Year 2020, Volume 7 , Issue 2, Pages 255 - 265 2020-06-13

Parametric or Non-parametric: Skewness to Test Normality for Mean Comparison

Fatih ORCAN [1]


Checking the normality assumption is necessary to decide whether a parametric or non-parametric test needs to be used. Different ways are suggested in literature to use for checking normality. Skewness and kurtosis values are one of them. However, there is no consensus which values indicated a normal distribution. Therefore, the effects of different criteria in terms of skewness values were simulated in this study. Specifically, the results of t-test and U-test are compared under different skewness values. The results showed that t-test and U-test give different results when the data showed skewness. Based on the results, using skewness values alone to decide about normality of a dataset may not be enough. Therefore, the use of non-parametric tests might be inevitable.
Normality test, Skewness, Mean comparison, Non-parametric tests
  • Abbott, M.L. (2011). Understanding educational statistics using Microsoft Excel and SPSS. United States: Wiley & Sons, Inc.
  • Altman, D.G. (1991). Practical statistics for medical research. London: Chapman and Hall
  • Bendayan, R., Arnau, J., Blanca, M.J. & Bono, R. (2014). Comparison of the procedures of Fleishman and Ramberg et al. for generating non-normal data in simulation studies. Anales de Psicología, 30(1), 364-371. https://dx.doi.org/10.6018/analesps.30.1.135911
  • Bulmer, M. G. (1979). Principles of statistics. Mineola, New York: Dover Publications Inc.
  • Büyüköztürk, Ş., Çokluk, Ö. & Köklü, N. (2014). Sosyal bilimler için istatistik (15th Edition). Ankara: Pegem Akademik.
  • Blanca, M.J., Arnau, J., Lopez-Montiel, D., Bono, R. & Bendayan, R. (2013). Skewness and kurtosis in real data samples. Methodology, 9(2), 78–84. https://dx.doi.org/10.1027/1614-2241/a000057
  • Blanca, M.J., Alarcon, R., Arnua, J., Bono, R. & Bendayan, R. (2017) Non-normal data: Is ANOVA still a valid option? Psicothema, 29(4), 552 557. https://dx.doi.org/10.7334/psicothema2016.383
  • Boslaugh, S. & Watters, P.A. (2008). Statistics in a nutshell. Sebastopol, CA: O’REILLY.
  • Cain, M.K., Zhang, Z. & Yuan, K. (2017) Univariate and multivariate skewness and kurtosis for measuring nonnormality: Prevalence, influence and estimation. Behav Res, 49, 1716–1735. https://dx.doi.org/0.3758/s13428-016-0814-1
  • Demir, E., Saatcioğlu, Ö. & İmrol, F. (2016). Uluslararası dergilerde yayımlanan eğitim araştırmalarının normallik varsayımları açısından incelenmesi, Current Research in Education, 2(3), 130 148. Retrieved from https://dergipark.org.tr/tr/pub/crd/issue/28292/300531
  • Demirdağ, S., & Kalafat, S. (2015). Meaning in life questionnaire (MLQ): The study of adaptation to Turkish, validity, and reliability. İnönü Üniversitesi Eğitim Fakültesi Dergisi, 16(2), 83-95. https://dx.doi.org/10.17679/iuefd.16250801
  • Field, A. (2009). Discovering Statistics Using SPSS (3rd Edition). London: SAGE Publications Ltd
  • Fleishman, A.I. (1978). A method for simulating non-normal distributions. Psychometrika, 43, 521-532. https://dx.doi.org/10.1007/BF02293811
  • Ghasemi, A. & Zahediasl, S. (2012). Normality tests for statistical analysis: A guide for non-statisticians. Int J Endocrinology & Metabolism, 10(2), 486 489. https://dx.doi.org/10.5812/ijem.3505
  • Glass, G., Peckham, P. & Sanders, J. (1972). Consequences of failure to meet assumptions underlying the fixed effects analyses of variance and covariance. Review of Educational Measurement, 42, 237-288.
  • Huck, S.W. (2012). Reading statistics and research (6th Edition). Boston, MA: Pearson
