A Brief Review of Tests for Normality

In statistics it is conventional to assume that the observations are normal. The entire statistical framework is grounded on this assumption and if this assumption is violated the inference breaks down. For this reason it is essential to check or test this assumption before any statistical analysis of data. In this paper we provide a brief review of commonly used tests for normality. We present both graphical and analytical tests here. Normality tests in regression and experimental design suffer from supernormality. We also address this issue in this paper and present some tests which can successfully handle this problem.

[1]  Anil K. Bera,et al.  Model specification tests: A simultaneous approach☆ , 1982 .

[2]  Egon S. Pearson,et al.  Relation between the shape of population distribution and the robustness of four simple test statistics , 1975 .

[3]  Md. Sohel Rana,et al.  A robust rescaled moment test for normality in regression , 2009 .

[4]  H. A. David,et al.  THE DISTRIBUTION OF THE RATIO, IN A SINGLE NORMAL SAMPLE, OF RANGE TO STANDARD DEVIATION , 1954 .

[5]  R. Geary.  THE RATIO OF THE MEAN DEVIATION TO THE STANDARD DEVIATION AS A TEST OF NORMALITY , 1935 .

[6]  R. Imon.  Analyzing Length or Size Biased Data: A Study on the Lengths of Peas Plants , 2015 .

[7]  A. H. M. Rahmatullah Imon,et al.  Simulation of Errors in Linear Regression: An Approach Based on Fixed Percentage Area , 2003, Comput. Stat..

[8]  Rory A. Fisher,et al.  The Moments of the Distribution for Normal Samples of Measures of Departure from Normality , 1930 .

[9]  M. Stephens.  EDF Statistics for Goodness of Fit and Some Comparisons , 1974 .

[10]  L. Shenton,et al.  Omnibus test contours for departures from normality based on √b1 and b2 , 1975 .

[11]  E. S. Pearson,et al.  Tests for departure from normality. Empirical results for the distributions of b2 and √b1 , 1973 .

[12]  P. J. Huber.  Robust Regression: Asymptotics, Conjectures and Monte Carlo , 1973 .

[13]  S. Weisberg,et al.  An Approximate Analysis of Variance Test for Non-Normality Suitable for Machine Calculation , 1975 .

[14]  N. Smirnov.  Table for Estimating the Goodness of Fit of Empirical Distributions , 1948 .

[15]  Karl Pearson,et al.  On the General Theory of Skew Correlation and Non-Linear Regression , 2010 .

[16]  AN Kolmogorov-Smirnov,et al.  Sulla determinazione empírica di uma legge di distribuzione , 1933 .

[17]  K. Mehrotra,et al.  Tests for Univariate and Multivariate Normality. , 1976 .

[18]  S. Weisberg,et al.  Residuals and Influence in Regression , 1982 .

[19]  R. Geary.  Testing for normality. , 1947, Biometrika.

[20]  A. Imon,et al.  Regression Residuals, Moments, and Their Use in Tests for Normality , 2003 .

[21]  Beat Kleiner,et al.  Graphical Methods for Data Analysis , 1983 .

[22]  T. W. Anderson,et al.  Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes , 1952 .

[23]  R. Koenker.  Robust methods in econometrics , 1981 .

[24]  S. Shapiro,et al.  An Approximate Analysis of Variance Test for Normality , 1972 .

[25]  G. Judge,et al.  The Theory and Practice of Econometrics , 1981 .

[26]  R. D'Agostino.  An omnibus test of normality for moderate and large size samples , 1971 .

[27]  R. D'Agostino.  Tests for the Normal Distribution , 2017 .

[28]  S. Shapiro,et al.  An Analysis of Variance Test for Normality (Complete Samples) , 1965 .

[29]  E. S. Pearson.  A FURTHER DEVELOPMENT OF TESTS FOR NORMALITY , 1930 .

[30]  John M. Chambers,et al.  Graphical Methods for Data Analysis , 1983 .