SOME NON-PARAMETRIC TESTS OF WHETHER THE LARGEST OBSERVATIONS OF A SET ARE TOO LARGE OR TO SMALL
Abstract
Considered is a large number n of observations which are statistically independent and drawn from continuous symmetrical populations. This paper presents some nonparametric tests of whether the r largest observations of the set are too large to be consistent with the hypothesis that these populations have a common median value. Tests of whether the r largest observations are to small to be consistent with this hypothesis are also considered. Here r is a given integer which is dependent of n. Subject to some weak restrictions, it is shown that the significance level of a test of the type presented tends to a value alpha as n increases. For no admissible value of n, however, does the significance level of this test exceed 2 alpha. If whether the largest observations are too large is considered, tests with values of a suitable for significance levels can be obtained for r > 4. Values of a suitable for significance levels can be obtained for any value of r if whether the largest observations are too small is investigated (n large).
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 27, 1950
- Accession Number
- AD0603814
Entities
People
- John E. Walsh
Organizations
- RAND Corporation