ROBUSTNESS AND POWER OF THE ONE MEAN T – STUDENT TEST AGAINST PRESENCE OF OUTLIERS.
DOI:
https://doi.org/10.47187/perf.v1i24.70Keywords:
outliers, t-Student, mean, inferenceAbstract
Previous studies reveal that samples with outliers alter the type I and type II error of a t-Student test for inference of a mean. The methodology that these works use to simulate extreme data consists of mixing two different normal in order to contaminate the data. We think that this technique is not the most appropriate, since, when making this process, the result is not a new normal, which is breaching the main assumption of the test. In this work, this methodology is repeated in order to verify the problems described, but atypical data are also generated from a single normal without the need for any contamination. Using this last methodology, and with a stochastic simulation process, the probability of type I and type II error is estimated, from which it is concluded that the t-Student is a robust test against the presence of outliers and its power does not depend of the number of extreme data generated in the sample.
Downloads
References
Leys C, Ley C, Klein O, Bernard P, Licata L. Detecting outliers: Do not use standard devia- tion around the mean, use absolute deviation around the median. Journal of Experimental Social Psychology. 2013; 49(4)
Miller J. Reaction time analysis with outlier exclusion: Bias varies with sample size. The quarterly journal of experimental psychology. 1991; 43(4).
Gervini D. Robust functional estimation using the median and spherical principal components. Biometrika. 2008; 95(3). Student. The probable error of a mean. Biometrika. 1908.
Barnett V, Lewis T. Outliers in statistical data. Wiley. 1974.
Hampel F, Ronchetti E, Rousseeuw P, Stahel WA. Robust statistics: the approach based on influence functions. 1st ed.: John Wiley & Sons; 2011.
Hawkins D. Identification of outliers. 11th ed.: Springer; 1980.
Wilcoxon F. Individual comparisons by ranking methods. Breakthroughs in statistics. 1992.
Kruskal W, Wallis A. Use of ranks in one-criterion variance analysis. Journal of the American statistical Association. 1952; 47.
Bradley J. A common situation conducive to bizarre distribution shapes. The American Statistician. 1977; 31(4).
Neave H, Granger C. A Monte Carlo study comparing various two-sample tests for differences in mean. Technometrics. 1968; 10(3).
Rasmussen JL. The power of Student's t and Wilcoxon W statistics: A comparison. Evalua- tion Review. 1985; 9(4).
Rasmussen JL. An evaluation of parametric and non-parametric tests on modified and non-modified data. British Journal of Mathematical and Statistical Psychology. 1986; 39(2).
Zimmerman D, Zumbo B. The relative power of parametric and nonparametric statistical methods. Lawrence Erlbaum Associates. 1993.
Zimmerman D. A note on the influence of outliers on parametric and nonparametric tests. The journal of general psychology. 1994; 121(4).
Rasmussen JL. An evaluation of parametric and non-parametric tests on modified and non-modified data. British Journal of Mathematical and Statistical Psychology. 1986; 39(2).
Cochran W. The x2 correction for continuity. Iowa State College Journal of Science. 1942; 16(1).
Rasch D, Guiard V. The robustness of parametric statistical methods. Psychology Science.
; 46.
Flores P, Ocana J. Heteroscedasticity irrelevance when testing means difference. SORT: sta- tistics and operations research transactions. 2018; 42(1).
Flores P, Ocaña J. Pretesting strategies for homoscedasticity when comparing means. Their robustness facing non-normality. Communications in Statistics-Simulation and Computation. 2019; 43.
Rouaud M. Probability, Statistics and Estimation: Propagation of Uncertainties in Experimental Measurement NC, USA: Lulu Press, Morrisville; 2013.
Team RC. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. 2019.
Wickham H. ggplot2: Elegant Graphics for Data Analysis New York: Springer-Verlag; 2016.
Allaire J, Horner J, Xie Y, Marti V, Porte N. markdown: Render Markdown with the C Library 'Sundown'; 2019.
Tukey J. Exploratory Data Analysis: Addison-Wesley; 1977.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
