SavedAdd your journal

Journals / İstatistikçiler Dergisi:İstatistik ve Aktüerya / 2013 / Cilt: 6 Sayı: 2

Comparing Robust Test Statistics in Unbalanced Designs

Dengesiz deney düzenlerinde sağlam test istatistiklerinin karşılaştırılması

Derya Karagöz
Pages
79–85
Publication Date
2013-06-01
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The simulations results show up that the proposed robust tests have a good performance.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Comparing Robust Test Statistics in Unbalanced Designs In this study, the violations of the assumptions, heteroscedasticity and non-normality are consedered in the one-way ANOVA.
📊
Key Findings & Data:In the simulation study, using different experimental designs, type I error risks of the improved robust test statistic for the Weibull distribution are obtained with respect to 2 different robust methods which are quantile and least square quantile.
💡
Conclusion & Impact:The simulations results show up that the proposed robust tests have a good performance.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:ANOVA · Weibull Dağılımı · Welch

Abstract

Comparing Robust Test Statistics in Unbalanced Designs In this study, the violations of the assumptions, heteroscedasticity and non-normality are consedered in the one-way ANOVA. Robust Brown-Forsythe (RBF) and robust modified Brown-Forsythe (RMBF) test statistics are developed for the non-normal data assumed to be Weibull distribution with outliers. In the simulation study, using different experimental designs, type I error risks of the improved robust test statistic for the Weibull distribution are obtained with respect to 2 different robust methods which are quantile and least square quantile. Unbalanced sample sizes with homogeneous and heterogeneous variances are considered for k=3,9 groups. The simulations results show up that the proposed robust tests have a good performance.

Özet

Bu çalışmada, tek yönlü varyans analizinde varyansların homojenliği ve dağılımın normalliği varsayım bozulumları ele alınmıştır. Aykırı değer içeren normal olmayan Weibull dağılımı için farklı varyanslı gruplarda sağlam Brown-Forsythe (RBF) ve sağlam Geliştirilmiş Brown-Forsythe (RMBF) test istatistiği önerilmiştir. Weibull dağılımı için geliştirilen sağlam test istatistiklerinin davranışı benzetim çalışması yapılarak 1. tip hata olasılıkları bakımından, yüzdelik ve yüzdelik en küçük kareler dayalı sağlam tahmin yöntemine göre grup sayısı k=3, 9 için incelenmiştir. Dengesiz gruplarda, eşit olmayan ortalamalı ve homojen olmayan varyanslı deneme kombinasyonları ele alınmıştır. Önerilen sağlam test istatistiklerinin varsayım bozulumlarına karşı iyi bir performansa sahip olduğu gösterilmiştir.

🔖

Cite This Article

Karagöz, D. (2013). Comparing Robust Test Statistics in Unbalanced Designs. İstatistikçiler Dergisi:İstatistik ve Aktüerya, Cilt: 6 Sayı: 2, 79–85. https://ajindex.com/articles/1502764

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (16)

  1. [1 ] J. Adrover, R.A. Maronna, and V.J. Yohai, 2004, Robust regression quantiles, Journal of Statistical Planning and Inferenc, 122, 187–202.
  2. [2 ] K. Boudt, D. Caliskan, and C. Croux, 2011, Robust explicit estimators of Weibull parameters, Metrika, 73, 187-209.
  3. [3 ] G.E.P. Box, 1953, Nonnormality and tests on variances, Biometrika, 40, 318-335.
  4. [4 ] M.B. Brown, and A.B. Forsythe, 1974, The small sample behavior of some statistics which test the equality of several means, Technometrics, 16, 129-132.
  5. [5 ] G.S. James, 1951, The comparasion of several groups of observations when the ratios of the population variances are unkown, Biometrika, 38, 324-329.
  6. [6 ] H.J. Keselman, R.R. Wilcox, 1999, The ’improved’ Brown and Forsythe test for mean equality: some things can’t be fixed, Communications in Statistics - Simulation and Computation, 28,6876
  7. [7 ] W.H. Kruskal and W.A. Wallis, 1952, Use of ranks in one criterion variance analysis, JASA, 47, 583-6
  8. [8 ] E.Kulinskaya,,R.G. Staudtev and H. Gao, 2003, Power approximations in testing for unequal means in a One-Way ANOVA weighted for unequal variances, Communications in Statistics Theory and Methods, 32,2353-2371.
  9. [9 ] N.B. Marks, 2005, Estimation of Weibull parameters from common percentiles, Journal of Applied Statistics, 32, 17-24.
  10. [10 ] D.V. Mehrotra, 1997, Improving the Brown-Forsythe solution to the Generalized Behrens Fisher problem, Communications in Statistics Simulation and Computation, 26, 1139-1145.
  11. [11 ] A.F. Özdemir, and S. Kurt, 2006, One Way Fixed Effect Analysis Of Variance Under Variance Heterogeneity And A Solution Proposal, Selçuk Journal of Applied Mathematics, 7, 81-91. [12 ] B. Şenoğlu, and M.L. Tiku, 2001, Analysis of variance in experimental design with nonnormal error distribution, Communication Statistics-Theory Method, 30, 1335-1352.
  12. [13 ] B. Şenoğlu, 2005, Robust 2 k Factorial Design with Weibull Error Distributions, Journal of Applied Statistics, 32, 1051-1066.
  13. [14 ] M.L. Tiku, and B. Şenoğlu, 2009, Estimation and hypothesis testing in BIB design and robustness, Computational Statistics and Data Analysis, 53, 3439-3451.
  14. [15 ] B.L. Welch, 1951, On the comparison of several mean values. Biometrika, 38, 330-336.
  15. [16 ] R.R. Wilcox, 1995, The practical importance of heteroscedastic methods, using trimmed means versus means, and designing simulation studies, British J. Math.Statist.Psych.,48, 99-114. [17 ] Wilcox, R.R., 1997, Introduction to Robust Estimation and Hypothesis Testing, Academic Press, New York.
  16. [8 ] E.Kulinskaya,,R.G. Staudtev and H. Gao, 2003, Power approximations in testing for unequal means in a One-Way ANOVA weighted for unequal variances, Communications in Statistics Theory and Methods, 32,2353-2371.