Illustration of Cochran test for two-way layouts
  with 0,1 (dichotomous) data

Success for four methods of soothing newborn babies
Source: Lehmann ``Nonparametrics: Statistical methods based on ranks''
  pages 267-270
See Lehmann p283 for the full data set.
k=4 treatment groups and n=12 subjects:

Starting random-number seed: 408408
(Enter a number on the command line to specify a different seed.)

Table of treatment group headings:
  WrmWa - WarmWater
  Rockg - Rocking
  Pacif - Pacifier
  Sound - Sound

Dichotomous data in a two-way layout:
     WrmWa  Rockg  Pacif  Sound  Block sum
  1.   0      0      0      0       0
  2.   0      1      0      0       1
  3.   0      0      1      0       1
  4.   0      0      0      0       0
  5.   1      1      1      1       4
  6.   0      1      1      1       3
  7.   1      1      0      0       2
  8.   0      1      0      1       2
  9.   0      1      1      1       3
 10.   0      0      1      0       1
 11.   1      1      0      1       3
 12.   1      1      1      1       4
Treatment group sums:
       4      8      6      6      24

Applying the Cochran test:
Treatment sums:  4  8  6  6  Total: 24
Block sums:  0  1  1  0  4  3  2  2  3  1  3  4
Cochran statistics:   L2sum=152   CC=3.69231
Large sample approximation:   C=3.69231   P=0.2967   df=3
Permutation test for L2sum=152
  using 100000 sets of within-block permutations:
  P = 33408/100000 = 0.3341   95% CI (0.331, 0.334, 0.337)

Apply the Friedman procedure as a comparison:

Data with Friedman (within-block) ranks:
        WarmWater     Rocking       Pacifier      Sound         
  1.       0  (2.5)      0  (2.5)      0  (2.5)      0  (2.5)   
  2.       0  (2)        1  (4)        0  (2)        0  (2)     
  3.       0  (2)        0  (2)        1  (4)        0  (2)     
  4.       0  (2.5)      0  (2.5)      0  (2.5)      0  (2.5)   
  5.       1  (2.5)      1  (2.5)      1  (2.5)      1  (2.5)   
  6.       0  (1)        1  (3)        1  (3)        1  (3)     
  7.       1  (3.5)      1  (3.5)      0  (1.5)      0  (1.5)   
  8.       0  (1.5)      1  (3.5)      0  (1.5)      1  (3.5)   
  9.       0  (1)        1  (3)        1  (3)        1  (3)     
 10.       0  (2)        0  (2)        1  (4)        0  (2)     
 11.       1  (3)        1  (3)        0  (1)        1  (3)     
 12.       1  (2.5)      1  (2.5)      1  (2.5)      1  (2.5)   
AvRanks:  (2.17)        (2.83)        (2.50)        (2.50)      

Carrying out classical Friedman test:
4 treatments, 12 subjects

Friedman statistic S'=3.69231   P=0.2967 (3 df, 14 tiegroups)
WITH NO TIE CORRECTION:
Friedman statistic S=1.60000   P=0.6594 (3 df)

Simulating the Friedman P-value using 100000 permutations:
  Friedman score (for simulations):  3632
  P = 33465/100000 = 0.3347   95% CI (0.332, 0.335, 0.338)

Random numbers used:  7,200,000