One-Way Layouts:
Kruskal-Wallis test for equality of location parameters
  Model:  X(i,j) dist X + theta_i ---  Test H_0: Theta are identical
  
Example 1:
Treatment #1: Control   #2: Obstruc.Air.Disease   #3: Asbestosis
Values relate to efficiency of ciliary dust clearance.
Table 6.1 in text page 192
 
Data in 3 treatment groups with sizes 5,4,5
 
  Trtment #1 (n=5)   2.9  3.0  2.5  2.6  3.2
  Trtment #2 (n=4)   3.8  2.7  4.0  2.4
  Trtment #3 (n=5)   2.8  3.4  3.7  2.2  2.0
 
Number of treatment groups and total number of observations:
 
     3    14

Assemble in a vertical array for analysis:
(Columns are Ordinal, Value, Treatment group, Midrank, Tiegroups
    1  2.90   1    8.0   0
    2  3.00   1    9.0   0
    3  2.50   1    4.0   0
    4  2.60   1    5.0   0
    5  3.20   1   10.0   0
    6  3.80   2   13.0   0
    7  2.70   2    6.0   0
    8  4.00   2   14.0   0
    9  2.40   2    3.0   0
   10  2.80   3    7.0   0
   11  3.40   3   11.0   0
   12  3.70   3   12.0   0
   13  2.20   3    2.0   0
   14  2.00   3    1.0   0
 
Parallel display with midranks:
   2.9 ( 8.0)    3.8 (13.0)    2.8 ( 7.0)
   3.0 ( 9.0)    2.7 ( 6.0)    3.4 (11.0)
   2.5 ( 4.0)    4.0 (14.0)    3.7 (12.0)
   2.6 ( 5.0)    2.4 ( 3.0)    2.2 ( 2.0)
   3.2 (10.0)                  2.0 ( 1.0)
 
By Treatment Group: Number, Rank Sum, Rank Average:
  Group #1  n=5   36.0   7.20
  Group #2  n=4   36.0   9.00
  Group #3  n=5   33.0   6.60

Kruskal-Wallis statistic:  H = 0.771429
 
Large-sample chi-square approximation for H:
No ties, so no tie correction needed

  P= 0.6800  (df=2)
 
Doing nsims simulations for the true P-value

nsims =

       10000

Initializing the RNG from the system clock at

startseed =

  2.0843e+005


H_and_Hscore =

    0.7714  801.0000

Number of simulations with values >= Hscore and total number:
 
        7122       10000

95% CI for true P-value bracketing estimate of true pvalue:
(Since H and Hscore >= 0, P-values are inherently two-sided.)
 
    0.7033    0.7122    0.7211

 
Test for an alternative of monotonic treatment-group medians:
The Jonckheere-Terpstra test statistic is very similar to
  the Kendall nonparametric correlation statistic between
  values and treatment-group numbers

jj =

    30

The Jonckheere-Terpstra test statistic mean, variance,
  Z-statistic, and one-sided normal P-value (assuming no ties):

Jmean_Jvar_Zval_NormPval =

   32.5000   72.9167   -0.2928    0.3848