Multiple Comparison with a Control for One-Way layouts
Control-other comparisons with multiple-comparison correction
 
Numbers of glucocorticoid receptor sites per Leukocyte cell
  for controls and 4 types of leukemia/anemia
The first treatment (the control) are normal subjects.
Hollander & Wolfe (Table 6.4, p201)
See OneWayMultComp.txt for more detail and more analyses
 
Grp #1 (n=14) Normal subjects (Control)
Grp #2 (n= 5) Hairy-cell anemia
Grp #3 (n= 6) Chronic lymphatic leukemia
Grp #4 (n= 4) Chronic myelocytic leukemia
Grp #5 (n= 8) Acute leukemia
  
Data:
    Grp#1    Grp#2    Grp#3    Grp#4    Grp#5
     3500     5710     2930     6320     3230
     3500     6110     3330     6860     3880
     3500     8060     3580    11400     7640
     4000     8080     3880    14000     7890
     4000    11400     4280              8280
     4000              5120             16200
     4300                               18250
     4500                               29900
     4500                                    
     4900                                    
     5200                                    
     6000                                    
     6750                                    
     8000                                    
 
5 treatment groups with 37 total observations:
 
Sample means and rank means for treatment groups:
  #1 (n=14):  DataAv=  4760.71   RankAv= 14.43
  #2 (n= 5):  DataAv=  7872.00   RankAv= 26.70
  #3 (n= 6):  DataAv=  3853.33   RankAv=  8.42
  #4 (n= 4):  DataAv=  9645.00   RankAv= 28.63
  #5 (n= 8):  DataAv= 11908.75   RankAv= 25.31
 
See OneWayMultComp for a table of observations and midranks
  and for the Kruskal-Wallis test.
 
MULTIPLE COMPARISONS WITH A CONTROL:
Which of the k-1  non-control treatment groups are significantly
  LARGER than the control, allowing for multiple comparisons?
(We could also ask for significantly different in absolute value, or
  even significantly smaller, but here we consider significantly greater.)
See Section 6.7 in the text.
 
As in OneWayMultComp.m, we use normalized Wilcoxon rank-sum differences,
  and base a multiple-comparison-corrected P-value for treatment #i on
  the number of times that the maximum of treatments #j vs. control group
  normalized comparisons is LARGER THAN the observed treatment #i vs
  control comparison. Since this is a one-sided procedure, absolute
  values are not used.
NOTE THAT this is the method of Steel (1959) (text p259) and NOT
  the Nemenyi-Damico-Wolfe method discussed in most of Section 6.7.
 
For comparison, the following are MULTIPLE-COMPARISON-UNCORRECTED P-values.
One-way Wilcoxon W and Z values:
  #2 vs. #1:  W= 80.0  E(W)= 50.0  Z= 2.788   P=0.0026 (1-sided, UNCORR)
  #3 vs. #1:  W= 43.0  E(W)= 63.0  Z=-1.655   P=0.9511 (1-sided, UNCORR)
  #4 vs. #1:  W= 63.0  E(W)= 38.0  Z= 2.667   P=0.0038 (1-sided, UNCORR)
  #5 vs. #1:  W=121.0  E(W)= 92.0  Z= 1.984   P=0.0236 (1-sided, UNCORR)
Maximum observed Z-value:  2.7885
Note that 2 have P<0.01 and 1 more have P<0.05.
 
Simulating P-values for MULTIPLE-COMPARISON-CORRECTED comparisons
  for groups #2-#5 vs control:
 
Initializing the random-number generator at
    12345678

Number of permutations:
       10000

One-sided MULTIPLE-COMPARISON-CORRECTED P-values:
  #2 vs #1:  Z= 2.788  P=   53/10000 = 0.0053
  #3 vs #1:  Z=-1.655  P= 9995/10000 = 0.9995
  #4 vs #1:  Z= 2.667  P=   91/10000 = 0.0091
  #5 vs #1:  Z= 1.984  P=  775/10000 = 0.0775
Note that 2 have P<0.01 and 0 more have P<0.05.