Main Article Content
Abstract
In Multivariate regression, we need to assess normality assumption simultaneously, not univariately. Univariate normal distribution does not guarantee the occurrence of multivariate normal distribution [1]. So we need to extend the assessment of univariate normal distribution into multivariate methods. One extended method is skewness and kurtosis as proposed by Mardia [2]. In this paper, we introduce the method, present the procedure of this method, and show how to examine normality assumption in multivariate regression study case using this method and expose the use of statistics software to help us in numerical calculation.
Received February 20, 2021
Revised March 8, 2021
Accepted March 10, 2021
Keywords
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References
- Field. A, Discovering Statistics Using SPSS, London: Sage Publication, 2009.
- K.V. Mardia, “Measures of multivariate skewness and kurtosis with applications”, Biometrika, vol.57, no.3, pp. 519-530, Dec 1970.
- E.C. Alexopoulos, “Introduction to multivariate regression analysis”, Hippokratia, vol.14, pp.23-28, December 2010.
- J. Osborne and E. Waters, “Four assumptions of multiple regression that researchers should always test”, Pract. Assess. Res. Eval., vol. 8, Jan 2002.
- D.S. Gregory and H.M. Jackson, “Logistic and linear regression assumptions: violation recognition and control”, in Proc. Pharma. SAS Users Group (PharmaSUG), Jun. 16-19, Pennsylvania, 2019. p.21.
- K.R. Das and A.H.M.R. Imon, “A brief review of test for normality”, Am. J. Theor. Appl. Stat., vol. 5, no. 1, pp. 5-12. Jan. 2016.
- Budiyono, Statistika untuk Penelitian, Surakarta: UNS Press, 2009.
- M.Williams, C.A.G. Grajales, and D. Kurkiewicz, “Assumptions of multiple regression: correcting two misconceptions”, Pract. Assess. Res. Eval., vol. 18, 2013.
- H.Y. Kim, “Statistical notes for clinical researchers: assessing normal distribution (2) using skewness and kurtosis”, Restor. Dent. Endo., vol. 38, no. 1, pp. 52-54, Feb. 2003.
- C.D. Lin, “Conducting test in multivariate regression”, in Proc. SAS Globar Forum. April 28-May 1, Texas, p. 13.
- J.L. Romeu and A. Ozturk, “A comparative study of goodness-of-fit for multivariate normality”, J. Multivar. Annal., vol.46, pp. 309-334, Aug. 1993.
- U. Khasanah, ”Penggunaan analisis regresi multivariat untuk memodelkan faktor-faktor yang memperngaruhi hasil belajar”, B.S. thesis, Math. Educ., Universitas PGRI Semarang, Semarang, INA.
- A.C. Rencher, Multivariate Statistical Inference and Applications, Canada: John Wiley and Sons, Inc. 1998.
- K.V. Mardia, “Assessment of multinormality and robustness of Hotelling’s T2 test”, J. R. Stat. Soc. Series C (Appl. Stats.),vol. 24, no. 2, pp. 163-171, 1975.
- M.K. Cain, Z. Zhang, and K.H. Yuan, “Univariate and multivariate skewness and kurtosis for measuring normality: prevalence, influence and estimastion”, Behav. Res. Methods, vol. 17, Oct 2016.
- Z.J. Zhang, K.H. Yuan, Y.Mai, M.K. Cain, H.Du, G.Jiang, H.Liu, A.Santoso, M.yang, X.Wang, and D. Mattew. “Univariate and Multivariate Skewness and Kurtosis Calculation”. Web power: Analysis Online. https://webpower.psychstat.org/models/kurtosis/ (accessed Feb 17, 2021)
- K.V. Mardia, “Application of some measure of multivariate skewness and kurtosis in testing normality and robustness studies”, Sankhya: Indian J. Stat. Series B, vol. 36, no. 2, pp. 115-128, May 1974.
References
Field. A, Discovering Statistics Using SPSS, London: Sage Publication, 2009.
K.V. Mardia, “Measures of multivariate skewness and kurtosis with applications”, Biometrika, vol.57, no.3, pp. 519-530, Dec 1970.
E.C. Alexopoulos, “Introduction to multivariate regression analysis”, Hippokratia, vol.14, pp.23-28, December 2010.
J. Osborne and E. Waters, “Four assumptions of multiple regression that researchers should always test”, Pract. Assess. Res. Eval., vol. 8, Jan 2002.
D.S. Gregory and H.M. Jackson, “Logistic and linear regression assumptions: violation recognition and control”, in Proc. Pharma. SAS Users Group (PharmaSUG), Jun. 16-19, Pennsylvania, 2019. p.21.
K.R. Das and A.H.M.R. Imon, “A brief review of test for normality”, Am. J. Theor. Appl. Stat., vol. 5, no. 1, pp. 5-12. Jan. 2016.
Budiyono, Statistika untuk Penelitian, Surakarta: UNS Press, 2009.
M.Williams, C.A.G. Grajales, and D. Kurkiewicz, “Assumptions of multiple regression: correcting two misconceptions”, Pract. Assess. Res. Eval., vol. 18, 2013.
H.Y. Kim, “Statistical notes for clinical researchers: assessing normal distribution (2) using skewness and kurtosis”, Restor. Dent. Endo., vol. 38, no. 1, pp. 52-54, Feb. 2003.
C.D. Lin, “Conducting test in multivariate regression”, in Proc. SAS Globar Forum. April 28-May 1, Texas, p. 13.
J.L. Romeu and A. Ozturk, “A comparative study of goodness-of-fit for multivariate normality”, J. Multivar. Annal., vol.46, pp. 309-334, Aug. 1993.
U. Khasanah, ”Penggunaan analisis regresi multivariat untuk memodelkan faktor-faktor yang memperngaruhi hasil belajar”, B.S. thesis, Math. Educ., Universitas PGRI Semarang, Semarang, INA.
A.C. Rencher, Multivariate Statistical Inference and Applications, Canada: John Wiley and Sons, Inc. 1998.
K.V. Mardia, “Assessment of multinormality and robustness of Hotelling’s T2 test”, J. R. Stat. Soc. Series C (Appl. Stats.),vol. 24, no. 2, pp. 163-171, 1975.
M.K. Cain, Z. Zhang, and K.H. Yuan, “Univariate and multivariate skewness and kurtosis for measuring normality: prevalence, influence and estimastion”, Behav. Res. Methods, vol. 17, Oct 2016.
Z.J. Zhang, K.H. Yuan, Y.Mai, M.K. Cain, H.Du, G.Jiang, H.Liu, A.Santoso, M.yang, X.Wang, and D. Mattew. “Univariate and Multivariate Skewness and Kurtosis Calculation”. Web power: Analysis Online. https://webpower.psychstat.org/models/kurtosis/ (accessed Feb 17, 2021)
K.V. Mardia, “Application of some measure of multivariate skewness and kurtosis in testing normality and robustness studies”, Sankhya: Indian J. Stat. Series B, vol. 36, no. 2, pp. 115-128, May 1974.