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Methods for incorporating ordinal information into analysis of variance: Generalizations of one‐tail tests
Author(s) -
Smith Philip T.,
Macdonald Ranald R.
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.tb00762.x
Subject(s) - ordinal data , statistics , mathematics , ordinal regression , variance (accounting) , econometrics , accounting , business
Methods for incorporating ordinal assumptions into the analysis of the means of k treatments ( k > 2) are critically reviewed. These methods are examined under three headings: (1) Global : statistics that give an overall assessment of the presence of a trend in the data (e.g. linear and isotonic regression); (2) Multiple comparisons : statistics based on the repetition (explicit or implicit) of comparisons between pairs of treatments; (3) Joint probability : two statistics are computed, one giving an overall assessment of the differences between the means, the other assessing the specifically ordinal information in the data; the joint significance level of these two statistics is then determined. Numerical examples of all the methods are provided.