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STATISTICAL POWER COMPARISONS FOR EQUAL SKEWNESS DIFFERENT KURTOSIS AND EQUAL KURTOSIS DIFFERENT SKEWNESS COEFFICIENTS IN NONPARAMETRIC TESTS

Year 2013, Issue: 18, 81 - 115, 02.12.2014

Abstract

References

  • Algina, J., Olejnik, S., &Ocanto, R. (1989). Type I error rates and power estimates for selected two-sample tests of scale. Journal of Educational Statistics, 14(4), 373-384.
  • Balakrishnan, N.,& Nevzorov, V.B. (2003). A primer on statistical distributions. Hoboken, New Jersey: A John Wiley & Sons, Inc.
  • Boslaugh, S., Watters, P. A. (2008). Statistics in a Nutshell. California: O’Reilly Media, Inc.
  • Brink, D. (2010). Statistics. Frederiksberg: Ventus Publishing ApS.
  • Conover. W. J. (1999). Practical nonparametric statistics (3 ed.). New York: John Wiley & Sons, Inc.
  • Daniel, W. W. (1990). Applied nonparametric statistics (2 ed.). Boston: PWS-Kent Publishing Company.
  • Everitt, B. S. (2006). The Cambridge dictionary of statistics (3 ed.). New York: Cambridge University Press.
  • Gamgam, H., Altunkaynak, B. (2008). Parametrik Olmayan Yöntemler: SPSS Uygulamalı. Ankara: Gazi Kitabevi.
  • Lee, C. H. (2007). A Monte Carlo study of two nonparametric statistics with comparisons of type I error rates and power. Unpublished doctoral dissertation, Faculty of the Graduate College of the Oklahoma State University, Stillwater.
  • Magel, R. C.,&Wibowo, S. H. (1997). Comparing the powers of the Wald-Wolfowitz and Kolmogorov-Smirnov tests. Biometrical Journal, 39(6), 665-675.
  • Marascuilo, L. A.,& McSweeney, M. (1977). Nonparametric and distribution-free methods for social science. Monterey, CA: Brooks/Cole Publishing Company.
  • Sheskin, D. J. (2000). Handbook of parametric and nonparametric statistical procedures. Baca Raton: Chapman & Hall/CRC.
  • Siegel, S.,& Castellan, J. N. J. (1988). Nonparametric statistics for the behavioral sciences (2 ed.). Boston, Massachusetts: McGraw-Hill.
  • Tabachnick, B. G., Fidell, L. S. (2007). Using Multivariate Statistics (5th ed). Boston: Pearson Education Inc.
  • Vogt, W. P. (2005). Dictionary of statistics and methodology: A nontechnical guide for the social sciences (3 ed.). Thousand Oaks, CA: Sage Publications.
  • Zimmerman, D. W. (2004). Inflation of type I error rates by unequal variance associated with parametric, nonparametric, and rank-transformation tests. Psicologica, 25, 103-133.

STATISTICAL POWER COMPARISONS FOR EQUAL SKEWNESS DIFFERENT KURTOSIS AND EQUAL KURTOSIS DIFFERENT SKEWNESS COEFFICIENTS IN NONPARAMETRIC TESTS

Year 2013, Issue: 18, 81 - 115, 02.12.2014

Abstract

Mann-Whitney and Kolmogorov-Smirnov two-sample tests are the most appropriate tests when the data, which are obtained from independent two-sample, are asked for testing by the help of nonparametric tests. Both Mann-Whitney and Kolmogorov-Smirnov two-sample tests are nonparametric statistics tests which are used to determine whether independent two-sample belongs to the same or similar populations. In this study, the statistical powers of these two tests are compared by analyzing the change in kurtosis coefficients under the assumption of equal skewness coefficients and analyzing the change in skewness coefficients under the assumption of equal kurtosis coefficients. Variances are assumed as heterogeneous for both situations and variance ratios 2, 3, 4, 1/2, 1/3 and 1/4 are used. Also, equal sample sizes of 4, 5, 8, 10, 12, 15, 16 and 20 are used as small and equal sample sizes. The results of the analyses revealed that Mann-Whitney test is more powerful between small and equal sample sizes of 4 to 10, and Kolmogorov-Smirnov two-sample test is more powerful between small and equal sample sizes of 12 to 20

