Skewness and kurtosis in real data samples

Methodology

Volumn 9, Issue 2, 2013, Pages 78-84

  Blanca, María J ^a   Arnau, Jaume ^b   López Montiel, Dolores ^a   Bono, Roser ^b   Bendayan, Rebecca ^a  

^a UNIVERSITY OF MÁLAGA   (Spain)

^b UNIVERSITY OF BARCELONA   (Spain)

Author keywords

Kurtosis; Normality; Shape distribution; Skewness

Indexed keywords

EID: 84878154162     PISSN: 16141881     EISSN: 16142241     Source Type: Journal    
DOI: 10.1027/1614-2241/a000057     Document Type: Article

References (66)

1. Akritas, M. G., & Brunner, E. (1997a). Nonparametric methods for factorial design with censored data. Journal of the American Statistical Association, 92, 568-576.
2. Akritas, M. G., & Brunner, E. (1997b). A unified approach to rank tests for mixed models. Journal of Statistical Planning and Inference, 61, 249-277. (Pubitemid 127169440)
3. Akritas, M. G., & Brunner, E. (2003). Nonparametric models for ANOVA and ANCOVA: A review. In M. G. Akritas & D. N. Politis (Eds.), Recent advances and trends in nonparametric statistics (pp. 79-91). Amsterdam, The Netherlands: Elsevier.
4. An, L., & Ahmed, E. (2008). Improving the performance of kurtosis estimator. Computational Statistic & Data Analysis, 52, 2669-2681.
5. Balanda, K. P., & MacGillivray, H. L. (1988). Kurtosis: A critical review. The American Statistician, 42, 111-119.
6. Balanda, K. P., & MacGillivray, H. L. (1990). Kurtosis and spread. Canadian Journal of Statistics, 18, 17-30.
7. Bonato, M. (2011). Robust estimation of skewness and kurtosis in distributions with infinite higher moments. Finance Research Letters, 8, 77-87.
8. Bradley, J. V. (1978). Robustness? British Journal of Mathematical and Statistical Psychology, 31, 144-152.
9. Brown, D. D., Weatherholt, T. N., & Burns, B. M. (2010). Attention skills and looking to television in children from low income families. Journal of Applied Developmental Psychology, 31, 330-338.
10. Brunner, E., Domhof, S., & Langer, F. (2002). Nonparametric analysis of longitudinal data in factorial experiments. New York, NY: Wiley.
11. Brunner, E., & Puri, M. L. (2002). A class of rank-score tests in factorial designs. Journal of Statistical Planning Inference, 103, 331-360.
12. Brys, G., Hubert, M., & Struyf, A. (2006). Robust measures of tail weight. Computational Statistics & Data Analysis, 50, 733-759. (Pubitemid 41375901)
13. Clinch, J. J., & Keselman, H. J. (1982). Parametric alternatives to the analysis of variance. Journal of Educational Statistics, 7, 207-214.
14. Cochran, W. G. (1947). Some consequences when the assumptions for the analysis of variance are not satisfied. Biometrics, 33, 22-38.
15. DeCarlo, L. T. (1997). On the meaning and use of kurtosis. Psychological Methods, 2, 292-307.
16. Fernández, P., Vallejo, G., Livacic-Rojas, P., & Tuero, E. (2010). Características y análisis de los diseños de medidas repetidas en la investigación experimental en España en los ú ltimos 10 años [Characteristics and analyses of the repeated measures designs in experimental research in Spain during the last ten years]. In Actas del XI Congreso de Metodología de las Ciencias Sociales y de la Salud (pp. 193-198). Málaga: UMA-Tecnolex.
17. Fleishman, A. I. (1978). A method for simulating non-normal distributions. Psychometrika, 43, 521-532.
18. Glass, G. V., Peckham, P. D., & Sanders, J. R. (1972). Consequences of failure to meet assumptions underlying the fixedeffects analysis of variance and covariance. Review of Educational Research, 42, 237-288.
19. Groeneveld, R. (1998). A class of quantile measures for kurtosis. The American Statistician, 51, 325-329.
20. Groeneveld, R., & Meeden, G. (1984). Measuring skewness and kurtosis. The Statistician, 33, 391-399.
