Illustration of Friedman and Aligned-Rank tests for two-way layouts
(Page test included for completeness)

Amounts of physical responses to suggestion under hypnosis as measured
  by electrical skin potential in millivolts
Source:  Lehmann, ``Nonparametrics: Statistical Methods Based on Ranks''
  page 264 (see also pp264-271)
k=4 treatment groups and n=8 subjects:

Starting random-number seed: 123456
(Enter a number on the command line to specify a different seed.)

Data with Friedman (within-block) ranks:
        Fear          Happiness     Depression    Calmness      
  1.    23.1  (4)     22.7  (3)     22.5  (1)     22.6  (2)  
  2.    57.6  (4)     53.2  (2)     53.7  (3)     53.1  (1)  
  3.    10.5  (3)      9.7  (2)     10.8  (4)      8.3  (1)  
  4.    23.6  (4)     19.6  (1)     21.1  (2)     21.6  (3)  
  5.    11.9  (1)     13.8  (4)     13.7  (3)     13.3  (2)  
  6.    54.6  (4)     47.1  (3)     39.2  (2)     37.0  (1)  
  7.    21.0  (4)     13.6  (1)     13.7  (2)     14.8  (3)  
  8.    20.3  (3)     23.6  (4)     16.3  (2)     14.8  (1)  
AvRanks:    (3.38)        (2.50)        (2.38)        (1.75)      

Carrying out classical Friedman test:
4 treatments, 8 subjects

Friedman statistic S'=6.45000   P=0.0917 (3 df, 0 tiegroups)

Simulating the Friedman P-value using 100000 permutations:
  Friedman score (for simulations):  1686
  P = 9509/100000 = 0.0951   95% CI (0.093, 0.095, 0.097)

The Page test:
4 treatments, 8 subjects
Page statistic L=180   E(L)=200   Centered=20
  Z=-2.44949   P=0.0143 (two-sided)
  Simulating the Page P-value using 100000 permutations
  based on two-sided Page score: 20
    P = 1498/100000 = 0.01498   95% CI (0.0142, 0.0150, 0.0157)

Data centered at block means with Kruskal-Wallis ranks:
        Fear           Happiness      Depression     Calmness       
  1.     0.38  (21)    -0.03  (18)    -0.23  (15)    -0.13  (16.5)  
  2.     3.20  (29)    -1.20  (11)    -0.70  (13)    -1.30  (9)     
  3.     0.68  (24)    -0.13  (16.5)   0.98  (25)    -1.52  (8)     
  4.     2.13  (27)    -1.88  (7)     -0.38  (14)     0.13  (19.5)  
  5.    -1.28  (10)     0.63  (23)     0.52  (22)     0.13  (19.5)  
  6.    10.13  (32)     2.63  (28)    -5.27  (2)     -7.48  (1)     
  7.     5.23  (31)    -2.17  (5)     -2.07  (6)     -0.97  (12)    
  8.     1.55  (26)     4.85  (30)    -2.45  (4)     -3.95  (3)     
AvRanks:    (25.00)       (17.31)       (12.63)       (11.06)     

Lehmann statistic Q=8.52954   P=0.03625 (3 df, 2 tiegroups)
  Lehmann score for permutations:  77215.5
  Simulating the aligned-rank P-value using 100000 permutations:
    P = 2344/100000 = 0.0234   95% CI (0.0225, 0.0234, 0.0244)

Random numbers used:  7,200,000