## Compute Mann-Whitney statistics for the Voter Performance Protocol

   ## Fill in CURRENT results for the calibration system - must be at least 100 entries.
   ## Valid values are 0 thru 28.  These arrays don't really need to be sorted, BTW.

   @cur_val = (

## Example of how to enter the CURRENT results: 
      28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,
      28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,
      28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,27,27,27,27,
      27,26,26,26,26,26,26,26,26,26,22,22,22,22,22,22,21,21,21,21,
      20,20,20,20,20,20,20,20,19,19,18,16,16,16,16,16,16,16,11, 9,
       9, 2

   );


   @nom_val = (

## Example of how to enter the NOMINAL results: 
## The following numbers are fictitious examples for imaginary calibration systems

## Nominal values for System X
       28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,
       28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,
       28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,
       28,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,
       27,27,27,26,26,26,26,26,24,24,24,23,23,23,23,22,20,16,14,11

## Nominal values for System Y - commented out
##        28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,
##        28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,
##        28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,27,27,27,
##        27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,26,26,26,26,
##        26,25,25,25,24,23,23,23,23,22,22,20,20,20,20,15,14,13,13,02

   );

   $nom_size = scalar (@nom_val);
   $cur_size = scalar (@cur_val);

   print "\n#Nominal values = $nom_size; #Current values = $cur_size; \n";

   print "\nWARNING: Array of current values has < 100 entries. \n"
      if ($cur_size < 100);

   print "\nWARNING: Array of nominal values has < 100 entries. \n"
      if ($nom_size < 100);

   # Compute U statistic
   $U = 0;
   foreach $this_nom (@nom_val)
   {
      die "\nERROR: Nominal value not in 0-28 range: $this_nom \n"
	  if ($this_nom < 0 || $this_nom > 28);

   foreach $this_cur (@cur_val)
   {
      die "\nERROR: Current value not in 0-28 range: $this_cur \n"
	  if ($this_cur < 0 || $this_cur > 28);

      if ($this_cur < $this_nom)
      {  $U += 1;
      }
      elsif ($this_cur == $this_nom)
      {  $U += 0.5;
      }
   }
   }

   # mean and Std. deviation for U
   $U_mean    = $nom_size * $cur_size / 2;
   $U_std_dev = sqrt ($nom_size * $cur_size * ($nom_size + $cur_size + 1) / 12);

   $z = ($U - $U_mean) / $U_std_dev;

   printf "U = %8.1f; z-score = %8.4f \n", $U, $z;
   ## printf "U_mean = %8.3f; U_std_dev = %8.3f \n\n", $U_mean, $U_std_dev;

   $signif_95 = 1.96;   # set for 95% confidence

   if ($z > 0 - $signif_95 && $z < $signif_95)
   {  print "Z-score is within 95% confidence interval; test is valid. \n";
   }
   else
   {  print "Z-score is outside 95% confidence interval; test is invalid. \n";
   }