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Univariate and multivariate skewness and kurtosis for measuring nonnormality: Prevalence, influence and estimation

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Cain, Meghan K., Zhang, Zhiyong, Yuan, Ke-Hai·2017·Behavior Research Methods

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Research works printed but not linked: 22

  1. Anscombe, F.J., & Glynn, W.J. (1983). Distribution of the Kurtosis Statistic b2 for Normal Samples Distribution of the Kurtosis Statistic b2 for Normal Samples. Biometrika, 70(1), 227. doi: 10.2307/2335960 . · doi:10.2307/2335960
  2. Blanca, M.J., Arnau, J., López-Montiel, D., Bono, R., & Bendayan, R. (2013). Skewness and Kurtosis in Real Data Samples Skewness and kurtosis in real data samples. Methodology: European Journal of Research Methods for the Behavioral and Social Sciences, 9(2), 78–84. doi: 10.1027/1614-2241/a000057 . · DOI · Paper page
  3. Bliss, C. (1967). Statistical Tests of Skewness and Kurtosis Statistical Tests of Skewness and Kurtosis. In Statistics in Biology: Statistical Methods for Research in the Natural Sciences Statistics in Biology: Statistical Methods for Research in the Natural Sciences (VOL 1, pp. 140–146). New York McGraw-Hill Book Company.
  4. Box, G.E., & Cox, D.R. (1964). An analysis of transformations An analysis of transformations. Journal of the Royal Statistical Society. Series B (Methodological), 211–252. Retrieved 2016-07-26, from. http://www.jstor.org/stable/2984418 .
  5. Corder, G.W., & Foreman, D.I. (2014). Nonparametric statistics: A step-by-step approach: Wiley.
  6. D’Agostino, R.B. (1970). Transformation to Normality of the Null Distribution of g 1 Transformation to Normality of the Null Distribution of g 1. Biometrika, 57(3), 679. doi: 10.2307/2334794 . · DOI · Paper page
  7. DeCarlo, L. (1997b). On the meaning and use of kurtosis. On the meaning and use of kurtosis. Psychological methods, 2(3), 292. doi: 10.1037/1082-989X.2.3.292 . · doi:10.1037/1082-989x.2.3.292 · Paper page
  8. Huber, P.J (1967). The behavior of maximum likelihood estimates under nonstandard conditions. In Proceedings of the fifth Berkeley symposium on mathematical statistics and probability (VOL. 1, pp. 221–233.
  9. Joanes, D., & Gill, C. (1998). Comparing measures of sample skewness and kurtosis Comparing measures of sample skewness and kurtosis. Journal of the Royal Statistical Society: Series D (The Statistician), 47(1), 183–189. doi: 10.1111/1467-9884.00122 10.1111/1467-9884.00122 . · DOI · Paper page
  10. Levine, D.W., & Dunlap, W.P. (1982). Power of the F test with skewed data: Should one transform or not? Power of the f test with skewed data: Should one transform or not?. Psychological Bulletin, 92(1), 272. doi: 10.1037/0033-2909.92.1.272 . · DOI
  11. Mardia, K.V. (1970). Measures of Multivariate Skewness and Kurtosis with Applications Measures of Multivariate Skewness and Kurtosis with Applications. Biometrika, 57(3), 519. doi: 10.2307/2334770 . · DOI
  12. Micceri, T. (1989). The unicorn, the normal curve, and other improbable creatures. The unicorn, the normal curve, and other improbable creatures. Psychological Bulletin, 105(1), 156. doi: 10.1037/0033-2909.105.1.156 . · doi:10.1037/0033-2909.105.1.156 · Paper page
  13. Palmer, E.M., Horowitz, T.S., Torralba, A., & Wolfe, J.M. (2011). What are the shapes of response time distributions in visual search?. Journal of Experimental Psychology: Human Perception and Performance, 37 (1), 58–71. Retrieved 2016-07-26, from 10.1037/a0020747 . · DOI · Paper page
  14. Sakia, R.M. (1992). The Box-Cox Transformation Technique: A Review. The Statistician, 41(2), 169. Retrieved 2016-07-26, from 10.2307/2348250 . · DOI · Paper page
  15. Scheffe, H. (1959). The analysis of variance. The analysis of variance. New York: Wiley.
  16. Shohat, J. (1929). Inequalities for Moments of Frequency Functions and for Various Statistical Constants. Biometrika, 21(1/4), 361. doi: 10.2307/2332566 . · doi:10.2307/2332566
  17. Tabachnick, B.G., & Fidell, L.S. (2012). Using Multivariate Statistics Using Multivariate Statistics (6 ed). Pearson.
  18. Wang, L., Zhang, Z., McArdle, J.J., & Salthouse, T.A. (2008). Investigating Ceiling Effects in Longitudinal Data Analysis. Multivariate Behavioral Research, 43(3), 476–496. doi: 10.1080/00273170802285941 . · DOI · Paper page
  19. Yanagihara, H., & Yuan, K.H. (2005). Four improved statistics for contrasting means by correcting and kurtosis. British Journal of Mathematical and Statistical Psychology, 58(2), 209–237. doi: 10.1348/000711005X64060 . · doi:10.1348/000711005x64060
  20. Yuan, K.H., & Bentler, P.M. (1998). Normal theory based test statistics in structural equation modelling. British Journal of Mathematical and Statistical Psychology, 51(2), 289– 309. · DOI · Paper page
  21. Yuan, K.H., Bentler, P.M., & Zhang, W. (2005). The Effect of Skewness and Kurtosis on Mean and Covariance Structure Analysis: The Univariate Case and Its Multivariate Implication. Sociological Methods & Research, 34(2), 240–258. doi: 10.1177/0049124105280200 . · DOI · Paper page
  22. Yuan, K.H., & Zhang, Z. (2012). Robust structural equation modeling with missing data and auxiliary variables. Psychometrika, 77(4), 803–826. doi: 10.1007/s11336-012-9282-4 . · DOI

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Metadata

Authors
Cain, M. K., Zhang, Z., & Yuan, K.-H.
Venue
Behavior Research Methods
Published
2016-10-17
Volume
49
Issue
5
Pages
1716-1735
ISSN
  • 1554-351X (ISSN-L)
  • 1554-3528
OpenAlex
W2538623560
Cited by
1,164
References
1
FWCI
29.54
Type
journal article
Language
en
Open access
bronze

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Cain, M. K., Zhang, Z., & Yuan, K.-H. (2017). Univariate and multivariate skewness and kurtosis for measuring nonnormality: Prevalence, influence and estimation. Behavior Research Methods. https://doi.org/10.3758/s13428-016-0814-1

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