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What Should be The Measure of Conformity to Normal Distribution (Normality) Test in Likert Type Digital and Face-To-Face Survey Data?

Year 2023, , 54 - 69, 25.10.2023
https://doi.org/10.34231/iuyd.1346463

Abstract

In statistics, it is assumed that the data suitable for parametric tests exhibit a normal distribution. In other words, before running parametric tests, it is essential to check whether the data set follows a normal distribution. Parametric tests can only be applied to data that adhere to a normal distribution. The Shapiro-Wilk and Kolmogorov-Smirnov (Lilliefors modification) tests are among the most commonly utilised methods for testing normality. However, these tests were originally developed for rational numbers. The use of these tests for Likert-type digital or face-to-face survey data has always been a topic of discussion. Even if the measurement tools consist of at least three items, the data sets are dominated by repeated values. Again, there are different opinions on the acceptable range for kurtosis and skewness values. With this study, it was determined that the Kolmogorov-Smirnov (Lilliefors modification) test is not suitable for testing the normality of Likert-type digital or face-to-face survey data. In addition, the coefficients of kurtosis and skewness within the range of (-1, +1) range are acceptable for normality. For this reason, it is recommended not to use goodness-of-fit tests such as Shapiro-Wilk or Kolmogorov-Smirnov for testing the normality of interval scale data collected through questionnaires.

References

  • De Carlo, L.T. (1997). “On the meaning and use of kurtosis”. Psychological Methods, 2, 292-307.
  • George, D., & Mallery, P. (2019). IBM SPSS statistics 26 step by step: A simple guide and reference. Fifteenth edition, Routledge.
  • Groeneveld, R. A., & Meeden, G. (1984). “Measuring Skewness and Kurtosis”. Journal of the Royal Statistical Society. Series D (The Statistician), 33(4), 391–399.
  • Hair, J. F., Black, W. C., Babin, B. J., Anderson, R. E., & Tatham, R. L. (2019). Multivariate data analysis, Eighth Edition. Cengage Learning EMEA.
  • Haşıloğlu, S.B. (2022). Pazarlama Araştırması ve Analitiği, Ankara: Nobel Yayınevi
  • Hopkins, K.D. & Weeks, D.L. (1990). “Tests for normality and measures of skewness and kurtosis: Their place in research reporting”. Educational and Psychological Measurement, 50, 717-729.
  • Kalburan, C., Hasiloglu, S.B., & Bardakci, A. (2019). “Does a difference in the number of response categories change the results for ACSI in the mobile phone sector?”. International Journal of Mobile Communications, 17(6), 746-759.
  • Keskin, S. (2006). “Comparison of several univariate normality tests regarding type I error rate and power of the test in simulation based small samples”. Journal of Applied Science Research, 2(5), 296-300.
  • Lilliefors, H.W. (19767). “On the Kolmogorov-Smirnov test for normality with mean and variance unknown”. Journal of the American Statistical Association, 62(318), 399-402.
  • Mendes, M., & Pala, A. (2003). “Type I error rate and power of three normality tests”. Pakistan Journal of Information and Technology, 2(2), 135-139.
  • Moors, J. J. A. (1986). “The meaning of kurtosis: darlington reexamined”. The American Statistician, 40, 283-284.
  • Newbold, P. (1988). Statistics for Business and Economics. Prentice Hall Inc., USA.
  • 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.
  • Shapiro, S. S., & Wilk, M. B. (1965). “An analysis of variance test for normality (complete samples)”. Biometrika, 52(3/4), 591-611.

Likert tipi dijital ve yüz yüze anket verilerinde normal dağılıma uygunluk (normallik) testi ölçüsü ne olmalıdır?

