Summary
Testing the equality of c means the application of the F-test depends on very restrictive assumptions such as normality and equal variances of the c populations. If these assumptions are not satisfied it is more appropriate to apply a robust version of the F-test. We consider the Welch test, a rank version of the Welch test, the trimmed Welch test and some nonparametric counterparts where each of them is very efficient for a special class of distributions. But usually the practising statistician has no clear idea of the underlying distribution. Therefore, an adaptive test should be applied which takes into account the given data. We compare the F-test with its robust and adaptive competitors under normality and nonnormality as well as under homoscedasticity and heteroscedasticity. The comparison is referred to level α and power β of the test and is carried out via Monte Carlo simulation. It turns out that the Welch test is the best one in the case of unequal variances, for equal variances, however, special rank tests are to prefer. It is also shown that the adaptive test behaves well over a broad class of distributions.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Beier, F. and Büning, H. (1997). An adaptive test against ordered alternatives. Computational Statistics and Data Analysis, 25, 441–452.
Brown, M. B. and Forsythe, A. B. (1974). The small sample behaviour of some statistics which test the equality of several means. Technometrics, 16, 129–132.
Biining, H. (1991). Robuste und adaptive Tests. Berlin, De Gruyter
Biining, H. (1994). Robuste and adaptive tests for the two-sample location problem, OR Spektrum, 16, 33–39.
Büning H. (1995). Adaptive Jonckheere-type tests for ordered alternatives. Diskussionsbeiträge des Fachbereichs Wirtschaftswissenschaft der Freien Universität Berlin, Nr. 7.
Büning, H. (1996). Adaptive tests for the c-sample location problem — the case of two-sided alternatives. Communications in Statistics — Theory and Methods, 25, 1569–1582.
Büning, H. (1997). Robust analysis of variance. Journal of Applied Statistics, 24, 319–332.
Büning, H. and Kössler, W. (1996). Robustness and efficiency of some tests for ordered alternatives in the c-sample location problem. Journal of Statistical Computation and Simulation, 55, 337–352.
Conover, W. J. and Iman, R. L. (1981). Rank transformation as a bridge between parametric and nonparametric statistics. The American Statistician, 35, 124–133.
Heiler, S., Michels, P. and Abberger, K. (1993). “Abiturzeugnisse und Studienwahl — Ein Beispiel zur Anwendung graphischer Verfahren in der Explorativen Datenanalyse”. Allgemeines Statistisches Archiv, 77, 166–182.
Hogg, R. V. (1974). Adaptive robust procedures. A partial review and some suggestions for future applications and theory. Journal of the American Statistical Association, 69, 909–927.
James, G. S. (1951): Tests of linear hypotheses in univariate and multivariate analysis when the ratios of the population variances are unknown. Biometrika, 38, 19–43.
Lee, H. and Fung, K. Y. (1983). Robust procedures for multi-sample location problems with unequal group variances. Journal of Statistical Computation and Simulation, 18, 125–143.
Leinhardt, S. and Wasserman, S.S. (1979). Teaching Regression: An exploratory approach. The American Statistician, 33, 196–203.
Puri, M. L. (1972). Some aspects of nonparametric inference. International Statistical Review, 40, 299–327.
Sen, P. K. (1962). On studentized non-parametric multi-sample location tests. Annals of Statistical Institute, 14, 119–131.
Tiku, M. L., Tan, W. Y. and Balakrishnan N. (1986): Robust Inference. New York, Marcel Dekker.
Welch, B. L. (1951). On the comparison of several mean values: An alternative approach. Biometrika, 38, 330–336.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Physica-Verlag Heidelberg
About this chapter
Cite this chapter
Büning, H. (1998). Some Robust and Adaptive Tests Versus F-Test for Several Samples. In: Galata, R., Küchenhoff, H. (eds) Econometrics in Theory and Practice. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-47027-1_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-47027-1_25
Publisher Name: Physica-Verlag HD
Print ISBN: 978-3-642-47029-5
Online ISBN: 978-3-642-47027-1
eBook Packages: Springer Book Archive