
COCHRAN TESTName:
The Cochran test assumes that there are c experimental treatments (c >= 2). The observations are arranged in r blocks, that is
The Friedman test is the usual nonparametric test for this kind of design. The Cochran test is applied for the special case of a binary response variable (i.e., it can have only one of two possible outcomes). Then the Cochran test is
<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.
COCHRAN TEST Y X1 X2 COCHRAN 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 Y1 to Yc, each with r rows), you can convert it to the format required by Dataplot with the commands:
LET NBLOCK = SIZE Y1 LET NTOTAL = K*NBLOCK LET BLOCK = SEQUENCE 1 1 NBLOCK FOR I = 1 1 NTOT LET Y2 TREAT= STACK Y1 Y2 Y3 Y4 Y5 COCHRAN TEST Y2 BLOCK TREAT
. Following example from p. 253 of Conover READ Y1 Y2 Y3 1 1 1 1 1 1 0 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 1 0 1 0 1 1 1 1 1 1 END OF DATA LET N1 = SIZE Y1 LET NTOT = 3*N1 LET BLOCK = SEQUENCE 1 1 N1 FOR I = 1 1 NTOT LET Y TREAT = STACK Y1 Y2 Y3 COCHRAN Y BLOCK TREATThis example generates the following output Cochran Test for TwoWay Randomized Complete Block Designs (Dichotomous Data) 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: 36 Number of Blocks: 12 Number of Treatments: 3 Test: Cochran Test Statistic: 2.800000 CDF of Test Statistic: 0.7534030 PValue: 0.2465970 Percent Points of the ChiSquare Reference Distribution  Percent Point Value  0.0 = 0.000 50.0 = 1.386 75.0 = 2.773 90.0 = 4.605 95.0 = 5.991 97.5 = 7.378 99.0 = 9.210 99.9 = 13.816 Conclusions (Upper 1Tailed Test)  Alpha CDF Critical Value Conclusion  10% 90% 4.605 Accept H0 5% 95% 5.991 Accept H0 2.5% 97.5% 7.378 Accept H0 1% 99% 9.210 Accept H0  
Date created: 12/05/2005 Last updated: 12/11/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 