K-Sample Rank Tests for Umbrella Alternatives
- 1 March 1981
- journal article
- research article
- Published by Taylor & Francis in Journal of the American Statistical Association
- Vol. 76 (373) , 175-181
- https://doi.org/10.1080/01621459.1981.10477625
Abstract
Distribution-free test procedures are proposed for the k-sample problem, where the alternatives of interest are of the form F 1 (x) ≥ ··· ≥ Fℓ(x) ≤ ··· ≤ Fk (x) for all x, with at least one strict inequality. These are referred to as umbrella alternatives, and both the ℓ (point of umbrella) known and ℓ unknown settings are considered. Small sample null distributions are discussed, and the results of a Monte Carlo power study are presented. A detailed example illustrating the use of the unknown umbrella point procedure is also given.Keywords
This publication has 9 references indexed in Scilit:
- k‐sample rank tests using pair‐specific scoring functionsThe Canadian Journal of Statistics / La Revue Canadienne de Statistique, 1977
- On Jonckheere's k-Sample Test Against Ordered AlternativesTechnometrics, 1971
- A revised deterioration formula for the wechsler adult intelligence scaleJournal of Clinical Psychology, 1966
- Some distribution‐freeK‐sample rank tests of homogeneity against ordered alternativesCommunications on Pure and Applied Mathematics, 1965
- Asymptotic Efficiency of a Class of $c$-Sample TestsThe Annals of Mathematical Statistics, 1964
- Asymptotic Behavior of Some Rank Tests for Analysis of VarianceThe Annals of Mathematical Statistics, 1954
- A DISTRIBUTION-FREE k-SAMPLE TEST AGAINST ORDERED ALTERNATIVESBiometrika, 1954
- Use of Ranks in One-Criterion Variance AnalysisJournal of the American Statistical Association, 1952
- The asymptotic normality and consistency of kendall’s test against trend, when ties are present in one rankingIndagationes Mathematicae, 1952