A Comparative Study of Four Normality Tests: Anderson-Darling, Shapiro-Wilk, Jarque-Bera, and Rsj

• In Event: AERA Poster Session 4
  In Poster Session: Poster Session (San Diego)

Abstract

This study compared four commonly mentioned normality tests Anderson-Darling test, Shapiro- Wilk, Jarque-Bera and Gel, and Gastwirth statistic (Rsj) using Monte Carlo simulation in R for sample sizes of 10, 30, 50, 75, 100, 200 with 10,000 replications through twenty distributions. Even though symmetric short-tailed and long-tailed, asymmetric short-tailed and long-tailed, near-normal distributions were used in previous studies, limited studies examined the tests through truncated normal distribution and contaminated normal distribution that is used to generate outliers, which may impact the power of normality tests. Truncated normal distribution does not assume the probability of every value in (-∞, +∞) compared with the normal distribution. The results of this study help researchers understand which tests perform better under different conditions.

Authors

• Shiya Liu, Ohio University

• Elife Ceviker, Ohio University

• Xiaorui Sun, Ohio University