preserve.
set printback=on.

* SIMPLE AND COMPLEX RANDOM ASSIGNMENT IN EXPERIMENTAL DESIGN (Version 2.0)
  Valentim R. Alferes, University of Coimbra (Portugal), 2014.

* WITHIN-SUBJECTS DESIGNS.
 
* Program: PC-Ls2345.sps
  Method 15: Positional Counterbalancing
  - Design 6M2: Repeated Measures Latin Square Design (t=2, n=2, p=2) 
  - Design 6M3: Repeated Measures Latin Square Design (t=3, n=3, p=3)
  - Design 6M4: Repeated Measures Latin Square Design (t=4, n=4, p=4) 
  - Design 6M5: Repeated Measures Latin Square Design (t=5, n=5, p=5) 
 
set printback=off.
set ovars labels onumbers values tvars labels tnumbers labels.
set olang=English small=0 errors=none decimal=dot.

/* User Specifications /*

* Enter the order (number of treatments) of the Latin square (2, 3, 4, or 5).
data list free/Order(f8.0).
begin data
5
end data.

set rng=mt mtindex=random.
if (order=2) rn=1.
if (order=3) rn=1.
if (order=4) rn=rnd(rv.uniform(.5,4.5)).
if (order=5) rn=rnd(rv.uniform(.5,56.5)).
execute.
save outfile='%temp%\fout0'.
new file.
data list free/Order(f8.0) Square(f8.0) Row(f8.0) Column_1(f8.0) 
Column_2(f8.0) Column_3(f8.0) Column_4(f8.0) Column_5(f8.0).
begin data
2 1 1 1 2 0 0 0 2 1 2 2 1 0 0 0 3 1 1 1 2 3 0 0 3 1 2 2 3 1 0 0 3 1 3 3 1
2 0 0 4 1 1 1 2 3 4 0 4 1 2 2 1 4 3 0 4 1 3 3 4 1 2 0 4 1 4 4 3 2 1 0 4 2
1 1 2 3 4 0 4 2 2 2 1 4 3 0 4 2 3 3 4 2 1 0 4 2 4 4 3 1 2 0 4 3 1 1 2 3 4
0 4 3 2 2 3 4 1 0 4 3 3 3 4 1 2 0 4 3 4 4 1 2 3 0 4 4 1 1 2 3 4 0 4 4 2 2
4 1 3 0 4 4 3 3 1 4 2 0 4 4 4 4 3 2 1 0 5 1 1 1 2 3 4 5 5 1 2 2 1 4 5 3 5
1 3 3 4 5 2 1 5 1 4 4 5 1 3 2 5 1 5 5 3 2 1 4 5 2 1 1 2 3 4 5 5 2 2 2 1 4
5 3 5 2 3 3 4 5 1 2 5 2 4 4 5 2 3 1 5 2 5 5 3 1 2 4 5 3 1 1 2 3 4 5 5 3 2
2 1 5 3 4 5 3 3 3 4 1 5 2 5 3 4 4 5 2 1 3 5 3 5 5 3 4 2 1 5 4 1 1 2 3 4 5
5 4 2 2 1 5 3 4 5 4 3 3 4 2 5 1 5 4 4 4 5 1 2 3 5 4 5 5 3 4 1 2 5 5 1 1 2
3 4 5 5 5 2 2 1 4 5 3 5 5 3 3 5 1 2 4 5 5 4 4 3 5 1 2 5 5 5 5 4 2 3 1 5 6
1 1 2 3 4 5 5 6 2 2 1 4 5 3 5 6 3 3 5 2 1 4 5 6 4 4 3 5 2 1 5 6 5 5 4 1 3
2 5 7 1 1 2 3 4 5 5 7 2 2 1 5 3 4 5 7 3 3 5 4 2 1 5 7 4 4 3 1 5 2 5 7 5 5
4 2 1 3 5 8 1 1 2 3 4 5 5 8 2 2 1 5 3 4 5 8 3 3 5 4 1 2 5 8 4 4 3 2 5 1 5
8 5 5 4 1 2 3 5 9 1 1 2 3 4 5 5 9 2 2 3 4 5 1 5 9 3 3 1 5 2 4 5 9 4 4 5 1
3 2 5 9 5 5 4 2 1 3 5 10 1 1 2 3 4 5 5 10 2 2 3 4 5 1 5 10 3 3 1 5 2 4 5 10 4
