# The LearningOnline Network with CAPA
# (Publication Handler
#
# $Id: lonproblemstatistics.pm,v 1.25 2002/08/14 16:18:55 stredwic Exp $
#
# Copyright Michigan State University Board of Trustees
#
# This file is part of the LearningOnline Network with CAPA (LON-CAPA).
#
# LON-CAPA is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# LON-CAPA is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with LON-CAPA; if not, write to the Free Software
# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
#
# /home/httpd/html/adm/gpl.txt
#
# http://www.lon-capa.org/
#
# (Navigate problems for statistical reports
# YEAR=2001
# 5/5,7/9,7/25/1,8/11,9/13,9/26,10/5,10/9,10/22,10/26 Behrouz Minaei
# 11/1,11/4,11/16,12/14,12/16,12/18,12/20,12/31 Behrouz Minaei
# YEAR=2002
# 1/22,2/1,2/6,2/25,3/2,3/6,3/17,3/21,3/22,3/26,4/7,5/6 Behrouz Minaei
# 5/12,5/14,5/15,5/19,5/26,7/16,7/25,7/29,8/5  Behrouz Minaei
#
###

package Apache::lonproblemstatistics; 

use strict;
use Apache::lonnet();
use Apache::lonhtmlcommon;
use Apache::loncoursedata;
use GDBM_File;

my $jr;

sub BuildProblemStatisticsPage {
    my ($cacheDB, $students, $courseID, $c, $r)=@_;
    my %cache;

    $jr = $r;

    unless(tie(%cache,'GDBM_File',$cacheDB,&GDBM_READER(),0640)) {
        $r->print('Unable to tie database.');
        return;
    }

    # Remove students who don't have the proper section.
    my @sectionsSelected = split(':',$cache{'sectionsSelected'});
    for(my $studentIndex=((scalar @$students)-1); $studentIndex>=0;
        $studentIndex--) {
        my $value = $cache{$students->[$studentIndex].':section'};
        my $found = 0;
        foreach (@sectionsSelected) {
            if($_ eq 'none') {
                if($value eq '' || !defined($value) || $value eq ' ') {
                    $found = 1;
                    last;
                }
            } else {
                if($value eq $_) {
                    $found = 1;
                    last;
                }
            }
        }
        if($found == 0) {
            splice(@$students, $studentIndex, 1);
        }
    }

    my $Ptr = '';
    $Ptr .= '<table border="0"><tbody>';
    $Ptr .= '<tr><td align="right"><b>Select Map</b></td>'."\n";
    $Ptr .= '<td align="left">';
    $Ptr .= &Apache::lonhtmlcommon::MapOptions(\%cache, 'ProblemStatistics',
                                               'Statistics');
    $Ptr .= '</td></tr>'."\n";
    $Ptr .= '<tr><td align="right"><b>Sorting Type:</b></td>'."\n";
    $Ptr .= '<td align="left">'."\n";
    $Ptr .= &Apache::lonhtmlcommon::AscendOrderOptions(
                                            $cache{'ProblemStatisticsAscend'}, 
                                            'ProblemStatistics',
                                            'Statistics');
    $Ptr .= '</td></tr>'."\n";
    $Ptr .= '<tr><td align="right"><b>Select Sections</b>';
    $Ptr .= '</td>'."\n";
    $Ptr .= '<td align="left">'."\n";
    my @sections = split(':',$cache{'sectionList'});
    $Ptr .= &Apache::lonhtmlcommon::MultipleSectionSelect(\@sections,
                                                          \@sectionsSelected,
                                                          'Statistics');
    $Ptr .= '</td></tr>'."\n";
    $Ptr .= &ProblemStatisticsButtons($cache{'DisplayFormat'}, 
                                      $cache{'DisplayLegend'});
    $Ptr .= '</table>';
    if($cache{'DisplayLegend'} eq 'Show Legend') {
        $Ptr .= &ProblemStatisticsLegend();
    }
    $r->print($Ptr);
    $r->rflush();

    my @Header = ("Homework Sets Order","#Stdnts","Tries","Mod",
                  "Mean","#YES","#yes","%Wrng","DoDiff",
                  "S.D.","Skew.","D.F.1st","D.F.2nd","Disc.");
    my $color=&setbgcolor(0);

#    my %Discuss=&Apache::loncoursedata::LoadDiscussion($courseID);
    my $lastStatus = (defined($cache{'StatisticsLastStatus'})) ?
                     $cache{'StatisticsLastStatus'} : 'Nothing';
    my $whichStudents = join(':::',sort(@$students));
    if(!defined($cache{'StatisticsCached'}) || 
       $lastStatus ne $cache{'Status'} ||
       $whichStudents ne $cache{'StatisticsWhichStudents'}) {
        if(defined($cache{'StatisticsCached'})) {
            untie(%cache);
            unless(tie(%cache,'GDBM_File',$cacheDB,&GDBM_WRCREAT(),0640)) {
                $r->print('Unable to tie database.');
                return;
            }
            my @statkeys = split(':::', $cache{'StatisticsKeys'});
            delete $cache{'StatisticsKeys'};
            delete $cache{'StatisticsCached'};
            foreach(@statkeys) {
                delete $cache{$_};
            }
        }
        untie(%cache);
        &Apache::loncoursedata::DownloadStudentCourseDataSeparate($students,
                                                                  'true',
                                                                  $cacheDB,
                                                                  'true', 
                                                                  'true',
                                                                  $courseID,
                                                                  $r, $c);
        if($c->aborted()) { return; }