21. Harvey, C., & Siddique, A. (1999). Autoregressive conditional skewness. Journal of Financial and Quantitative Analysis, 34, 465-487.
22. Harvey, C., & Siddique, A. (2000). Conditional skewness in asset pricing test. Journal of Finance, 55, 1263-1295.
23. Harwell, M. R. (2003). Summarizing Monte Carlo results in methodological research: The single-factor, fixed-effects ANOVA case. Journal of Educational Statistics, 28, 45-70.
24. Henderson, A. R. (2006). Testing experimental data for univariate normality. Clinica Chimica Acta, 366, 112-129. (Pubitemid 43330972)
25. Heritier, S., Cantoni, E., Copt, S., & Victoria-Feser, M. P. (2009). Robust methods in biostatistics. West Sussex, UK: Wiley.
26. Hill, M. A., & Dixon, W. J. (1982). Robustness in real life: A study of clinical laboratory data. Biometrics, 38, 377-396.
27. Hogg, R. V. (1974). Adaptive robust procedures: A partial review and some suggestions for future applications and theory. Journal of the American Statistical Association, 69, 909-927.
28. Hogg, R. V. (1982). On adaptive statistical inferences. Communications in Statistics: Theory and Methods, 11, 2531-2542.
29. Hogg, R. V., Fisher, D. M., & Randles, D. H. (1975). A twosample adaptive distribution-free test. Journal of the American Statistical Association, 70, 656-661.
30. Hwang, S., & Satchell, S. (1999). Modeling emerging market risk premia using higher moments. International Journal of Finance and Economics, 4, 271-296.
31. Keselman, H. J., Algina, J., Lix, L. M., Wilcox, R. R., & Deering, K. N. (2008). A generally robust approach for testing hypotheses and setting confidence intervals for effect sizes. Psychological Methods, 13, 110-129.
32. Keselman, H. J., Huberty, C. J., Lix, L. M., Olejnik, S., Cribbie, R. A., Donahue, B., & Levin, J. R. (1998). Statistical practices of education researchers: An analysis of the ANOVA, MANOVA, and ANCOVA analyses. Review of Educational Research, 68, 350-386. (Pubitemid 128376783)
33. Kobayashi, K. (2005). Analysis of quantitative data obtained from toxicity studies showing non-normal distribution. Journal of Toxicological Science, 30, 127-134. (Pubitemid 40806140)
34. Kondo, K. (1977). The log-normal distribution of the incubation time of exogenous diseases. Japanese Journal of Human Genetics, 21, 217-237.
35. Lei, M., & Lomax, R. G. (2005). The effect of varying degrees on nonnormality in structural equation modeling. Structural Equation Modeling, 12, 1-27. (Pubitemid 40163161)
36. Levine, D. W., & Dunlap, W. P. (1982). Power of the F test with skewed data: Should one transform or not? Psychological Bulletin, 9, 22-80.
37. Lix, L. M., Keselman, J. C., & Keselman, H. J. (1996). Consequences of assumptions violations revisited: A quantitative review of alternatives to the one-way analysis of variance F test. Review of Educational Research, 66, 579-620. (Pubitemid 127024751)
38. Luh, W. M., & Guo, J. H. (2001). Using Johnson's transformation and robust estimators with heteroscedastic test statistics: An examination of the effects of nonnormality and heterogeneity in the nonorthogonal two-way ANOVA design. British Journal of Mathematical and Statistical Psychology, 54, 79-94.
39. Luh, W. M., & Guo, J. H. (2004). Improved robust test statistic base on trimmed means and Hall's transformation for twoway ANOVA models under non-normality. Journal of Applied Statistics, 31, 623-643.
40. Micceri, T. (1989). The unicorn, the normal curve, and other improbable creatures. Psychological Bulletin, 105, 156-166.
41. Pearson, E. S. (1931). The analysis of variance in cases of nonnormal variation. Biometrika, 23, 114-133.
