Abstract
The assumption of normality is very important because it is used in many statistical procedures such as Analysis of variance, linear regression analysis, discriminant analysis and t-tests. The three common procedures are used for assessing the assumption of normality that is graphical methods, numerical methods and formal normality tests. In the literature, significant amount of normality tests are available. In this paper, only eight different tests of normality are discussed. The tests consider in the present study are Shapiro Wilk, Shapiro Francia, Kolmogrov Smirnov, Anderson Darling, Cramer von Mises, Jarque Bera, Geary and Lilliefors test. Power comparisons of each test are obtained by using Monte Carlo computation of sample data generated from different alternate distributions by using 5% level of significance. The results show that power of each test is affected by sample size and alternate distribution. Shapiro Francia and Kolmogrov Smirnov test perform well for Cauchy exponential distribution respectively. For t-distribution Geary, Shapiro Francia and Jarque Bera test perform well for degrees of freedom 5, 10 and 15 respectively.
Highlights
The results reveal that the proposed estimator which based on the double ranked set sampling technique is more effective than ranked set sampling and simple random sampling
A comprehensive study of the power of accessible normality tests has been performed and observed that the power of these tests has been affected by changing the sample size, level of significance and alternate distribution
Shapiro Francia test leads under alternate Cauchy distribution at 5% and 1% level of significance followed by Watson test and Anderson Darling test
Summary
Many parametric methods (like correlation, regression, t – test, analysis of variance etc) require normality assumption. The assumption of normality is one of the most important assumptions of parametric procedures because of its extensive range of practical applications. In that respect is perhaps no distribution which is stated to be totally normal. The question is usually asked; whether or not the population from which dataset has been drawn can be adequately modeled with the normal distribution for the intended purpose
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