Supplementary Exercise 3.40 of IPS7e 
------------------------------------

We first describe how to carry out the blocking and randomization using Table A 
in PSLS (or Table B in IPS), starting from line 125, say. To begin with, sort the 
subjects by (increasing) weight and divide them in blocks of four (see list below). 
Then WITHIN each block, select from Table A the digits 1-4 in random order. The first 
digit selected receives treatment A, the second treatment B, the third treatment
C and the final treatment D (without selecting the digit). For example, the first
three useable digits in line 125 are 4-1-2. This produces the treatment
allocation shown below. See below for another way of using the digits in the table.

     name       excw    block  treatment
  1  Williams     22      1       B
  2  Festinger    24      1       C
  3  Hernandez    25      1       D
  4  Moses        25      1       A
  5  Santiago     27      2       A
  6  Kendall      28      2       D
  7  Mann         28      2       C
  8  Smith        29      2       B
  9  Brunk        30      3       C
 10  Obrach       30      3       A
 11  Rodriguez    30      3       B
 12  Loren        32      3       D
 13  Jackson      33      4       A
 14  Stall        33      4       C
 15  Brown        34      4       D
 16  Dixon        34      4       B
 17  Birnbaum     35      5       B
 18  Tran         35      5       C
 19  Nevesky      39      5       A
 20  Wilansky     42      5       D

Note: It would be equally valid to use Table A in a different way by
letting the first digit 1-4 encountered correspond to the treatment for
the first subject (1~A, 2~B, 3~C, 4~D), the second digit encountered
correspond to the treatment for the second subject, and so on. For the
first block this would give (starting from line 125):

      subject        init weight  block  treatment

   1  Williams             22      1         D
   2  Festinger            24      1         A
   3  Hernandez            25      1         B
   4  Moses                25      1         C

Next, we give Minitab commands and output:

 WOpen "R:\Chapter 3\ex03_040.mtw".

 Sort;
   By 'excw';
   Original.
 Name c3 "block"
 Set 'block'
   1( 1 : 5 / 1 )4
   End.

Three approaches are discussed. The first and simplest one splits the
worksheet into separate worksheets for each block. Then the random
assignment to treatments will take place in each worksheet, using
methods for reordering values in a column. This approach is a bit
clumsy, by giving us 5 new worksheets when we would probably be happy
with a single one. The Minitab command for splitting worksheets is 
in the Data menu; further details are left for the interested student.

The second method is similar but all operations are done within the 
a single worksheet (for simplicity, we will do this in a new worksheet,
but it could also be done within the original worksheet). We need to 
"unstack" the column of (sorted) names by blocks to give us 5 columns 
of names (one for each block). Each of these 5 columns can then be 
reordered randomly, and afterwards the letters A, B, C and D can be 
assigned from top to bottom.

 Unstack ('name');
   Subscripts 'block';
   NewWS;
   VarNames.

 Base 140906.
 Sample 4 'name_1' 'name_1'.
 Sample 4 'name_2' 'name_2'.
 Sample 4 'name_3' 'name_3'.
 Sample 4 'name_4' 'name_4'.
 Sample 4 'name_5' 'name_5'.

 Name c9 "treatment"
 TSet 'treatment'
   1(  "A" "B" "C" "D" )1
   End.
 Print 'name_1'-'treatment'.

Data Display 

Row  name_1     name_2    name_3     name_4   name_5    treatment
  1  Williams   Mann      Loren      Stall    Wilansky  A
  2  Hernandez  Santiago  Brunk      Brown    Tran      B
  3  Festinger  Smith     Rodriguez  Jackson  Birnbaum  C
  4  Moses      Kendall   Obrach     Dixon    Nevesky   D


The third method version is simpler to carry out but perhaps more difficult to follow.
We use a single column of random numbers to generate a random order of the
subjects, and we achieve this random order WITHIN blocks by sorting by the
random numbers within each block.

Results for: ex03_040.mtw
 Base 140906.
 Name c4 "random"
 Random 20 'random';
   Uniform 0.0 1.0.
 Sort;
   By 'block' 'random';
   After.
 Name c9 "treatment"
 TSet 'treatment'
   5(  "A" "B" "C" "D" )1
   End.
 Print 'name'-'treatment'.

Data Display 
                                                    Sorted  Sorted    Sorted
Row  name       excw  block    random  Sorted name    excw   block    random  treatment
  1  Williams     22      1  0.095396  Williams         22       1  0.095396  A
  2  Festinger    24      1  0.711095  Moses            25       1  0.374238  B
  3  Hernandez    25      1  0.837232  Festinger        24       1  0.711095  C
  4  Moses        25      1  0.374238  Hernandez        25       1  0.837232  D
  5  Santiago     27      2  0.599327  Smith            29       2  0.061293  A
  6  Kendall      28      2  0.135048  Kendall          28       2  0.135048  B
  7  Mann         28      2  0.433419  Mann             28       2  0.433419  C
  8  Smith        29      2  0.061293  Santiago         27       2  0.599327  D
  9  Brunk        30      3  0.845573  Obrach           30       3  0.080645  A
 10  Obrach       30      3  0.080645  Rodriguez        30       3  0.207099  B
 11  Rodriguez    30      3  0.207099  Brunk            30       3  0.845573  C
 12  Loren        32      3  0.907534  Loren            32       3  0.907534  D
 13  Jackson      33      4  0.453547  Brown            34       4  0.193934  A
 14  Stall        33      4  0.855887  Jackson          33       4  0.453547  B
 15  Brown        34      4  0.193934  Stall            33       4  0.855887  C
 16  Dixon        34      4  0.989148  Dixon            34       4  0.989148  D
 17  Birnbaum     35      5  0.849369  Nevesky          39       5  0.302916  A
 18  Tran         35      5  0.457210  Tran             35       5  0.457210  B
 19  Nevesky      39      5  0.302916  Birnbaum         35       5  0.849369  C
 20  Wilansky     42      5  0.917628  Wilansky         42       5  0.917628  D