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A nonparametric multiple comparison test for differences in scale parameters. (English) Zbl 0691.62045
Summary: 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.

MSC:
62G10 Nonparametric hypothesis testing
62E20 Asymptotic distribution theory in statistics
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References:
[1] Ansari AR, Bradley RA (1960) Rank sum tests for dispersion. Annals of Mathematical Statistics 31:1174–1189 · Zbl 0104.37302
[2] Bartlett MS (1937) Properties of sufficiency and statistical tests. Proceedings from the Royal Statistical Society, Ser. A, 160:268–282 · Zbl 0016.41201
[3] Box GEP (1953) Normality and tests of variance. Biometrika 40:318–335 · Zbl 0051.10805
[4] 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
[5] Kruskal WH, Wallis WA (1952) Use of rank sums in one criterion analysis of variance. Journal of the American Statistical Association 47:583–621 · Zbl 0048.11703
[6] Layard MWJ (1968) Robust large sample tests for homogeneity of variances. Journal of the American Statistical Association 63:195–198
[7] Lehman EL (1951) Consistency and unbiasedness of certain nonparametric tests. Annals of Mathematical Statistics 22:165–179 · Zbl 0045.40903
[8] 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 · Zbl 0041.26103
[9] Miller RG Jr (1966) Simultaneous statistical inference. McGraw-Hill, New York
[10] Miller RG Jr (1968) Jackknifing variances. Annals of Mathematical Statistics 39:567–582 · Zbl 0162.50201
[11] Mood AM (1954) On the asymptotic efficiency of certain nonparametric two-sample tests. Annals of Mathematical Statistics 25:514–522 · Zbl 0057.11603
[12] Puri ML (1965) On some tests of homogeneity of variances. Annals of Institute of Statistical Mathematics 17:323–330 · Zbl 0161.16202
[13] Puri ML (1966) Multisample scale problem: unknown location parameters. Annals of the Institute of Statistical Mathematics 18:99–106
[14] 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 · Zbl 0104.37501
[15] Steel RGD (1960) Rank sum test for comparing all pairs of treatments. Technometric 2:179–207 · Zbl 0094.13803
[16] Sukhatme BV (1958) Testing in hypothesis that two populations differ only in location. Annals of Mathematical Statistics 29:60–78 · Zbl 0085.35405
[17] 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 · Zbl 0322.62048
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