Geodesic
On testing hypotheses in the generalized Skillings-Mack random blocks setting
Kybernetika, Tome 47 (2011) no. 5, pp. 657-677

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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.
Classification : 62G10
Keywords: rank test; random blocks; hypotheses testing; increasing treatment effect; asymptotic distribution 
@article{KYB_2011__47_5_a0,
     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},
     publisher = {mathdoc},
     volume = {47},
     number = {5},
     year = {2011},
     mrnumber = {2850455},
     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/