Publication Date


Document Type


First Advisor

Laud, Purushottam, 1948-

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mathematical Sciences


Statistics; Scale analysis (Psychology)


In this thesis several two-sample and multisample nonparametric tests £or scale with both known and unknown location parameters are reviewed. A nonparametric multiple comparison test for differences in location is also studied. A new nonparametric multiple comparison test for differences in scale parameters is suggested. Its small sample and asymptotic properties are investigated. The test suggested is a modification of a nonparametric multiple comparison test for differences in location. The test is distribution- free and has reasonable power for small samples. The asymptotic distribution of the test statistic is that of the minimum of the components of a multivariate normal vector. Modifications of the test when the location parameters are unknown and unequal are suggested. This modified test is not asymptotically distribution-free for all underlying location-scale parameter families. However, we give sufficient conditions on the families under which the test is asymptotically distribution-free.


Includes bibliographical references.


57 pages




Northern Illinois University

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