42. Qazi, S., DuMez, D., & Uckun, F. M. (2007). Meta analysis of advanced cancer survival data using lognormal parametric fitting: A statistical method to identify effective treatment protocols. Current Pharmaceutical Design, 13, 1533-1544. (Pubitemid 46860859)
43. Ramberg, J. S., Dudewicz, E. J., Tadikamalla, P. R., & Mykytka, E. F. (1979). A probability distribution and its uses in fitting data. Technometrics, 21, 201-214.
44. Rassmussen, J. L. (1985). The power of Student's t and Wilcoxon statistics. Evaluation Review, 9, 505-510.
45. Rauf, M., Wener, C., & Brunner, E. (2008). Analysis of highdimensional repeated measures designs: The one sample case. Computational Statistics and Data Analysis, 53, 416-427.
46. Reed, J. F., & Stark, D. B. (1996). Hinge estimators of location: Robust to asymmetry. Computer Methods and Programs in Biomedicine, 49, 11-17. (Pubitemid 26057784)
47. Ruppert, D. (1987). What is kurtosis? An influence function approach. The American Statistician, 41, 1-5.
48. Sawilowsky, S. S., & Blair, R. C. (1992). A more realistic look at the robustness and Type II error properties of the t test to departures from normality. Psychological Bulletin, 111, 353-360.
49. Scheffé, H. (1959). The analysis of variance. New York, NY: Wiley.
50. Schmider, E., Ziegler, M., Danay, E., Beyer, L., & Bühner, M. (2010). Is it really robust? Reinvestigating the robustness of ANOVA against violations of the normal distribution assumption. Methodology, 6, 147-151.
51. Shah, D. A., & Madden, L. V. (2004). Nonparametric analysis of ordinal data in design factorial experiment. Phytopathology, 94, 33-43. (Pubitemid 38503975)
52. Shang-Wen, Y., & Ming-Hua, H. (2010). Estimation of air traffic longitudinal conflict probability based on the reaction time of controllers. Safety Science, 48, 926-930.
53. Srivastava, A. B. L. (1959). Effect of non-normality on the power function of t-test. Biometrika, 46, 114-122.
54. Tiku, M. L. (1964). Approximating the general nonnormal variance-ratio sampling distribution. Biometrika, 51, 83-95.
55. Tiku, M. L. (1971). Power function of the F-test under nonnormal situations. Journal of the American Statistical Association, 66, 913-916.
56. Vale, C. D., & Maurelli, V. A. (1983). Simulating multivariate nonnormal distributions. Psychometrika, 48, 451-464.
57. Van Der Linder, W. J. (2006). A lognormal model for response times on test items. Journal of Educational and Behavioral Statistics, 31, 181-204.
58. Wilcox, R. R. (1993). Analysing repeated measures or randomized block design using trimmed means. British Journal of Mathematical and Statistical Psychology, 46, 63-76.
59. Wilcox, R. R. (1995). ANOVA: A paradigm for low power and misleading measures of effect sizes? Review of Educational Research, 65, 51-77.
60. Wilcox, R. R. (2001). Fundamentals of modern statistical methods: Substantially improving power and accuracy. New York, NY: Springer.
61. Wilcox, R. R. (2002). Understanding the practical advantages of modern ANOVA methods. Journal of Clinical and Adolescent Psychology, 31, 399-412. (Pubitemid 37117522)
62. Wilcox, R. R. (2003). Applying contemporary statistical techniques. San Diego, CA: Academic Press.
63. Wilcox, R. R. (2005). Introduction to robust estimation and hypothesis testing (2nd ed.). San Diego, CA: Academic Press.
64. Wilcox, R. R. (2009). Understanding conventional methods and modern insights. New York, NY: Oxford University Press.
65. Wilcox, R. R., & Keselman, H. J. (2001). Using trimmed means to compare K measures corresponding to two independent groups. Multivariate Behavioral Research, 36, 421-444.
66. Wu, P. C. (2007). Modern one-way ANOVA F methods: Trimmed means, one step M-estimators and bootstrap methods. Journal of Quantitative Research, 1, 155-173.