1989 | OriginalPaper | Buchkapitel
The hypothesis of symmetry
verfasst von : Prof. Dr. rer. nat. Konrad Behnen, Prof. Dr. rer. nat. Georg Neuhaus
Erschienen in: Rank Tests with Estimated Scores and Their Application
Verlag: Vieweg+Teubner Verlag
Enthalten in: Professional Book Archive
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As in Chapter 3 the basic problem is the comparison of a new treatment with a standard, but in contrast to Chapter 3 we don’t have two independent samples. Usually we have paired observations (Y i , Z i ), i = 1,..., n, where the Y-components are the measurements under the standard treatment whereas the Z -components are the measurements under the new treatment. It’s assumed that the design of the experiment allows the pairs (Y1, Z1),..., (Y n , Z n ) to be independent random variables with values in ℝ2. It’s not realistic to assume the stochastic independence of the components Y i and Z i , since the Y i -measurement and the Z i -measurement are usually taken at matched pairs or even at the same experimental unit, e.g. left-right treatments or pre-post treatments, but we assume the differences Z1 - Y1,..., Z n - Y n to be i.i.d. random variables.