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Testing for differences between means with ordered hypotheses
Author(s) -
Macdonald Ranald R.,
Smith Philip T.
Publication year - 1983
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.2044-8317.1983.tb00763.x
Subject(s) - statistic , variance (accounting) , statistics , mathematics , statistical hypothesis testing , product (mathematics) , econometrics , computer science , geometry , accounting , business
A technique for incorporating an experimenter's predictions of orderings of the treatment means into an analysis of variance testing procedure is presented. The experimenter's predictions are assessed in terms of a statistic based on the ordering of the means (e.g. Kendall's tau). The product of the significances of this statistic and of F is used to obtain the significance level. In comparison with other approaches simulations show this to be the most appropriate technique where the experimenter can predict the order of the treatment means but wishes to have reasonable power even if the predicted ordering is wrong.