macro
circnorm r; 
    Label ID.

#Copyright © 20 November 2000 Mathews and Malnar All rights reserved
#Rev. 1.0 for Minitab V13.2 (Bek)
#Rev. 1.1 (PGM) extended line to last point plotted and minor modifications
#Rev. 1.2 (Bek) added a label subcommand for graphing routine, combined func.
#Rev. 1.3. (Bek) updated to Minitab V14

#This macro is used to construct a probability plot for circular
#normal data.  The macro input is one column containing the response
#and an optional ID column used in graphing. The 
#macro calculates the mid band percentiles and the corresponding zeta
#values. The probability plot shows the responses verses their zeta
#values and reference lines are drawn at some key percentage values. A
#best fit line passing through the origin is superimposed on the data.
#This macro may be altered to show the calculating columns, 
#otherwise there is only graphical output.     

#Mathews Malnar & Bailey, Inc.
#217 Third Street, Fairport Harbor, OH 44077
#(440)350-0911
#pmathews@apk.net

#MM&B offers a 20 page document describing the circular normal distribution
#and QC procedures for handling circular normal data. Training is also available.
#Call or email for details.

#This macro sould be copied into the Minitab source macros directory for
#immediate use, otherwise a change directory (cd) command will be needed.



#Example call:
#	mtb> %circnorm c1    #where, c1 is the column of responses.
#		Label c2.    #where, c2 is a column of labels
#Copy the following line, minus the leading #, to the command line:
#%circnorm c1
#    Label c2.

mcolumn r ID sortedr sortID index percent Zeta labels refperc sum abssum
mconstant NResp	slope xcoordin ycoordin		

let sum=sum(r)
let abssum=sum(abs(r))
If sum=abssum 			#tests for positive data values

     If Label
       sort r ID sortedr sortID
       Copy sortedr sortID sortedr sortID;
          Omit sortedr = '*'.
     Else
       sort r sortedr 
       Copy sortedr sortedr;
          Omit sortedr = '*'.
     Endif.                     #Label sorting routine

  let NResp=N(sortedr)
   set index
     1:NResp
     end. 

  let percent=(index-0.5)/NResp
  let Zeta=SQRT(-2*loge(1-percent))

  let slope=mean(sortedr)/mean(Zeta)	#slope of line through circular normal data

  set labels		#reference lines
    0.01
    0.10
    0.50
    0.90
    0.99
    end.

  let refperc=SQRT(-2*loge(1-labels))
  let refperc=ROUND(refperc,3)
  Text labels labels; 
      Maxwidth 80.
  let xcoordin=SQRT(-2*loge(1-percent(Nresp)))   #zeta for last point
    if xcoordin < 3.035
       let xcoordin=3.035   #set zeta to 99th percentile when there are few points
    endif
  let ycoordin=xcoordin*slope	#predicted response for last point at end of line

if Label                     #Plots data with IDs
Plot sortedr * Zeta;
  Scale 1;
    LDisplay 1 1 1 0;
    MODEL 1;
      Tick refperc;
      Min 0;
      Label labels;
    EndMODEL;
  Scale 2;
    LDisplay 1 1 1 0;
  AxLabel 1 "Probability";
    PSize 9;
  AxLabel 2 "Response";
    PSize 9;
  Grid 2;
  Data 0.1 0.9 0.1 0.9;
  NoJitter;
  Data 0.1 0.9 0.1 0.9;
  Symbol;
    Type 1;
    Color 16;
    Size 0.5;
  Datlab sortID;
    PSize 6;
    Placement -1 1;
    Offset 0 0.0125;
  Reference 1 refperc;
    Side 0;
    MODEL 1;
  Title "Circular Normal Probability Plot";
   Footnote &
      "Mathews and Malnar, November 2000";
    PSize 7;
  Footnote;
    FPanel;
  Line 0 0 xcoordin ycoordin;
    Color 2;
  NoDTitle.
else
Plot sortedr * Zeta;
  Scale 1;
    LDisplay 1 1 1 0;
    MODEL 1;
      Tick refperc;
      Min 0;
      Label labels;
    EndMODEL;
  Scale 2;
    LDisplay 1 1 1 0;
  AxLabel 1 "Probability";
    PSize 9;
  AxLabel 2 "Response";
    PSize 9;
  Grid 2;
  Data 0.1 0.9 0.1 0.9;
  NoJitter;
  Data 0.1 0.9 0.1 0.9;
  Symbol;
    Type 1;
    Color 16;
    Size 0.5;
  Reference 1 refperc;
    Side 0;
    MODEL 1;
  Title "Circular Normal Probability Plot";
   Footnote &
      "Mathews and Malnar, November 2000";
    PSize 7;
  Footnote;
    FPanel;
  Line 0 0 xcoordin ycoordin;
    Color 2;
  NoDTitle.
endif 

Else 		                 #when one or more data values are negative 
     Note 
     Note Circular normal data must all be postive.
     Note Please check data before running macro again.
  
endif.                   #ends main if statement 

endmacro.