Robustness and Asymptotic Theory of Tests of Location under Violation of Normality Assumption

Ibrahim Ali1, Nicholas P. Dibal2, Yusuf A. Mohammed2

1Department of Mathematics and Computer Science, Borno State University, Njimtilo, Maiduguri, Nigeria,
2Department of Mathematical Sciences, University of Maiduguri, Borno State Nigeria

*Corresponding author’s Email: ibrahimali@bosu.edu.ng, doi.org/10.55639/607.262524


ABSTRACT

The distribution of data can be normal or followed a certain distribution. Therefore, data collected requires checking normality assumption before applied to any hypothesis testing. Hence, this work investigates the robustness and asymptotic properties of one sample test statistics when data follows a particular distribution in order to identify the best one to test hypothesis about one population parameter on one sample tests statistics. The one sample test statistics considered are t, z, Sign and Wilcoxon Sign Rank test. A
simulation replicated 1000 times was conducted at three sample sizes
which are 10, 20 and 40 from uniform, exponential, and gamma distributions. Data analysis revealed that the z-test is the most accurate for all the sample sizes for a data from uniform distribution followed by t-test at small and moderate sample sizes while Wilcoxon sign rank-test is the most robust test to gamma and exponential distributions at all the sample sizes.

Keywords:

Robustness,
Asymptotic,
Normality violation,
Monte Carlo
Simulation