Nonparametric one-way layouts:
Kruskal-Wallis, Jonckheere-Terpstra, and multiple comparison tests.

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

The data:
Number of treatments: 3    Total number of observations: 15
Trtment #1 (n=5):     53     31    139      5     16
Trtment #2 (n=5):     75     64    205     97    139
Trtment #3 (n=5):     54    139    194   1253    275

Data with midranks (RA=Rank-Average of treatment group):
 #1 (RA= 4.0):    53( 4.0)   31( 3.0)  139(10.0)    5( 1.0)   16( 2.0)
 #2 (RA= 8.8):    75( 7.0)   64( 6.0)  205(13.0)   97( 8.0)  139(10.0)
 #3 (RA=11.2):    54( 5.0)  139(10.0)  194(12.0) 1253(15.0)  275(14.0)

Carrying out the Kruskal-Wallis test:

Recall that for the Kruskal-Wallis test:
  H = (12/(N*(N+1)))*Sum n_i*(RankAverage - (N+1)/2)^2
    (with no tie correction)
  HPrime = Hstat WITH tie correction.
Here:
  Rank-Average=8.0  (Ntot=15, ntreatments=3)
  H(Prime)=6.76835   Tiesum=24   Tiecorr=0.992857   H(NoCorr)=6.72
  Large-sample Chisquare approx.:  P=0.0339 (HP=6.76835, df=2)
  Without the tie correction:      P=0.0347 (H=6.72,  df=2)

Now SIMULATING the exact P-value of the Kruskal-Wallis test:
  Hobs = Sum RankSum_i^2/n_i = 1094.4

Simulating the true KW P-value with n=1000 permutations:
  P = 25/1000 = 0.0250   95% CI: (0.0153, 0.0347)

Simulating the true KW P-value with n=10000 permutations:
  P = 238/10,000 = 0.0238   95% CI: (0.0208, 0.0268)

Simulating the true KW P-value with n=100000 permutations:
  P = 2472/100,000 = 0.0247   95% CI: (0.0238, 0.0257)

Are the treatment groups increasing in treatment-group order?
Carry out the Jonckheere-Terpstra test to find out:

Statistic J=62.5   Min: 0.00  Mean: 37.50  Max: 75.00
  J = 62.5   E(J)=37.5   Var(J)=89.5833 (NOT tie-corrected)
  J = 62.5   E(J)=37.5   Var(J)=88.8919 (tie-corrected)
  Large-sample approximation:  Z=2.6516  P=0.00801 (2-sided, T.C.)

Now SIMULATING the exact P-value of the Jonckheere-Terpstra test:

Simulating the true JT P-value (n=100000 simulations, Jscore=25.0):
  P = 586/100,000 = 0.00586   95% CI: (0.00539, 0.00633) (2-sided)

Random numbers used:  2,954,000