New Robust Parametric Test Statistics Based on Absolute Deviations for Variance Hypothesis Testing

Music City Center 

This paper presents some new parametric test statistics for hypothesis testing population variances. These statistics are based on mean absolute deviations from the population mean, sample mean, and median. They are designed for single and two-independent-sample scenarios. The asymptotic distributions are derived, and test statistics are obtained in both absolute and ordered forms. Challenges associated with having an acceptable Type 1 error of the test statistics in small sample situations necessitated their modifications. The modifier is a function of the sample size(s) and another parameter d, 0<=d<=1. The value(s) of d at which the test statistics produced an acceptable Type 1 error rate were determined through Monte Carlo Simulation Studies, and their power and robustness were also examined and compared with the existing ones. The modified test statistics provide better Type 1 error, power, and robustness compared to existing ones. Results from real-life data applications support the simulation studies.

New Parametric Test statistics

Variance

Monte Carlo Simulation Studies

Type I error

Power

Robustness 

Royal Statistical Society