A Comparative Study of Tests Power for Homogeneity of Variances

Sabina Denkowska; Kamil Fijorek; Marcin Salamaga; Andrzej Sokołowski

doi:https://doi.org/10.59139/ps.2009.03-04.2

Sabina Denkowska Uniwersytet Ekonomiczny w Krakowie , Kamil Fijorek Uniwersytet Ekonomiczny w Krakowie , Marcin Salamaga Uniwersytet Ekonomiczny w Krakowie , Andrzej Sokołowski Uniwersytet Ekonomiczny w Krakowie Przegląd Statystyczny. Statistical Review, vol. 56, 2009, 3-4, pages: 26-39 Published online: 31 December 2009 DOI https://doi.org/10.59139/ps.2009.03-04.2

393 Views 20 Downloads

ARTICLE

(Polish) PDF

ABSTRACT

Some statistical tests, for example the analysis of variance, assume that variances are equal across groups or samples. Tests for homogeneity of variances can be used to verify that assumption and for pooling of data from different sources to yield an improved estimated variance. Tests for homogeneity of variances can be used usually under assumption of normal distributions or nearly normal distributions. In this paper some tests for homogeneity of variances are examined under the null hypothesis and under the alternative, for various sample sizes, for various symmetric and asymmetric distributions. Monte Carlo simulations has been used for this. In this paper the following procedures have been analyzed: Levene’a test, Brown-Forsythe test, Fligner-Killeen test and O’Brientest.

KEYWORDS

tests for homogeneity of variances, Monte Carlo, Levene’s test, Brown-Forsythe test, Fligner- Killeen test, O’Brien test

REFERENCES

[1] Abdi H., [2007], O’Brien test for homogeneity of variance, [w:] N.J. Salkind (red.), Encyclopedia of Measurement and Statistics, Thousand Oaks (CA), Sage, pp. 701-704.

[2] Conover W.J., Johnson M.E., Johnson M.M., [1981], A Comparative Study of Tests for Homogeneity of Variances, with Applications to the Outer Continental Shelf Bidding Data, Technometrics, Vol. 23, No. 4, s. 351-361.

[3] Domański Cz., [1986], Teoretyczne podstawy testów nieparametrycznych i ich zastosowanie w naukach ekonomiczno-społecznych, Acta Universitatis Lodziensis, Wyd. UŁ, s. 233-240.

[4] Domański Cz., [1990], Testy statystyczne, PWE.

[5] Domański Cz., Pruska K., [2000], Nieklasyczne metody statystyczne, PWE.

[6] Flinger M.A., Killeen T.J., [1976], Distribution-Free Two-Sample Tests for Scale, „Journal of the American Statistical Association”, 71, 210-213.

[7] Lehmann E.L., (1959), Testing Statistical Hypothesis, New York, John Wiley.

[8] Levene, H., [1960], In Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling, I. Olkin et al. (red.), Stanford University Press, s. 278-292.

[9] Xu-Feng N., [2004], Statistical Procedures for Testing Homogeneity of Water Quality Parameters, Department of Statistics Florida State University Tallahassee.

[10] Zieliński W., [1999], Wybrane testy statystyczne, Fundacja „Rozwój SGGW”, Warszawa.