INTERVAL ESTIMATION FOR THE DIFFERENCE OF TWO INDEPENDENT NONNORMAL POPULATION VARIANCES

Abstract

This study focuses on interval estimation with sample variance estimators based on Winsorized Mean and Trimmed Mean for the difference of the variances of two nonnormal populations. In the simulation study, confidence intervals based on these estimators for the difference of the variances of two non-normally distributed populations were compared in terms of coverage probabilities and average length widths. According to simulation study, it was determined that the coverage probabilities of confidence intervals obtained with estimators based on both Winsorized and Trimmed means were very close to the nominal confidence level in any case. However, it was seen that the average length widths of confidence intervals obtained with sample variance estimator based on Trimmed Mean were narrower compared to the average length widths of confidence intervals obtained with sample variance estimator based on Winsorized Mean. In addition, it was determined that these results were the same when the Type I error is different. According to these results, it will be appropriate to prefer interval estimations obtained with sample variance estimator based on Trimmed Mean since it provides narrower confidence interval for the difference of the variances of two nonnormal populations.

Keywords

• Winsorized Mean,Trimmed Mean,Bootstrap,Interval Estimation,Coverage Probability

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