An Improved Confidence Interval for The Difference between Standard Deviations of Normal Distributions Using a Ranked Set Sampling

Abstract

In this paper, a confidence interval is derived for the difference between the standard deviations of normal distributions using the method of variance of estimates recovery. This confidence interval was improved using the estimators of the standard deviations using ranked set sampling (RSS) instead of the standard method using simple random sampling (SRS). An evaluation of the performance of the proposed confidence interval based on RSS compared to the existing one based on SRS was conducted via a Monte Carlo simulation study. The results revealed that the proposed confidence interval based on RSS performed more efficient than the existing one based on SRS in terms of the coverage probability and average length. A confidence interval comparison is also illustrated using a real data example in the area of medical science.