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Determining whether an experimental group is stochastically larger than a control
Author(s) -
Wilcox Rand R.
Publication year - 1990
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1990.tb00944.x
Subject(s) - simple (philosophy) , group (periodic table) , mathematics , statistics , control (management) , function (biology) , subject (documents) , econometrics , computer science , artificial intelligence , physics , epistemology , philosophy , quantum mechanics , evolutionary biology , library science , biology
Let μ x and μ y be the means of a control and an experimental group, respectively. The usual method of comparing the two groups is in terms of μ x ‐μ y by testing H 0 :μ x = μ y . This approach might suffice when the corresponding distributions differ only in location. When the distributions differ in other respects, a shift function can be more informative. For example, it might be the case that the typical subjects who perform poorly under a standard method will, on the average, benefit from a new treatment, while the new treatment is actually detrimental for the typical subject who does well under the established procedure. Another possibility, which is illustrated in the paper, is that μ y >μ x might be true even though for most subjects the experimental group is detrimental. This paper describes a simple method for determining whether these situations have occurred.