Geodesic
On testing hypotheses in the generalized Skillings-Mack random blocks setting
Kybernetika, Tome 47 (2011) no. 5, pp. 657-677 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The testing of the null hypothesis of no treatment effect against the alternative of increasing treatment effect by means of rank statistics is extended from the classical Friedman random blocks model into an unbalanced design allowing treatments not to be applied simultaneously in each random block. The asymptotic normality of the constructed rank test statistic is proved both in the setting not allowing ties and also for models with presence of ties. As a by-product of the proofs a multiple comparisons rule based on rank statistics is obtained for the case when the null hypothesis of no treatment effect is tested against the general alternative of its negation.
The testing of the null hypothesis of no treatment effect against the alternative of increasing treatment effect by means of rank statistics is extended from the classical Friedman random blocks model into an unbalanced design allowing treatments not to be applied simultaneously in each random block. The asymptotic normality of the constructed rank test statistic is proved both in the setting not allowing ties and also for models with presence of ties. As a by-product of the proofs a multiple comparisons rule based on rank statistics is obtained for the case when the null hypothesis of no treatment effect is tested against the general alternative of its negation.
Classification : 62G10
Keywords: rank test; random blocks; hypotheses testing; increasing treatment effect; asymptotic distribution 
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     author = {Rubl{\'\i}k, Franti\v{s}ek},
     title = {On testing hypotheses in the generalized {Skillings-Mack} random blocks setting},
     journal = {Kybernetika},
     pages = {657--677},
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     zbl = {1238.62056},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2011_47_5_a0/}
}
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Rublík, František. On testing hypotheses in the generalized Skillings-Mack random blocks setting. Kybernetika, Tome 47 (2011) no. 5, pp. 657-677. http://geodesic.mathdoc.fr/item/KYB_2011_47_5_a0/

[1] Conover, W. J.: Rank tests for one sample, two samples, and k samples without the assumption of a continuous distribution function. Ann. Statist. 1 (1973), 1105–1125. | DOI | MR | Zbl

[2] Conover, W. J.: Practical Nonparametric Statistics. Third edition. John Wiley & Sons, Inc., New York 1999.

[3] Friedman, M.: The use of ranks to avoid the assumption of normality implicit in the analysis of variance. J. Amer. Statist. Assoc. 32 (1937), 675–701. | DOI

[4] Hájek, J.: A Course in Noparametric Statistics. Holden Day, San Francisco 1969. | MR

[5] Hájek, J., Šidák, Z., Sen, P. K.: Theory of Rank Tests. Academic Press, New York 1999. | MR

[6] Lehmann, E. L.: Nonparametrics. Statistical Methods Based on Ranks. Springer Science and Business Media, New York 2006. | MR | Zbl

[7] Page, E. B.: Ordered hypotheses for multiple treatments: A significance test for linear ranks. J. Amer. Statist. Assoc. 58 (1963), 216–230. | DOI | MR | Zbl

[8] Skillings, J. H., Mack, G. A.: On the use of a Friedman–type statistic in balanced and unbalanced block designs. Technometrics 23 (1981), 171–177. | DOI | Zbl