Year 2023, , 54 - 69, 25.10.2023
https://doi.org/10.34231/iuyd.1346463

Abstract

İstatistikte, parametrik testlere uygun verilerin normal dağılım sergilediği kabul edilir. Başka bir ifade ile parametrik testler yapabilmek için öncelikli olarak veri setinin normal dağılıma uygun olup olmadığına bakılır. Normal dağılıma uygun olan verilerle parametrik testler yapılabilir. Shapiro-Wilk ve Kolmogorov-Smirnov (Lilliefors modifikasyonu), normallik testleri arasında en çok kullanılanlardır. Ancak bu testler rasyonel sayılar temel alınarak geliştirilmiştir. Likert tipi dijital veya yüz yüze anket verileri için bu testlerin kullanımı her zaman bir tartışma konusu olmuştur. Ölçme araçları en az üç maddeden meydana geliyor olsa dahi veri setlerinde tekrarlı değerler hakimdir. Yine basıklık çarpıklık değerleri için kabul edilebilir uygun aralık üzerine de farklı görüşler bulunmaktadır. Bu çalışma ile Kolmogorov-Smirnov (Lilliefors modifikasyonu) testinin Likert tipi dijital veya yüz yüze anket verilerinin normallik testi için uygun olmadığı tespit edilmiştir. Ayrıca (-1, +1) aralığındaki basıklık ve çarpıklık katsayıları, normallik için kabul edilebilirdir. Bu nedenle anket yolu ile toplanan aralıklı ölçek verileri normallik testi için Shapiro-Wilk veya Kolmogorov-Smirnov gibi uyum iyiliklerinin kullanılmaması önerilmektedir.

References

  • De Carlo, L.T. (1997). “On the meaning and use of kurtosis”. Psychological Methods, 2, 292-307.
  • George, D., & Mallery, P. (2019). IBM SPSS statistics 26 step by step: A simple guide and reference. Fifteenth edition, Routledge.
  • Groeneveld, R. A., & Meeden, G. (1984). “Measuring Skewness and Kurtosis”. Journal of the Royal Statistical Society. Series D (The Statistician), 33(4), 391–399.
  • Hair, J. F., Black, W. C., Babin, B. J., Anderson, R. E., & Tatham, R. L. (2019). Multivariate data analysis, Eighth Edition. Cengage Learning EMEA.
  • Haşıloğlu, S.B. (2022). Pazarlama Araştırması ve Analitiği, Ankara: Nobel Yayınevi
  • Hopkins, K.D. & Weeks, D.L. (1990). “Tests for normality and measures of skewness and kurtosis: Their place in research reporting”. Educational and Psychological Measurement, 50, 717-729.
  • Kalburan, C., Hasiloglu, S.B., & Bardakci, A. (2019). “Does a difference in the number of response categories change the results for ACSI in the mobile phone sector?”. International Journal of Mobile Communications, 17(6), 746-759.
  • Keskin, S. (2006). “Comparison of several univariate normality tests regarding type I error rate and power of the test in simulation based small samples”. Journal of Applied Science Research, 2(5), 296-300.
  • Lilliefors, H.W. (19767). “On the Kolmogorov-Smirnov test for normality with mean and variance unknown”. Journal of the American Statistical Association, 62(318), 399-402.
  • Mendes, M., & Pala, A. (2003). “Type I error rate and power of three normality tests”. Pakistan Journal of Information and Technology, 2(2), 135-139.
  • Moors, J. J. A. (1986). “The meaning of kurtosis: darlington reexamined”. The American Statistician, 40, 283-284.
  • Newbold, P. (1988). Statistics for Business and Economics. Prentice Hall Inc., USA.
  • 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.
  • Shapiro, S. S., & Wilk, M. B. (1965). “An analysis of variance test for normality (complete samples)”. Biometrika, 52(3/4), 591-611.
There are 14 citations in total.

Details

Primary Language English
Subjects Data Analysis, Operations Research, Statistical Data Science, Marketing (Other)
Journal Section Research Article
Authors

Selçuk Burak Haşıloğlu 0000-0003-4512-6531

Melda Hasiloglu Ciftciler This is me 0000-0002-1922-5328

Publication Date October 25, 2023
Published in Issue Year 2023

Cite

APA Haşıloğlu, S. B., & Hasiloglu Ciftciler, M. (2023). What Should be The Measure of Conformity to Normal Distribution (Normality) Test in Likert Type Digital and Face-To-Face Survey Data?. İnternet Uygulamaları Ve Yönetimi Dergisi, 14(2), 54-69. https://doi.org/10.34231/iuyd.1346463