A Power Comparison of Various Tests of Univariate Normality on Ex-Gaussian Distributions
Abstract
A power analysis of seven normality tests against the Ex-Gaussian distribution (EGd) is presented. The EGd is selected on the basis that it is a particularly well-suited distribution to accommodate positively skewed distributions such as those observed in reaction times data. A pre-assessment of the power of the selected tests across various types of distributions was done via a meta-analysis and a comparison with other power analyses reported in the literature was also performed. General recommendations are given as to which tests should be used to test normality in data suspected to resemble an EG distribution. Additionally, some topics for future research regarding the use of confidence intervals and the computation of accurate critical values are outlined.
References
(2010). A new estimator of entropy and its application in testing normality. Journal of Statistical Computation and Simulation, 80, 1151–1162.
(2011). Monte Carlo comparison of seven normality tests. Journal of Statistical Computation and Simulation, 81, 965–972.
(2010). Analysing reaction times. International Journal of Psychological Research, 3, 12–28.
(1982). Evidence from auditory simple reaction times for both change and level detectors. Perception & Psychophysics, 32, 117–133.
(1974). Some effects of non-normal distribution shape on the magnitude of the Pearson product moment correlation coefficient. Interamerican Journal of Psychology, 8, 261–287.
(2007). A power comparison of goodness-of-fit tests for normality based on the likelihood ratio and the non-likelihood ratio. Thailand Statistician, 5, 57–68.
(2004). Fitting distributions using maximum likelihood: Methods and packages. Behaviour Research Methods, Instruments, & Computers, 36, 742–756.
(2010). Hierarchical Bayes models for response time data. Psychometrika, 75, 613–632.
(2011). A critical assessment of simulated critical values. Communications in Statistics – Simulation and Computation, 40, 719–727.
(1986). Goodness-of-fit techniques. New York, NY: Marcel Dekker.
(2005). Using neuronal latency to determine sensory-motor processing pathways in reaction time tasks. Journal of Neurophysiology, 93, 2974–2986.
(1987). Better bootstrap confidence intervals [with discussion]. Journal of the American Statistical Association, 82, 171–200.
(1993). An Introduction to the Bootstrap. New York, London: Chapman and Hall.
(2006). Comprehensive study of tests for normality and symmetry: Extending the Spiegelhalter test. Journal of Statistical Computation and Simulation, 76, 803–816.
(2006). Morphometric evidences for regional variation in potential of neural plasticity. International Journal of Morphology, 24, 181–186.
(2002). Evaluating the adequacy of simulating maximum and minimum daily air temperature with the normal distribution. Journal of Applied Meteorology, 41, 744–753.
(1965). Inferred components of reaction time as a function of foreperiod duration. Journal of Experimental Psychology, 69, 382–386.
(1996). Sample quantiles in statistical packages. American Statistician, 50, 361–365.
(2010). Reproductive biology of a grassland songbird community in northcentral Montana. Wilson Journal of Ornithology, 122, 455–464.
(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, 25, 296–300.
(1986). Response times: Their role in inferring elementary mental organization. New York, NY: Oxford University Press.
(2010). The shifting boxplot. A boxplot based on essential summary statistics around the mean. International Journal of Psychological Research, 3, 37–46.
(2007, October) October. RT analysis with the Weibull-Gaussian convolution model. Poster presented at the 23rd Annual Meeting of the ISP, Tokyo, Japan.
(2005). A comparison of the randomization test with the F test when error is skewed. Behaviour Research Methods, 37, 426–435.
(1989). A warning about median reaction time. Journal of Experimental Psychology: Human Perception and Performance, 14, 539–543.
(2009). The effects of lack of normality and homogeneity of variance on analysis of variance and clonal heritability in in vitro clonal propagation traits. In Vitro Cellular and Developmental Biology – Plant, 45, 783–794.
(2007). Geostatistical analysis for estimation of mean rainfalls in Andhra Pradesh, India. International Journal of Geology, 3, 35–51.
(2005). Caffeine improves endurance in 75-yr-old citizens: A randomized, double-blind, placebo-controlled, crossover study. Journal of Applied Physiology, 99, 2302–2306.
(2008). The logarithmic transformation and the geometric mean in reporting experimental IgE results: What are they and when and why to use them? Annals of Allergy. Asthma & Immunology, 100, 333–337.
. (2011). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing.
(2010). Power comparison of some selected normality tests. Proceedings of the Regional Conference on Statistical Sciences (RCSS’10), June 14–18, 2010 (pp. 126–138). Kota Baru, Malaysia. Retrieved from www.instatmy.org.my/index.php?option=com_content&view=article&id=12
(1992). Type I error and the number of iterations in Monte Carlo studies of robustness. British Journal of Mathematical and Statistical Psychology, 45, 283–288.
(2010). An empirical power comparison of univariate goodness-of-fit tests for normality. Journal of Statistical Computation and Simulation, 80, 545–591.
(1982a). An extension of Shapiro and Wilk’s W test for normality to large samples. Applied Statistics, 31, 115–124.
(1982b). Algorithm AS 181: The W test for Normality. Applied Statistics, 31, 176–180.
(1995). Remark AS R94: A remark on Algorithm AS 181: The W test for normality. Applied Statistics, 44, 547–551.
(2010). Is it really robust? Reinvestigating the robustness of ANOVA against violations of the normal distribution assumption. Methodology, 6, 147–151.
(2004). Nonparametric analysis of ordinal data in designed factorial experiments. Phytopathology, 94, 33–43.
(2011). Spatial variability of macronutrient for soil fertilization management: A case study on Urmia plain. International Journal of Soil Science, 6, 49–59.
(2007). Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, 23, 1–46.
(2007). A cautionary note on the use of the Kolmogorov-Smirnov test for normality. Monthly Weather Review, 135, 1151–1157.
(2008). A power comparison and simulation study of goodness-of-fit tests. Computers and Mathematics with Applications, 56, 1617–1625.
(2002). Testing for normality. New York, NY: CRC Press.
(2008). Echocardiographic parameters in athletes of different sports. Journal of Sports and Medicine, 7, 151–156.
(2009). A generalization of Shapiro-Wilk’s test for multivariate normality. Communications in Statistics – Theory and Methods, 38, 1870–1883.
(2008). Effective analysis of reaction time data. Psychological Record, 58, 475–482.
(1998). How many discoveries have been lost by ignoring modern statistical methods? American Psychologist, 53, 300–314.
(2007). A comparison of various tests of normality. Journal of Statistical Computation and Simulation, 77, 175–183.
(2011). Comparison of various types of normality tests. Journal of Statistical Computation and Simulation, 81, 2141–2155.
(2010). Normality test based on a truncated mean characterization. Communications in Statistics – Simulation and Computation, 39, 1818–1843.
(1998). Invalidation of parametric and nonparametric statistical tests by concurrent violation of two assumptions. The Journal of Experimental Education, 67, 55–68.
