INTERVAL ESTIMATION FOR THE DIFFERENCE OF TWO INDEPENDENT NONNORMAL POPULATION VARIANCES

Year 2017, Volume: 30 Issue: 3, 117 - 129, 20.09.2017

HAYRİYE ESRA Akyüz , Hamza Gamgam , Abdullah Yalçınkaya

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

References

• 1. Bryk, A.S., Raudenbush, S.W., "Heterogeneity of variance in experimental studies: A challenge to conventional interpretations", Psychological Bulletin, 104(3):396-404, (1988).
• 2. Bell, K.J.L., Irwig, L., Craig, J.C., Macaskill, P., "Use of randomized trials to decide when to monitor response to new treatment", British Medical Journal, 336(7640):361–365, (2008).
• 3. Cojbasica, V., Tomovica, A., "Nonparametric confidence intervals for population variance of one sample and the diffeence of variances of two samples", Computational Statistics and Data Analysis, 51(12):5562-5578, (2007).
• 4. Niwitpong, S., "Confidence intervals for the difference of two normal population variances", Proceedings of World Academy of Science, Engineering and Technology, 5(8):602-605, (2011).
• 5. Niwitpong, S., "A note on coverage probability of confidence interval for the difference between two normal variances", Applied Mathematical Sciences, 6(67):3313-3320, (2012).
• 6. Herbert, R.D., Hayen, A., Macaskill, P., Walter, S.D., "Interval estimation for the difference of two independent variances", Communications in Statistics Simulation and Computation, 40(5): 744–758, (2011).
• 7. Suwan, S. and Niwitpong, S., "Interval estimation for a linear function of variances of nonnormal distributions that utilize the kurtosis", Applied Mathematical Sciences, 7(99):4909-4918, (2013).
• 8. Panik, M.J., "Advanced statistics from an elementary point of view", Amsterdam, Elsevier, 802p., (2005).
• 9. Casella, G., Berger, R.L., "Statistical inference", 2nd ed., Duxbury Thomson Learning, USA, 686p., (2001).
• 10. Scheffé, H., "The Analysis of Variance", Wiley, New York, 477p., (1959).