Environmental and Ecological Statistics

, Volume 6, Issue 2, pp 105-118

First online:

Distribution-free ranked-set sample procedures for umbrella alternatives in the m-sample setting

  • Bradley A. HartlaubAffiliated withDepartment of Mathematics, Kenyon College
  • , Douglas A. WolfeAffiliated withDepartment of Statistics, The Ohio State University

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In settings where measurements are costly and/or difficult to obtain but ranking of the potential sample data is relatively easy and reliable, the use of statistical methods based on a ranked-set sampling approach can lead to substantial improvement over analogous methods associated with simple random samples. Previous nonparametric work in this area has been concentrated almost exclusively on the one- and two-sample location problems. In this paper we develop ranked-set sample procedures for the m-sample location setting where the treatment effect parameters follow a restricted umbrella pattern. Distribution-free testing procedures are developed for both the case where the peak of the umbrella is known and for the case where it is unknown. Small sample and asymptotic null distribution properties are provided for the peak-known test statistic.

distribution-free m-sample setting ranked-set sampling umbrella alternatives