Abstract
A nonparametric multiple comparison test for differences in scale parameters is suggested The asymptotic distribution of the test statistic is derived. A modification of the test when the location parameters are unknown and unequal is suggested. This modified test is not asymptotically distribution free for all underlying location-scale families; however, we give sufficient conditions on the families under which the test is asymptotically distribution free.
Similar content being viewed by others
References
Ansari AR, Bradley RA (1960) Rank sum tests for dispersion. Annals of Mathematical Statistics 31:1174–1189
Bartlett MS (1937) Properties of sufficiency and statistical tests. Proceedings from the Royal Statistical Society, Ser. A, 160:268–282
Box GEP (1953) Normality and tests of variance. Biometrika 40:318–335
Conover WJ, Johnson ME, Johnson MM (1981) A comparative study of tests for homogeneity of variances, with applications to the outer continental shelf binding data. Technometrics 23:351–362
Kruskal WH, Wallis WA (1952) Use of rank sums in one criterion analysis of variance. Journal of the American Statistical Association 47:583–621
Layard MWJ (1968) Robust large sample tests for homogeneity of variances. Journal of the American Statistical Association 63:195–198
Lehman EL (1951) Consistency and unbiasedness of certain nonparametric tests. Annals of Mathematical Statistics 22:165–179
Mann HB, Whitney DR (1947) On a test of whether one of two random variables is stochastically larger than the other. Annals of Mathematical Statistics 18:50–60
Miller RG Jr (1966) Simultaneous statistical inference. McGraw-Hill, New York
Miller RG Jr (1968) Jackknifing variances. Annals of Mathematical Statistics 39:567–582
Mood AM (1954) On the asymptotic efficiency of certain nonparametric two-sample tests. Annals of Mathematical Statistics 25:514–522
Puri ML (1965) On some tests of homogeneity of variances. Annals of Institute of Statistical Mathematics 17:323–330
Puri ML (1966) Multisample scale problem: unknown location parameters. Annals of the Institute of Statistical Mathematics 18:99–106
Seigel S, Turkey J (1960) A nonparametric sum of ranks procedure for relative spread in unpaired samples. Journal of the American Statistical Association 55:429–445
Steel RGD (1960) Rank sum test for comparing all pairs of treatments. Technometric 2:179–207
Sukhatme BV (1958) Testing in hypothesis that two populations differ only in location. Annals of Mathematical Statistics 29:60–78
Tsai WS, Duran BS, Lewis TO (1975) Small sample behavior of some multisample nonparametric tests for scale. Journal of the American Statistical Association 70:791–796
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Stevens, G. A nonparametric multiple comparison test for differences in scale parameters. Metrika 36, 91–106 (1989). https://doi.org/10.1007/BF02614081
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02614081