Econometrics Project Completed

2004

Author Contact: Lauren Dong, Statistics Canada; e-mail: Lauren.Dong@statcan.can; FAX: (613) 951-3292 David Giles*, Dept. of Economics, University of Victoria, P.O. Box 1700, STN CSC, Victoria, B.C., Canada V8W 2Y2; e-mail: dgiles@uvic.ca; FAX: (250) 721-6214 * Corresponding co-author Abstract The empirical likelihood ratio (ELR) test for the problem of testing for normality in a linear regression model is derived in this paper. The sampling properties of the ELR test and four other commonly used tests are explored and analyzed using Monte Carlo simulation. The ELR test has good power properties against various alternative hypotheses.

International Statistical Review/Revue Internationale …, 1987

Using the Lagrange multiplier procedure or score test on the Pearson family of distributions we obtain tests for normality of observations and regression disturbances. The tests suggested have optimum asymptotic power properties and good finite sample performance. Due to their simplicity they should prove to be useful tools in statistical analysis.

Background: An important aspect of the "description" of a variable is the shape of its distribution, which tells you the frequency of values from different ranges of the variable. Typically, as most of the statistical tests are based on the normality assumption, a researcher is interested in how well the distribution can be approximated by the normal distribution. Unless there are extreme violations of the normality assumptions, approved statistical tests usually provide accurate results. Although simple descriptive statistics can provide some information relevant to this issue, more precise information can be obtained by performing one of the tests of normality to determine whether the sample comes from a normally distributed population or not.

papers.ssrn.com

Journal of Biometrics & Biostatistics, 2016

The problem of testing for normality is fundamental in both theoretical and empirical statistical research. This paper compares the performances of eighteen normality tests available in literature. Since a theoretical comparison is not possible, MonteCarlo simulation were done from various symmetric and asymmetric distributions for different sample sizes ranging from 10 to 1000. The performance of the test statistics are compared based on empirical Type I error rate and power of the test. The simulations results show that the Kurtosis Test is the most powerful for symmetric data and Shapiro Wilk test is the most powerful for asymmetric data.

Many of the test statistics which are used to test H 0 : í µí¼ƒ = í µí¼ƒ 0 are constructed under a postulated model. However, when the postulated model is not correct, the true significance level í µí»¼′ will be different from that of the postulated model. The significance level í µí»¼ is used whether or not the hypothesis will be rejected. So, determining the true significance level is important in hypothesis tests. In this paper, the true significance level for testing hypothesis about location and scale parameters under different contaminated distributions is obtained when the normality assumption is violated. As a result, the robustness of significance levels is investigated.

American Journal of Mathematics and Statistics, 2018

The goal of this study is to investigate the best goodness-of-fit test among five selected normality tests under various continuous non-normal distributions using power as criteria. The tests were compared when the normal parameters are unknown and sample sizes are 10, 30, 50, 100, 300, 500 and 1000 were iterated 1000 times each with 0.01, 0.05, and 0.10 level of significance, using the Monte Carlo technique. We study the procedures based on five well-known normality tests: the Anderson–Darling, Cramer–von Mises, Shapiro–Wilk, Jarque–Bera and Chi-Square. Evidence from the simulation study reveals that the performance of the five normality test statistics varies with the level of significance, sample size and alternative distributions.

The quantitative methods for psychology, 2023

Academic textbooks, statistical literature, and publication guidelines provide conflicting, ambiguous and often incomplete answers to the question of how researchers should handle the normality assumption for classical general linear model tests when conducting their analyses. Previous studies have shown that normality violations can impact on type I errors, power, parameter estimates and standard error estimates of classical tests. This paper reviews the arguments in favour and against normality testing, the role of the central limit theorem, types of violations that tests within the general linear model are susceptible to, methods for evaluating the normality assumption, and the paradox that normality tests have low power in small sample sizes where the influence of assumption violations are likely to be most profound. A Monte Carlo simulation study was used to evaluate the power of 18 normality tests across 18 alternative distributions, and the effect of normality deviations on estimates of centrality, scatter and regression coefficients. The results demonstrate that the type of normality test and distribution matters, and that a conditional testing procedure utilising normality tests to select between classic, non-parametric and robust tests should not be used. Instead, an alternative procedure for managing the normality assumption is advised, and demonstrated in the supplementary materials using R code and data that are provided.