References

  • Algina, J., Olejnik, S., &Ocanto, R. (1989). Type I error rates and power estimates for selected two-sample tests of scale. Journal of Educational Statistics, 14(4), 373-384.
  • Balakrishnan, N.,& Nevzorov, V.B. (2003). A primer on statistical distributions. Hoboken, New Jersey: A John Wiley & Sons, Inc.
  • Boslaugh, S., Watters, P. A. (2008). Statistics in a Nutshell. California: O’Reilly Media, Inc.
  • Brink, D. (2010). Statistics. Frederiksberg: Ventus Publishing ApS.
  • Conover. W. J. (1999). Practical nonparametric statistics (3 ed.). New York: John Wiley & Sons, Inc.
  • Daniel, W. W. (1990). Applied nonparametric statistics (2 ed.). Boston: PWS-Kent Publishing Company.
  • Everitt, B. S. (2006). The Cambridge dictionary of statistics (3 ed.). New York: Cambridge University Press.
  • Gamgam, H., Altunkaynak, B. (2008). Parametrik Olmayan Yöntemler: SPSS Uygulamalı. Ankara: Gazi Kitabevi.
  • Lee, C. H. (2007). A Monte Carlo study of two nonparametric statistics with comparisons of type I error rates and power. Unpublished doctoral dissertation, Faculty of the Graduate College of the Oklahoma State University, Stillwater.
  • Magel, R. C.,&Wibowo, S. H. (1997). Comparing the powers of the Wald-Wolfowitz and Kolmogorov-Smirnov tests. Biometrical Journal, 39(6), 665-675.
  • Marascuilo, L. A.,& McSweeney, M. (1977). Nonparametric and distribution-free methods for social science. Monterey, CA: Brooks/Cole Publishing Company.
  • Sheskin, D. J. (2000). Handbook of parametric and nonparametric statistical procedures. Baca Raton: Chapman & Hall/CRC.
  • Siegel, S.,& Castellan, J. N. J. (1988). Nonparametric statistics for the behavioral sciences (2 ed.). Boston, Massachusetts: McGraw-Hill.
  • Tabachnick, B. G., Fidell, L. S. (2007). Using Multivariate Statistics (5th ed). Boston: Pearson Education Inc.
  • Vogt, W. P. (2005). Dictionary of statistics and methodology: A nontechnical guide for the social sciences (3 ed.). Thousand Oaks, CA: Sage Publications.
  • Zimmerman, D. W. (2004). Inflation of type I error rates by unequal variance associated with parametric, nonparametric, and rank-transformation tests. Psicologica, 25, 103-133.
There are 16 citations in total.

Details

Primary Language English
Journal Section Makaleler
Authors

Ötüken Senger

Publication Date December 2, 2014
Published in Issue Year 2013 Issue: 18

Cite

APA Senger, Ö. (2014). STATISTICAL POWER COMPARISONS FOR EQUAL SKEWNESS DIFFERENT KURTOSIS AND EQUAL KURTOSIS DIFFERENT SKEWNESS COEFFICIENTS IN NONPARAMETRIC TESTS. Istanbul University Econometrics and Statistics E-Journal(18), 81-115.
AMA Senger Ö. STATISTICAL POWER COMPARISONS FOR EQUAL SKEWNESS DIFFERENT KURTOSIS AND EQUAL KURTOSIS DIFFERENT SKEWNESS COEFFICIENTS IN NONPARAMETRIC TESTS. Istanbul University Econometrics and Statistics e-Journal. December 2014;(18):81-115.
Chicago Senger, Ötüken. “STATISTICAL POWER COMPARISONS FOR EQUAL SKEWNESS DIFFERENT KURTOSIS AND EQUAL KURTOSIS DIFFERENT SKEWNESS COEFFICIENTS IN NONPARAMETRIC TESTS”. Istanbul University Econometrics and Statistics E-Journal, no. 18 (December 2014): 81-115.
EndNote Senger Ö (December 1, 2014) STATISTICAL POWER COMPARISONS FOR EQUAL SKEWNESS DIFFERENT KURTOSIS AND EQUAL KURTOSIS DIFFERENT SKEWNESS COEFFICIENTS IN NONPARAMETRIC TESTS. Istanbul University Econometrics and Statistics e-Journal 18 81–115.
IEEE Ö. Senger, “STATISTICAL POWER COMPARISONS FOR EQUAL SKEWNESS DIFFERENT KURTOSIS AND EQUAL KURTOSIS DIFFERENT SKEWNESS COEFFICIENTS IN NONPARAMETRIC TESTS”, Istanbul University Econometrics and Statistics e-Journal, no. 18, pp. 81–115, December 2014.
ISNAD Senger, Ötüken. “STATISTICAL POWER COMPARISONS FOR EQUAL SKEWNESS DIFFERENT KURTOSIS AND EQUAL KURTOSIS DIFFERENT SKEWNESS COEFFICIENTS IN NONPARAMETRIC TESTS”. Istanbul University Econometrics and Statistics e-Journal 18 (December 2014), 81-115.
JAMA Senger Ö. STATISTICAL POWER COMPARISONS FOR EQUAL SKEWNESS DIFFERENT KURTOSIS AND EQUAL KURTOSIS DIFFERENT SKEWNESS COEFFICIENTS IN NONPARAMETRIC TESTS. Istanbul University Econometrics and Statistics e-Journal. 2014;:81–115.
MLA Senger, Ötüken. “STATISTICAL POWER COMPARISONS FOR EQUAL SKEWNESS DIFFERENT KURTOSIS AND EQUAL KURTOSIS DIFFERENT SKEWNESS COEFFICIENTS IN NONPARAMETRIC TESTS”. Istanbul University Econometrics and Statistics E-Journal, no. 18, 2014, pp. 81-115.
Vancouver Senger Ö. STATISTICAL POWER COMPARISONS FOR EQUAL SKEWNESS DIFFERENT KURTOSIS AND EQUAL KURTOSIS DIFFERENT SKEWNESS COEFFICIENTS IN NONPARAMETRIC TESTS. Istanbul University Econometrics and Statistics e-Journal. 2014(18):81-115.