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for significance at the 0.05 level, one-tailed, with three conditions, are 56 for 4 subjects (the lowest number that is capable of giving a significant result at this level), 54 for 5 subjects, 91 for 7 subjects, 128 for 10 subjects, 190 for 15 subjects and 251 for 20 subjects..
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For example, a number of subjects might each be given three trials at the same task, and we predict that performance will improve from trial to trial. A test of the significance of the trend between conditions in this situation was developed by
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against the alternative that there is a difference in trend. Friedman's test considers the alternative hypothesis that the central tendencies of the observations under the
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If a measure of the overall correlation between the conditions and the data is required, it can be calculated as
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The Page test is most often used with fairly small numbers of conditions and subjects. The minimum values of
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Page, E. B. (1963). "Ordered hypotheses for multiple treatments: A significance test for linear ranks".
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a number of subjects (or other randomly sampled entities) are all observed in each of them, and
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conditions in the order implied by the alternative hypothesis, and assign each of them a rank
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for multiple comparisons between ordered correlated variables is the counterpart of
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which summarizes the association of continuous variables. It is also known as
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Jonckheere, A. R. (1954). "A test of significance for the relation between
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483:{\displaystyle {(12L-3kn(n+1)^{2})^{2} \over kn^{2}(n^{2}-1)(n+1)}}
242:{\displaystyle m_{1}<m_{2}<m_{3}<\cdots <m_{n}.\,}
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we predict that the observations will have a particular order.
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conditions are different without specifying their order.
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To test whether there is a significant trend, values of
555:= 1, this reduces to the familiar Spearman coefficient.
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and add all the products together; this sum is called
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674:(2nd ed.). Boston: PWS-Kent. pp. 279–284.
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can be compared with those tabulated by Page (1963).
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594:Journal of the American Statistical Association
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637:British Journal of Statistical Psychology
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668:"Page's test for ordered alternatives"
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22:Page test
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575:(1954).
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