
PAGE TESTName:
The distinction between the Friedman test and the Page test is that the Page test is used when you want to test for ordered effects. By ordered effects, we mean that treatment 1 is less than or equal to treatment 2 which is less than or equal to treatment 3 and so on (and at least one of these should be strictly less than). As with the Friedman test, assumes that there are k experimental treatments (k >= 2). The observations are arranged in p blocks, that is
Let R(X_{ij}) be the rank assigned to X_{ij} within block i (i.e., ranks within a given row). Average ranks are used in the case of ties. The ranks are summed to obtain
Then the Page test is
where <y> is the response variable; <block> is a variable that identifies the block; <treat> is a variable that identifies the treatment; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
PAGE TEST Y X1 X2 PAGE TEST Y BLOCK TREATMENT SUBSET BLOCK > 2
If your data are in a format similar to that given in the DESCRIPTION section (i.e., you have colums Y_{1} to Y_{k}, each with b rows), you can convert it to the format required by Dataplot with the commands:
LET BLOCKID = SEQUENCE 1 1 NBLOCK LET Y BLOCK TREAT = REPLICATED STACK Y1 Y2 Y3 Y4 Y5 BLOCKID PAGE TEST Y BLOCK TREAT
LET A = PAGE TEST NORMALIZED Y X1 X2 LET A = PAGE TEST CDF Y X1 X2 LET A = PAGE TEST PVALUE Y X1 X2 The PAGE TEST returns the T4 value described above and the PAGE TEST NORMALIZED returns the T5 value described above. Enter HELP STATISTICS to see what commands can use these statistics.
. Test Page test as given in . Conover (1999), "Practical NonParametric Statistics" . Third Edition, pp. 380381. . read y treat block 79 1 1 78 1 2 72 1 3 66 1 4 75 1 5 64 1 6 68 1 7 70 1 8 76 2 1 76 2 2 74 2 3 65 2 4 75 2 5 66 2 6 70 2 7 72 2 8 77 3 1 76 3 2 77 3 3 68 3 4 72 3 5 65 3 6 68 3 7 78 3 8 84 4 1 80 4 2 78 4 3 72 4 4 74 4 5 69 4 6 74 4 7 76 4 8 82 5 1 80 5 2 75 5 3 65 5 4 77 5 5 68 5 6 70 5 7 77 5 8 end of data . let statval = page test y block treat let statva2 = page test normalized y block treat let cdf = page test cdf y block treat let pval = page test pvalue y block treat . set write decimals 4 page test y block treatThe following output is generated. PARAMETERS AND CONSTANTS STATVAL  401.5000 STATVA2  2.9345 CDF  0.9983 PVAL  0.0017 Page Two Factor Test Response Variable: Y GroupID Variable (Block): BLOCK GroupID Variable (Treatment): TREAT H0: u1 = u2 = ... = uk Ha: u1 <= u2 <= ... <= uk Summary Statistics: Total Number of Observations: 40 Number of Blocks: 8 Number of Treatments: 5 Test: Page Test Statistic: 401.5000 Page Normalized Test Statistic: 2.9344 CDF of Test Statistic: 0.9983 PValue: 0.0016 Percent Points of the Normal Reference Distribution  Percent Point Value  50.0 = 0.000 75.0 = 0.674 90.0 = 1.282 95.0 = 1.645 97.5 = 1.960 99.0 = 2.326 99.9 = 3.089 Conclusions (Upper 1Tailed Test)  Alpha CDF Critical Value Conclusion  10% 90% 1.282 Reject H0 5% 95% 1.645 Reject H0 2.5% 97.5% 1.960 Reject H0 1% 99% 2.326 Reject H0  
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Date created: 03/08/2013 