
FRIEDMAN TESTName:
The Friedman test assumes that there are k experimental treatments (k ≥ 2). The observations are arranged in b 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 Friedman test is
If the hypothesis of identical treatment effects is rejected, it is often desirable to determine which treatments are different (i.e., multiple comparisons). Treatments i and j are considered different if
<SUBSET/EXCEPT/FOR qualification> 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.
FRIEDMAN TEST Y X1 X2 FRIEDMAN 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 FRIEDMAN TEST Y BLOCK TREAT
The treatment ranks and multiple comparisons are written to the file dpst2f.dat in the current directory. Comparisons that are statistically significant at the 95% level are flagged with a single asterisk while comparisons that are statistically significant at the 99% level are flagged with two asterisks.
LET A = FRIEDMAN TEST CDF Y X1 X2 LET A = FRIEDMAN TEST PVALUE Y X1 X2 Enter HELP STATISTICS to see what commands can use these statistics.
2011/4: Reformatted Output SKIP 25 READ FRIEDMAN.DAT Y BLOCK TREAT SET WRITE DECIMALS 5 FRIEDMAN Y BLOCK TREATThe following output is generated. Friedman Two Factor Test Response Variable: Y First GroupID Variable: BLOCK Second GroupID Variable: TREAT H0: Treatments Have Identical Effects Ha: Treatments Do Not Have Identical Effects Summary Statistics: Total Number of Observations: 48 Number of Blocks: 12 Number of Treatments: 4 Test: Friedman Test Statistic (Original): 8.09734 Sum of Squares of Ranks (A1): 356.50000 Correction Factor (C1): 300.00000 Friedman Test Statistic (Conover): 3.19219 CDF of Test Statistic: 0.96378 PValue: 0.03621 Percent Points of the F Reference Distribution  Percent Point Value  0.0 = 0.000 50.0 = 0.805 75.0 = 1.435 90.0 = 2.258 95.0 = 2.891 97.5 = 3.543 99.0 = 4.437 99.9 = 6.883 Conclusions (Upper 1Tailed Test)  Alpha CDF Critical Value Conclusion  10% 90% 2.258 Reject H0 5% 95% 2.891 Reject H0 2.5% 97.5% 3.543 Accept H0 1% 99% 4.437 Accept H0  
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Date created: 2/3/2004 