4 5 2 1 3 5 10 5 5 4 1 3 2 5 11 1 1 2 3 4 5 5 11 2 2 3 5 1 4 5 11 3 3 1 4 5 2
5 11 4 4 5 1 2 3 5 11 5 5 4 2 3 1 5 12 1 1 2 3 4 5 5 12 2 2 3 5 1 4 5 12 3 3 1
4 5 2 5 12 4 4 5 2 3 1 5 12 5 5 4 1 2 3 5 13 1 1 2 3 4 5 5 13 2 2 3 1 5 4 5 13
3 3 4 5 1 2 5 13 4 4 5 2 3 1 5 13 5 5 1 4 2 3 5 14 1 1 2 3 4 5 5 14 2 2 3 1 5
4 5 14 3 3 4 5 2 1 5 14 4 4 5 2 1 3 5 14 5 5 1 4 3 2 5 15 1 1 2 3 4 5 5 15 2 2
3 4 5 1 5 15 3 3 4 5 1 2 5 15 4 4 5 1 2 3 5 15 5 5 1 2 3 4 5 16 1 1 2 3 4 5 5
16 2 2 3 5 1 4 5 16 3 3 4 1 5 2 5 16 4 4 5 2 3 1 5 16 5 5 1 4 2 3 5 17 1 1 2 3
4 5 5 17 2 2 3 5 1 4 5 17 3 3 4 2 5 1 5 17 4 4 5 1 2 3 5 17 5 5 1 4 3 2 5 18 1
1 2 3 4 5 5 18 2 2 3 5 1 4 5 18 3 3 4 2 5 1 5 18 4 4 5 1 3 2 5 18 5 5 1 4 2 3
5 19 1 1 2 3 4 5 5 19 2 2 3 1 5 4 5 19 3 3 5 4 1 2 5 19 4 4 1 5 2 3 5 19 5 5 4
2 3 1 5 20 1 1 2 3 4 5 5 20 2 2 3 1 5 4 5 20 3 3 5 4 2 1 5 20 4 4 1 5 3 2 5 20
5 5 4 2 1 3 5 21 1 1 2 3 4 5 5 21 2 2 3 4 5 1 5 21 3 3 5 1 2 4 5 21 4 4 1 5 3
2 5 21 5 5 4 2 1 3 5 22 1 1 2 3 4 5 5 22 2 2 3 4 5 1 5 22 3 3 5 2 1 4 5 22 4 4
1 5 2 3 5 22 5 5 4 1 3 2 5 23 1 1 2 3 4 5 5 23 2 2 3 4 5 1 5 23 3 3 5 2 1 4 5
23 4 4 1 5 3 2 5 23 5 5 4 1 2 3 5 24 1 1 2 3 4 5 5 24 2 2 3 5 1 4 5 24 3 3 5 4
2 1 5 24 4 4 1 2 5 3 5 24 5 5 4 1 3 2 5 25 1 1 2 3 4 5 5 25 2 2 4 1 5 3 5 25 3
3 1 5 2 4 5 25 4 4 5 2 3 1 5 25 5 5 3 4 1 2 5 26 1 1 2 3 4 5 5 26 2 2 4 5 1 3
5 26 3 3 1 2 5 4 5 26 4 4 5 1 3 2 5 26 5 5 3 4 2 1 5 27 1 1 2 3 4 5 5 27 2 2 4
5 3 1 5 27 3 3 1 2 5 4 5 27 4 4 5 1 2 3 5 27 5 5 3 4 1 2 5 28 1 1 2 3 4 5 5 28
2 2 4 5 3 1 5 28 3 3 1 4 5 2 5 28 4 4 5 1 2 3 5 28 5 5 3 2 1 4 5 29 1 1 2 3 4
5 5 29 2 2 4 5 1 3 5 29 3 3 1 4 5 2 5 29 4 4 5 2 3 1 5 29 5 5 3 1 2 4 5 30 1 1
2 3 4 5 5 30 2 2 4 5 3 1 5 30 3 3 1 4 5 2 5 30 4 4 5 2 1 3 5 30 5 5 3 1 2 4 5
31 1 1 2 3 4 5 5 31 2 2 4 1 5 3 5 31 3 3 5 2 1 4 5 31 4 4 1 5 3 2 5 31 5 5 3 4
2 1 5 32 1 1 2 3 4 5 5 32 2 2 4 1 5 3 5 32 3 3 5 4 2 1 5 32 4 4 1 5 3 2 5 32 5
5 3 2 1 4 5 33 1 1 2 3 4 5 5 33 2 2 4 5 3 1 5 33 3 3 5 1 2 4 5 33 4 4 1 2 5 3
5 33 5 5 3 4 1 2 5 34 1 1 2 3 4 5 5 34 2 2 4 5 3 1 5 34 3 3 5 4 1 2 5 34 4 4 1
2 5 3 5 34 5 5 3 1 2 4 5 35 1 1 2 3 4 5 5 35 2 2 4 1 5 3 5 35 3 3 5 2 1 4 5 35
4 4 3 5 2 1 5 35 5 5 1 4 3 2 5 36 1 1 2 3 4 5 5 36 2 2 4 1 5 3 5 36 3 3 5 4 1
2 5 36 4 4 3 5 2 1 5 36 5 5 1 2 3 4 5 37 1 1 2 3 4 5 5 37 2 2 4 1 5 3 5 37 3 3
5 4 2 1 5 37 4 4 3 5 1 2 5 37 5 5 1 2 3 4 5 38 1 1 2 3 4 5 5 38 2 2 4 5 1 3 5
