Volume: 1 Issue: 1, 43 - 48, 29.07.2011

Ufuk Ekiz Meltem Ekiz

Abstract

Bu çalışmada, farklı yığınlardaki p tane tesadüfi değişken arasındaki korelasyon matrislerinin eşitliği hipotezinin test edilmesinde permütasyonların oluşturulmasına dayalı Shipley’in önerdiği test istatistiğinin I. tip hata olasılıkları Monte-Carlo yöntemiyle hesaplanmıştır. Normal ve karma-normal dağılımlı üç yığın için ayrı ayrı incelenen deneysel I.tip hata olasılıkları, örnek çapları 3 ile 10 arasında değişkenlik gösterirken ve anlamlılık düzeyi 0.05, 0.10 ve 0.20 iken elde edilmiştir. Simülasyon sonuçlarına göre, normal dağılan veri için tahmin edilen deneysel olasılık değerleri beklenen α’nın çok yakınında değerler vermiştir. Karma-normal veri için sonuçların tümünün α’dan küçük değerler olması, test istatistiğinin normal dağılmayan (karma-normal) veri için de sağlam olduğunu göstermiştir.

Keywords

Korelasyon matrislerinin eşitliği Permütasyon testi Değişebilirlik

References

  • Krzanowski, W.J. (1993). Permutational tests for correlation matrices. Statistics and Computing 3, 37- 44.
  • Manly, B.F., Rayner, J.C.W. (1987). The comparison of sample covariance matrices using likelihood ratio tests. Biometrika 74, 841-847.
  • Riska, B. (1985). Group size factors and geographic variation of morphometric correlation. Ecology 39, 792-803.
  • Sakaori, F. (2002). Permutation test for equality of correlation coefficients in two populations. Commun. Statist.- Simula. 31(4), 641-651.
  • Shipley, B. (2000). A Permutation procedure for testing the equality of pattern hypotheses across groups involving correlation or covariance matrices. Statistics and Compu- ting 10, 253-257.
  • Smith, H., Gnanadesikan, R., Hughes, J.B. (1962). Multivariate analysis of variance (MANOVA). Biometrics. 18(1), 22-41.
There are 6 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Ufuk Ekiz

Meltem Ekiz This is me

Publication Date July 29, 2011
Published in Issue Year 2010 Volume: 1 Issue: 1

Cite

APA Ekiz, U., & Ekiz, M. (2011). TESTING THE EQUALITY OF THE CORRELATION MATRICES WITH THE PERMUTATION TEST. Anadolu University Journal of Science and Technology B - Theoretical Sciences, 1(1), 43-48.
AMA Ekiz U, Ekiz M. TESTING THE EQUALITY OF THE CORRELATION MATRICES WITH THE PERMUTATION TEST. AUBTD-B. July 2011;1(1):43-48.
Chicago Ekiz, Ufuk, and Meltem Ekiz. “TESTING THE EQUALITY OF THE CORRELATION MATRICES WITH THE PERMUTATION TEST”. Anadolu University Journal of Science and Technology B - Theoretical Sciences 1, no. 1 (July 2011): 43-48.
EndNote Ekiz U, Ekiz M (July 1, 2011) TESTING THE EQUALITY OF THE CORRELATION MATRICES WITH THE PERMUTATION TEST. Anadolu University Journal of Science and Technology B - Theoretical Sciences 1 1 43–48.
IEEE U. Ekiz and M. Ekiz, “TESTING THE EQUALITY OF THE CORRELATION MATRICES WITH THE PERMUTATION TEST”, AUBTD-B, vol. 1, no. 1, pp. 43–48, 2011.
ISNAD Ekiz, Ufuk - Ekiz, Meltem. “TESTING THE EQUALITY OF THE CORRELATION MATRICES WITH THE PERMUTATION TEST”. Anadolu University Journal of Science and Technology B - Theoretical Sciences 1/1 (July 2011), 43-48.
JAMA Ekiz U, Ekiz M. TESTING THE EQUALITY OF THE CORRELATION MATRICES WITH THE PERMUTATION TEST. AUBTD-B. 2011;1:43–48.
MLA Ekiz, Ufuk and Meltem Ekiz. “TESTING THE EQUALITY OF THE CORRELATION MATRICES WITH THE PERMUTATION TEST”. Anadolu University Journal of Science and Technology B - Theoretical Sciences, vol. 1, no. 1, 2011, pp. 43-48.
Vancouver Ekiz U, Ekiz M. TESTING THE EQUALITY OF THE CORRELATION MATRICES WITH THE PERMUTATION TEST. AUBTD-B. 2011;1(1):43-8.
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