Öz
In this study, a new testing approach to significance test for correlation between two normally distributed random variables is proposed. This new approach is robust to the outliers that are incompatible with the sign of the correlation. To evaluate and compare power performance of the proposed approach with that of usual the Pearson t-test for correlation in the case of this type of a few outliers, a simulation study is conducted. As a result of the simulation study, it has been found that the proposed approach performs better than the usual t-test in the presence of such outliers. In addition, it seemed that the nice performance of the new approach continues to exist provided that thesde outliers constitute approximately no more than 5% or 6% of the sample.
Anahtar Kelimeler
Kolmogorov-Smirnov goodness of fit test Cramer-von Mises goodness of fit test Empirical power comparison Simulation
Kaynakça
- Bain, L. J. & Engelhardt, M. 1992. Introduction to Probability and Mathematical Statistics (2nd ed.), Duxbury Press, Belmont, California, 644p.
- Bishara, A. J., & Hittner, J. B. 2012. Testing the significance of a correlation with non-normal data: Comparison of Pearson, Spearman, transformation, and resampling approaches. Psychological Methods, 17, 399-417.
- Conover, W.J. 1999. Practical Nonparametric Statistics (3rd ed.), John Wiley & Sons, New York, 592p.
- El-Fallah, M., & El-Salam, A. 2006. A robust measure for the correlation coefficient. J. King Saud Univ., 19, Admin. Sci. 1, 41-50.
- Evandt O., Coleman, S., Ramalhoto M.F. & Lottum, C.V. Y.J. 2004. A little known Robust Estimator of the Correlation Coefficient and Its Use in a Robust Graphical Test for Bivariate Normality with Applications in Aluminum Industry, Mathematical Programming, Qual.Reliab.Engng. Int. 20, 433-456.
- Huber, P. J. 2004. Robust Statistics, John Wiley & Sons, USA, 308p.
- King, J. E. 2003. What have we learned from 100 years of robustness studies on r? Paper presented at the annual meeting of the Southwest Educational Research Association, San Antonio, Texas, US. February.
- Pernet CR, Wilcox, R. and Rousselet, G.A. 2013. Robust correlation analyses: false positive and power validation using a new open source Matlab toolbox. Front. Psychology 3:606. doi: 10.3389/fpsyg.2012.00606
- Scott, W.F. 2000. Tables of Cramer-Von Mises Distributions, Commun.Statist.-Theory Meth. 29(1), 227-235.
- Stephens, M.A. 1974. EDF Statistics for Goodness-of-Fit and Some Comparisons, J.Amer.Statist.Assoc. 69, 730-737.
- Stephens, M.A. 1977. Goodness-of-Fit for the Extreme-Value Distribution, Biometrika 64, 583-588.
- Wackerly D.D., Mendenhall, W. & Scheaffer, R.L. 2007. Mathematical Statistics with Applications ( 7th ed.), Australia, Brooks/Cole,896p. Wilcox, R. R. 2012. Introduction to robust estimation and hypothesis testing(3rd ed.), Academic Press, USA, 690p.
Öz
Bu çalışmada iki normal dağılımlı rasgele değişken arasındaki korelâsyonun anlamlılık testi için yeni bir test yaklaşımı önerilmektedir. Bu yeni yaklaşım korelâsyonun işareti ile uyumlu olmayan aykırı değerlere karşı sağlamdır. Korelasyonun anlamlılığının testi için kullanılan geleneksel Pearson t-testi ile önerilen test yaklaşımının güç performanslarını karşılaştırmak amacıyla, bu tür aykırı değerlerin birkaç tanesinin varlığı durumunda bir benzetim çalışması gerçekleştirilmiştir. Bu benzetim çalışması sonucunda, önerilen yaklaşımın korelâsyonlar için olan Pearson t-testinden daha iyi performans gösterdiği görülmüştür. Bu tür aykırı değerler örneklemin yaklaşık olarak %5 ya da %6’sından daha fazlasını oluşturmamak kaydıyla yeni yaklaşıma ilişkin bu iyi performansın devam ettiği söylenebilmektedir.
Anahtar Kelimeler
Kolmogorov-Smirnov uyum iyiliği testi Cramer-von Mises uyum iyiliği testi Deneysel güç karşılaştırması Simülasyon
Kaynakça
- Bain, L. J. & Engelhardt, M. 1992. Introduction to Probability and Mathematical Statistics (2nd ed.), Duxbury Press, Belmont, California, 644p.
- Bishara, A. J., & Hittner, J. B. 2012. Testing the significance of a correlation with non-normal data: Comparison of Pearson, Spearman, transformation, and resampling approaches. Psychological Methods, 17, 399-417.
- Conover, W.J. 1999. Practical Nonparametric Statistics (3rd ed.), John Wiley & Sons, New York, 592p.
- El-Fallah, M., & El-Salam, A. 2006. A robust measure for the correlation coefficient. J. King Saud Univ., 19, Admin. Sci. 1, 41-50.
- Evandt O., Coleman, S., Ramalhoto M.F. & Lottum, C.V. Y.J. 2004. A little known Robust Estimator of the Correlation Coefficient and Its Use in a Robust Graphical Test for Bivariate Normality with Applications in Aluminum Industry, Mathematical Programming, Qual.Reliab.Engng. Int. 20, 433-456.
- Huber, P. J. 2004. Robust Statistics, John Wiley & Sons, USA, 308p.
- King, J. E. 2003. What have we learned from 100 years of robustness studies on r? Paper presented at the annual meeting of the Southwest Educational Research Association, San Antonio, Texas, US. February.
- Pernet CR, Wilcox, R. and Rousselet, G.A. 2013. Robust correlation analyses: false positive and power validation using a new open source Matlab toolbox. Front. Psychology 3:606. doi: 10.3389/fpsyg.2012.00606
- Scott, W.F. 2000. Tables of Cramer-Von Mises Distributions, Commun.Statist.-Theory Meth. 29(1), 227-235.
- Stephens, M.A. 1974. EDF Statistics for Goodness-of-Fit and Some Comparisons, J.Amer.Statist.Assoc. 69, 730-737.
- Stephens, M.A. 1977. Goodness-of-Fit for the Extreme-Value Distribution, Biometrika 64, 583-588.
- Wackerly D.D., Mendenhall, W. & Scheaffer, R.L. 2007. Mathematical Statistics with Applications ( 7th ed.), Australia, Brooks/Cole,896p. Wilcox, R. R. 2012. Introduction to robust estimation and hypothesis testing(3rd ed.), Academic Press, USA, 690p.
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 6 Haziran 2014 |
| Yayımlandığı Sayı | Yıl 2014 Cilt: 7 Sayı: 1 |