38 3 3 5 1 2 4 5 38 4 4 3 2 5 1 5 38 5 5 1 4 3 2 5 39 1 1 2 3 4 5 5 39 2 2 4 5
3 1 5 39 3 3 5 2 1 4 5 39 4 4 3 1 5 2 5 39 5 5 1 4 2 3 5 40 1 1 2 3 4 5 5 40 2
2 4 5 1 3 5 40 3 3 5 4 2 1 5 40 4 4 3 1 5 2 5 40 5 5 1 2 3 4 5 41 1 1 2 3 4 5
5 41 2 2 5 1 3 4 5 41 3 3 1 4 5 2 5 41 4 4 3 5 2 1 5 41 5 5 4 2 1 3 5 42 1 1 2
3 4 5 5 42 2 2 5 4 1 3 5 42 3 3 1 2 5 4 5 42 4 4 3 5 2 1 5 42 5 5 4 1 3 2 5 43
1 1 2 3 4 5 5 43 2 2 5 4 3 1 5 43 3 3 1 2 5 4 5 43 4 4 3 5 1 2 5 43 5 5 4 1 2
3 5 44 1 1 2 3 4 5 5 44 2 2 5 4 1 3 5 44 3 3 1 5 2 4 5 44 4 4 3 1 5 2 5 44 5 5
4 2 3 1 5 45 1 1 2 3 4 5 5 45 2 2 5 4 3 1 5 45 3 3 1 5 2 4 5 45 4 4 3 1 5 2 5
45 5 5 4 2 1 3 5 46 1 1 2 3 4 5 5 46 2 2 5 4 1 3 5 46 3 3 1 5 2 4 5 46 4 4 3 2
5 1 5 46 5 5 4 1 3 2 5 47 1 1 2 3 4 5 5 47 2 2 5 1 3 4 5 47 3 3 4 2 5 1 5 47 4
4 1 5 2 3 5 47 5 5 3 4 1 2 5 48 1 1 2 3 4 5 5 48 2 2 5 1 3 4 5 48 3 3 4 5 1 2
5 48 4 4 1 2 5 3 5 48 5 5 3 4 2 1 5 49 1 1 2 3 4 5 5 49 2 2 5 1 3 4 5 49 3 3 4
5 2 1 5 49 4 4 1 2 5 3 5 49 5 5 3 4 1 2 5 50 1 1 2 3 4 5 5 50 2 2 5 4 3 1 5 50
3 3 4 1 5 2 5 50 4 4 1 5 2 3 5 50 5 5 3 2 1 4 5 51 1 1 2 3 4 5 5 51 2 2 5 4 1
3 5 51 3 3 4 2 5 1 5 51 4 4 1 5 3 2 5 51 5 5 3 1 2 4 5 52 1 1 2 3 4 5 5 52 2 2
5 4 3 1 5 52 3 3 4 5 1 2 5 52 4 4 1 2 5 3 5 52 5 5 3 1 2 4 5 53 1 1 2 3 4 5 5
53 2 2 5 1 3 4 5 53 3 3 4 2 5 1 5 53 4 4 3 5 1 2 5 53 5 5 1 4 2 3 5 54 1 1 2 3
4 5 5 54 2 2 5 1 3 4 5 54 3 3 4 5 1 2 5 54 4 4 3 2 5 1 5 54 5 5 1 4 2 3 5 55 1
1 2 3 4 5 5 55 2 2 5 4 1 3 5 55 3 3 4 1 5 2 5 55 4 4 3 5 2 1 5 55 5 5 1 2 3 4
5 56 1 1 2 3 4 5 5 56 2 2 5 4 1 3 5 56 3 3 4 5 2 1 5 56 4 4 3 1 5 2 5 56 5 5 1
2 3 4
end data.
match files/file=*/table='%temp%\fout0'/by order.
execute.
sel if(rn=square).
execute.
delete variables rn.
set results=no.
flip variables=all.
set results=yes.
sel if(var001<>0).
execute.
set results=no.
flip variables=all/newname=case_lbl.
set results=yes.
delete variables case_lbl.
value labels all 1'A' 2'B' 3'C' 4'D' 5'E'.
value labels order square row -1'x'.
oms/select tables/if commands=["summarize"]
 subtypes=["case processing summary"]/destination viewer=no.
formats all(f8.0).
summarize/tables=all/format=list nocasenum nototal /cells=none
 /title='Square 1: Selected Standard Latin Square'/footnote
 'Order 2: There is only one standard Latin square\nOrder 3: There is '+
