Illustration of nonparametric tests for two-way layouts
Friedman and Page tests.

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

The Friedman test for a two-way layout
Time for Rounding First Base under Three Different Strategies
Text (Hollander & Wolfe), Table 7.1, p2743 treatments, 22 subjects

The data with Friedman (within-block) ranks:
        Round Out     Narrow Angle  Wide Angle    
  1.    5.40 (1)      5.50 (2)      5.55 (3)      
  2.    5.85 (3)      5.70 (1)      5.75 (2)      
  3.    5.20 (1)      5.60 (3)      5.50 (2)      
  4.    5.55 (3)      5.50 (2)      5.40 (1)      
  5.    5.90 (3)      5.85 (2)      5.70 (1)      
  6.    5.45 (1)      5.55 (2)      5.60 (3)      
  7.    5.40 (2.5)    5.40 (2.5)    5.35 (1)      
  8.    5.45 (2)      5.50 (3)      5.35 (1)      
  9.    5.25 (3)      5.15 (2)      5.00 (1)      
 10.    5.85 (3)      5.80 (2)      5.70 (1)      
 11.    5.25 (3)      5.20 (2)      5.10 (1)      
 12.    5.65 (3)      5.55 (2)      5.45 (1)      
 13.    5.60 (3)      5.35 (1)      5.45 (2)      
 14.    5.05 (3)      5.00 (2)      4.95 (1)      
 15.    5.50 (2.5)    5.50 (2.5)    5.40 (1)      
 16.    5.45 (1)      5.55 (3)      5.50 (2)      
 17.    5.55 (2.5)    5.55 (2.5)    5.35 (1)      
 18.    5.45 (1)      5.50 (2)      5.55 (3)      
 19.    5.50 (3)      5.45 (2)      5.25 (1)      
 20.    5.65 (3)      5.60 (2)      5.40 (1)      
 21.    5.70 (3)      5.65 (2)      5.55 (1)      
 22.    6.30 (2.5)    6.30 (2.5)    6.25 (1)      

AvData:    5.54          5.53          5.46       
AvRanks:  (2.41)        (2.14)        (1.45)      

Friedman statistic S'=11.1429   P=0.0038 (2 df, 4 tiegroups)

Simulating the Friedman P-value using 100000 permutations:
  Friedman score (for simulations):  6042
  P = 345/100000 = 0.00345  95% CI (0.0031, 0.0034, 0.0038)

Large-sample approximation WITHOUT tie correction:
  S=10.6364   P=0.0049   (2 d.f.)

The Page (increasing alternative) test for a two-way layout
Cotton strength index as a function of potash in fertilizer
Text (Hollander & Wolfe), Table 7.5, p2865 treatments, 3 subjects

The data with Friedman (within-block) ranks:
        144#/acre     108#/acre     72#/acre      54#/acre      36#/acre      
  1.    7.46 (2)      7.17 (1)      7.76 (4)      8.14 (5)      7.63 (3)      
  2.    7.68 (2)      7.57 (1)      7.73 (3)      8.15 (5)      8.00 (4)      
  3.    7.31 (1)      7.80 (3)      7.74 (2)      7.87 (4)      7.93 (5)      

AvData:    7.48          7.51          7.74          8.05          7.85       
AvRanks:  (1.67)        (1.67)        (3.00)        (4.67)        (4.00)      

Page statistic L=158   E(L)=135   Z=2.65581   P=0.0079 (two-sided)
  Simulating the Page P-value using 100000 permutations:
    P = 490/100000 = 0.00490  95% CI (0.0045, 0.0049, 0.0053)

Random numbers used:  5,600,000