Skip to content
Research Article Open access CC BY 3.0

Normality Assessment, a Substantial Appraisal in Medical Studies: A Simulation Study for Power Comparison of Various Types of Normality Tests

Hamed Tabesh, Ahmad Heidari, Azadeh Saki

Current Journal of Applied Science and Technology · pp. 2646–2660 · Published 10 May 2014

10.9734/BJAST/2014/8921

Abstract

Background: In medical research, statistical tests have become more important. Several parametric procedures are available but each of them requires normality assumption. As normality violation may affect interpretation and inferences reliability and validity, so importance of normal distribution is undeniable. Although several normality tests available for software users but the power of each test in specified situation is not clear. Methods: The aim of this study is to compare the power of nine normality tests. In this paper power of Jarque-Bera test, D’Agostino and Pearson test, Chi-square test, Kolmogrov-Smirnov test, Lilliefors test, Cramer-Von Mises test, Anderson-Darling test, Shapiro-Wilk test and Shapiro-Francia test compared via Monte Carlo simulation of sample data generated from alternative distributions that follow symmetric, skewed, skewed & heavy tailed, highly skewed and highly skewed & heavy tailed distributions. Results: Simulation study shows that Shapiro-Francia test under symmetric, skewed, skewed& heavy tailed and highly skewed& heavy tailed distributions perform better than others. Also, Shapiro-Wilk performs better when underlying distribution is skewed. Conclusion: Although, Shapiro-Francia and Shapiro-Wilk have greater power than their competitors but their powers are still low for small sample size. So their singly use is not recommended.

Normality test Power Monte Carlo Simulation Tukey g-and-h distribution

References (19)

  1. 1 An analysis of variance test for normality (complete samples) [DOI]
  2. 2 Applied Linear Statistical Models [DOI]
  3. 3 Applied Linear Statistical Models [DOI]
  4. 4 On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown [DOI]
  5. 5 A test for normality of observations and regression residuals
  6. 6 A Test of Goodness of Fit [DOI]
  7. 7 A Comparative Study of Various Tests for Normality [DOI]
  8. 8 An Approximate Analysis of Variance Test for Normality [DOI]
  9. 9 Comparisons of various types of normality tests [DOI]
  10. 10 On the composition of elementary errors [DOI]
  11. 11 On the Kolmogorov-Smirnov Test for the Exponential Distribution with Mean Unknown [DOI]
  12. 12 Investigation of Four Different Normality Tests in Terms of Type 1 Error Rate and Power under Different Distributions
  13. 13 Tests for departure from normality: Comparison of powers [DOI]
  14. 14 Testing experimental data for univariate normality [DOI]
  15. 15 Tests for Departure from Normality
  16. 16 A Toolkit for Testing for Non-Normality in Complete and Censored Samples [DOI]
  17. 17 A pocket‐calculator algorithm for the shapiro‐francia test for non‐normality: An application to medicine [DOI]
  18. 18 Parametric Probability Densities and Distribution Functions for Tukey g -and- h Transformations and their Use for Fitting Data
  19. 19 A Note on Tests of Normality

Cited by 4

Pilot Workload Identification During Engine Failure Landings

Jiajun Yuan, Huaxia Lin, Chenyang Zhang · Promet - Traffic&Transportation · 2026

Theoretical considerations when simulating data from the g-and-h family of distributions.

O. L. O. Astivia, Kroc Edward · British Journal of Mathematical & Statistical Psychology · 2022

Empirical Distribution Function (EDF) Statistics

Michael A. Stephens · Wiley StatsRef: Statistics Reference Online · 2016

Showing 3 of 4 known citations — external sources report more than can currently be individually listed.

Related research

Article metrics

Real usage data collected on this platform.

64

Page views

0

PDF downloads

16

Outbound clicks

4

Citations

Views over time

Views by country

Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".

Traffic sources

Referring site, by host.

Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.