  • Iyer, D.N., Sharp, B.M. & Brush, T.H. (2017). Knowledge creation and innovation performance: An exploration of competing perspectives on organizational systems. Universal Journal of Management, 5(6), 261 270. https://dx.doi.org/10.13189/ujm.2017.050601
  • Kim, H. (2013). Statistical notes for clinical researchers: assessing normal distribution (2) using skewness and kurtosis. Open lecture on statistics (NA), 52 54. https://dx.doi.org/10.5395/rde.2013.38.1.52
  • Lei, M. & Lomax, R.G. (2005). The effect of varying degrees of nonnormality in structural equation modeling. Structural Equation Modeling, 12(1), 1 27. https://dx.doi.org/10.1207/s15328007sem1201_1
  • Miot, H.A. (2016). Assessing normality of data in clinical and experimental trials. Jornal Vascular Brasileiro 16(2) 88-91. https://dx.doi.org/10.1590/1677-5449.041117
  • Orçan, F. (2020). Sosyal bilimlerde istatistik SPSS ve Excel uygulamaları (1st Edition). Ankara: Anı Yayıncılık.
  • Park, H.M. (2008). Univariate analysis and normality test using sas, stata, and spss. Working Paper. The University Information Technology Services (UITS) Center for Statistical and Mathematical Computing, Indiana University
  • Perry, J.L., Dempster, M. & McKay, M.T. (2017) Academic self-efficacy partially mediates the relationship between scottish index of multiple deprivation and composite attainment score. Frontiers in Psychology, (8), NA. https://dx.doi.org/10.3389/fpsyg.2017.01899
  • Razali N.M. & Wah, Y.B. (2011). Power comparisons of Shapiro-Wilk, Kolmogorov-Smirnov, Lilliefors and Anderson-Darling tests, Journal of Statistical Modeling and Analytics, 2(1), 21 33. Retrieved from: https://www.researchgate.net/publication/267205556
  • Rachon, J., Gordan, M. & Kieser, M. (2012). To test or not to test: Preliminary assessment of normality when comparing two independent samples, BMC Medical Research Methodology, (12),81. https://dx.doi.org/10.1186/1471-2288-12-81
  • Ramos, C., Costa, P.A., Rudnicki, T., et al. (2018). The effectiveness of a group intervention to facilitate posttraumatic growth among women with breast cancer. Psycho‐Oncology, (27), 258–264. https://dx.doi.org/10.1002/pon.4501
  • Rietveld, T. & van Hout, R. (2015). The t test and beyond: Recommendations for testing the central tendencies of two independent samples in research on speech, language and hearing pathology. Journal of Communication Disorders, (58), 158 168. https://dx.doi.org/10.1016/j.jcomdis.2015.08.002
  • Schucany, W.R. & Tony N.G., H.K. (2006). Preliminary goodness-of-fit tests for normality do not validata the one-sample student t. Communications in Statistics – Theory and Methods, 35, 2275-2286. https://dx.doi.org/10.1080/03610920600853308
  • Şirin, Y.E., Aydın, Ö. & Bilir, F.P. (2018). Transformational-transactional leadership and organizational cynicism perception: physical education and sport teachers sample. Universal Journal of Educational Research, 6(9), 2008 2018. https://dx.doi.org/10.13189/ujer.2018.060920
  • West, S.G., Finch, J.F. & Curran, P.J. (1995). Structural equation models with nonnormal variables: problems and remedies. In RH Hoyle (Ed.). Structural equation modeling: Concepts, issues and applications. Newbery Park, CA: SAGE.
Primary Language en
Subjects Education, Scientific Disciplines
Published Date June
Journal Section Articles
Authors

Orcid: 0000-0003-1727-0456
Author: Fatih ORCAN (Primary Author)
Institution: Trabzon Üniversitesi
Country: Turkey


Dates

Publication Date : June 13, 2020

APA Orcan, F . (2020). Parametric or Non-parametric: Skewness to Test Normality for Mean Comparison . International Journal of Assessment Tools in Education , 7 (2) , 255-265 . DOI: 10.21449/ijate.656077