Preliminary tests of homogeneity- type I error rates under non-normality

Islam, Tanweer (2016): Preliminary tests of homogeneity- type I error rates under non-normality.

Abstract

Many statistical procedures utilize preliminary tests to enhance the accuracy of the final inferences. Preliminary tests like Goldfeld-Quandt (GQ) and Levene-type tests are used to assess the assumption of equality of population variances with normality as the underlying distributional assumption. Such tests must be used with care as the final inferences are conditional on the performance of these tests at first stage. This study explores the size distortions of GQ and Levene-type tests under non-normality. The results do not warrant the use of GQ & Levene test under non-normality as the size distortions are as high as 88 & 48% for the respective statistics. However, the modified form of Levene test (BF-test) retains its size properties except for the multi-model alternatives with relatively big outliers.

• Item Type: MPRA Paper
• Language: English
• Keywords: Size Distortions, Levene test, equality of variances
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling

References

Baiarda, F. U., & Grobbelaar, A. O. (2009). A comparison of one- versus two-stage surgery in an experimental model of functional muscle transfer woth interposed nerve grafting. Journal of Plastic, Reconstructive & Aesthetic Surgery, 62, 1042-1047.

Banks, M. L., Roma, P. G., & Folk, J. E. (2011). Effects of the delta-opioid agonist SNC80 on the abuse liability of methadone in rhesus monkeys: a behavioural economic analysis. Psychopharmacology, 431-439.

Bispo, R., Marques, T. A., & Pestana, D. (2012). Statistical power of goodness-of-fit tests based on the empirical distribution function for type-I right-censored data. Journal of Statistical Computation and Simulation, 82(2), 173-181.

Chawda, M., Hucker, P., Whitehuse, S. L., Crawford, R. W., English, H., & Donnelly, W. J. (2009). Comparison of Cemented vs Uncemented Positioning Using an Imageless Navigation System. The Journal of Athroplasty, 24(8).

Correia, M. d., Neck, R., Panagiotidis, T., & Richter, C. (2008). An empirical investigation of the sustainability of the public deficit in Portugal. Springer-Verlag, 5, 209-223.

Francis, J. R., & Simon, D. T. (1987). A Test of Audit Pricing in the Small-Client Segment of the U. S. Audit Market. The Accounting Review, 6(1), 145-157.

Gastwirth, J. L., Gel, Y. R., & Miao, W. (2009). The Impact of Levene’s Test of Equality of Variances on Statistical Theory and Practice. Statistical Science, 24(3), 343-360.

Goldfeld, S. M., & Quandt, R. E. (1965). Some Tests for Homoscedasticity. Journal of the American Statistical Association, 60(310), 539-547.

Grinband, J., Wager, T. D., Ferrera, V. P., & Hirsch, J. (2008). Detection of time-varying signals in event-related fMRI designs. Neuro Image, 43, 509-520.

Islam, T. U. (2017). Stringency-based ranking of normality tests. Communications in Statistics - Simulation and Computation, 46(1), 655-668.

Pearson, E. S., D’ Agostino, R. B., Bowman, K. O. (1977). Tests for departure from normality: Comparison of power. Biometrika 64(02):231–246.

Romao, X., Delgado, R., & Costa, A. (2010). An empirical power comparison of univariate goodness-of-fit tests for normality. Journal of Statistical Computation and Simulation, 80(5), 1-47.

Schucany, W. R., & Ng, H. K. (2006). Preliminary Goodness-of-fit Tests for Normality do not Validate the One-Sample Studendt t. Communication in Statistics- Theory and Methods, 35(12), 2275-2286.

Shapiro, S. S., Wilk, M. B., & Chen, H. J. (1968). A Comparative Study of Various Tests for Normality. Journal of the American Statistical Association, 63(324), 1343-1372.

Tang, C.-H., & Jang, S. (. (2007). Revisit to the determinants of capital structure: A comparison between lodging firms and software firms. Hospitality Management, 26, 175-187.

Thadewald, T., Büning, H. (2007). Jarque-Bera test and its competitors for testing normality- A power comparison. Journal of Applied Statistics 34(1):87–105.

Yap, B. W., & Sim, C. H. (2011). Comparisons of various types of normality tests. Journal of Statistical Computation and Simulation, 81(12),1-15.

Yazici, B., & Yolacan, S. (2007). A comparison of various tests of normality. Journal of Statistical Computation and Simulation, 77(02), 175-183.

Zeileis, A., & Hothorn, T. (2002). Diagnostic Checking in Regression Relationships. R News, 3(3), 7-10.

Zhang, J.,Wu, Y. (2005). Likelihood-ration tests for normality. Computational Statistics & Data Analysis 49:709–721.