Statistical Powers of Univariate Normality Tests: Comparative Analysis of 2016 Election Process in Uganda

Abstract

The study conducted an empirical comparison of powers of the univariate normality tests using real data for consistency with simulated data. The main objective was to compare the empirical power of the normality tests using natural data for consistency. Six normality tests were selected from the Empirical Distribution Function (EDF), the Correlation and Regression family of normality tests and moment-based normality tests were considered in this study. From the EDF family of normality tests, the Kolmogorov-Smirnov test (Lilliefors correction) and Anderson-Darling normality tests were chosen. From the regression and correlation family of distributions, Shapiro-Wilk and Shapiro-Francia normality tests were chosen. Jaque-Bera and D’Agostino Pearson normality tests were chosen from the moment family of normality tests. The data adopted in this study comprised of the 2016 Uganda election results as cited by Solomon (2016). The analysis was done using a combination of different statistical packages (EXCEL, R and STATA). The data was gathered from the Uganda Electoral Commission website and cleaned using EXCEL package. After the data cleaning process, the data analysis was done using a combination of R (S-plus programing). The analysis involved writing computer programs that tested the data for normality of the different normality tests specified in the study. All the graphical visualizations were done in STATA. The results of the analysis indicate that S-W produced the most powerful results, followed by S-F, D-A, K-S, J-B and lastly A-D. The data thus indicates that the moment-based tests results are better than the EDF-based tests due to huge kurtosis and skewness statistics in the data. The study thus recommends that it is vital to deal with outliers before carrying out any further statistical tests, and the moment-based tests should be applied in the instances where the data is known to have instances of kurtosis and skewness.