 'only one standard Latin square\nOrder 4: Random selection of one of '+
 'the 4 standard Latin squares\nOrder 5: Random selection of one of the '+
 '56 standard Latin squares'.
delete variables order square row.
set results=no.
flip variables=all.
set results=yes.
set rng=mt mtindex=random.
compute rn=rv.uniform(0,1).
execute.
compute permcols=$casenum.
execute.
sort cases by rn(a).
variable labels permcols'Permutation'.
formats permcols(f8.0).
summarize/tables=permcols/format=list nocasenum nototal
 /title='Random Permutation for the Columns of Square 1'/cells=none.
delete variables rn permcols.
set results=no.
flip variables=all/newname=case_lbl.
set results=yes.
delete variables case_lbl.
compute Row=$casenum.
execute.
value labels all 1'A' 2'B' 3'C' 4'D' 5'E'.
value labels row -1'x'.
formats all(f8.0).
summarize/tables=row all/format=list nocasenum nototal
 /title='Square 2: Random Permutation of Square 1 Columns'/cells=none.
compute rn=rv.uniform(0,1).
execute.
if($casenum=1) rn=0.
execute.
sort cases by rn(a).
compute permrows=row.
execute.
variable labels permrows'Permutation'.
value labels permrows 1'Fixed in 1st place'.
formats all(f8.0).
summarize/tables=permrows/format=list nocasenum nototal
 /title='Random Permutation for the n-1 Last Rows of Square 2'/cells=none.
delete variables rn permrows.
formats all(f8.0).
summarize/tables=row all/format=list nocasenum nototal
 /title='Square 3: Random Permutation of Square 2 Rows'/cells=none.
delete variables row.
set results=no.
flip variables=all.
set results=yes.
compute myname=$casenum.
execute.
string yourname(a8).
compute yourname='P_'.
execute.
string finalname(A8).
compute finalname=concat(rtrim(yourname),ltrim(string(myname,f5))).
execute.
delete variables case_lbl myname yourname.
set results=no.
flip all/newname=finalname.
set results=yes.
delete variables case_lbl.
value labels all 1'A' 2'B' 3'C' 4'D' 5'E'.
compute Unit=$casenum.
execute.
formats all(f8.0).
summarize/tables=unit all/format=list nocasenum nototal
/title='Final Randomization (Square 3)' /footnote 'P = Period. \n'+
 'If necessary, repeat the syntax for each new set of n units.'/cells=none.
save outfile='%userprofile%\desktop\FinalRandomization.sav'/keep unit all.
get file='%userprofile%\desktop\FinalRandomization.sav'.
erase file='%temp%\fout0'.
restore.