        unless(tie(%cache,'GDBM_File',$cacheDB,&GDBM_READER(),0640)) {
            $r->print('Unable to tie database.');
            return;
        }
        my ($problemData) = &ExtractStudentData(\%cache, $students);
        &CalculateStatistics($problemData, \%cache);
        untie(%cache);

        unless(tie(%cache,'GDBM_File',$cacheDB,&GDBM_WRCREAT(),0640)) {
            $r->print('Unable to tie database.');
            return;
        }
        foreach(keys(%$problemData)) {
            $cache{$_} = $problemData->{$_};
        }
        $cache{'StatisticsKeys'} = join(':::', keys(%$problemData));
        $cache{'StatisticsCached'} = 'true';
        $cache{'StatisticsLastStatus'} = $cache{'Status'};
        $cache{'StatisticsWhichStudents'} = $whichStudents;
        untie(%cache);

        unless(tie(%cache,'GDBM_File',$cacheDB,&GDBM_READER(),0640)) {
            $r->print('Unable to tie database.');
            return;
        }
    }

    my $orderedProblems = &SortProblems(\%cache, 
                                        $cache{'ProblemStatisticsSort'},
                                        $cache{'ProblemStatisticsAscend'});
    &BuildStatisticsTable(\%cache, $cache{'DisplayFormat'}, $orderedProblems, 
                          \@Header, $r, $color);
    untie(%cache);

    return;
}

sub BuildGraphicChart {
    my ($graph,$cacheDB,$courseDescription,$r)=@_;
    my %cache;
    my $max = 0;

    unless(tie(%cache,'GDBM_File',$cacheDB,&GDBM_READER(),0640)) {
        return '<html><body>Unable to tie database.</body></html>';
    }
   
    my @problems = split(':::', $cache{'problemList'});
    my @values = ();
    foreach (@problems) {
        my $data = 0;
        if($graph eq 'DoDiffGraph') {
            $data = sprintf("%.2f", $cache{$_.':degreeOfDifficulty'}),
        } else {
            $data = sprintf("%.1f", $cache{$_.':percentWrong'}),
        }
        if($max < $data) {
            $max = $data;
        }
        push(@values, $data);
    }
    untie(%cache);

    my $sendValues = join(',', @values);
    my $sendCount = scalar(@values);

    my $title = '';
    if($graph eq 'DoDiffGraph') {
	$title = 'Degree-of-Difficulty';
    } else {
	$title = 'Wrong-Percentage';
    }
    my @GData = ($courseDescription, 'Problems', $title, $max, $sendCount, 
                 $sendValues);

    $r->print('</form>'."\n");
    $r->print('<IMG src="/cgi-bin/graph.gif?'.(join('&', @GData)).'" border="1" />');
    $r->print('<form>'."\n");

    return;
}

#---- Problem Statistics Web Page ---------------------------------------

sub CreateProblemStatisticsTableHeading {
    my ($headings,$r)=@_;

    my $Str='';
    $Str .= '<tr>'."\n";
    $Str .= '<th bgcolor="#ffffe6">P#</th>'."\n";
    foreach(@$headings) {
	$Str .= '<th bgcolor="#ffffe6">'.'<a href="/adm/statistics?reportSelected=';
        $Str .= &Apache::lonnet::escape('Problem Statistics');
        $Str .= '&ProblemStatisticsSort=';
        $Str .= &Apache::lonnet::escape($_).'">'.$_.'</a>&nbsp</th>'."\n";
    }
    $Str .= "\n".'</tr>'."\n";    

    return $Str;
}

sub BuildStatisticsTable {
    my ($cache,$displayFormat,$orderedProblems,$headings,$r,$color)=@_;

#6666666
#    my $file="/home/httpd/perl/tmp/183d.txt";
#    open(OUT, ">$file");
#6666666
##     &Apache::lonstatistics::Create_PrgWin($r);
##777777
##    my (%Activity) = &LoadActivityLog();
##    $r->print('<script>popwin.document.popremain.remaining.value="'.
##              'Loading Discussion...";</script>');
##    my ($doDiffFile) = &LoadDoDiffFile();

##777777
##    $Str .= &Classify($discriminantFactor, $students);

     if($displayFormat ne 'Display CSV Format') {
        $r->print('<table border="0"><tr><td bgcolor="#777777">'."\n");
        $r->print('<table border="0" cellpadding="3">'."\n");
        $r->print(&CreateProblemStatisticsTableHeading($headings, $r));
    } else {
        $r->print('<br>');
    }

    my $count = 1;
    foreach(@$orderedProblems) {
        my ($sequence,$problem,$part)=split(':', $_);
        if($cache->{'StatisticsMaps'} ne 'All Maps'  &&
           $cache->{'StatisticsMaps'} ne $cache->{$sequence.':title'}) {
            next;
        }

        my $ref = '<a href="'.$cache->{$problem.':source'}.
                  '" target="_blank">'.$cache->{$problem.':title'}.'</a>';
#        my $ref = $cache->{$problem.':title'};
        my $title = $cache->{$problem.':title'};
        my $source = 'source';
        my $tableData = join('&', $ref, $title, $source,
                       $cache->{$_.':studentCount'},
                       $cache->{$_.':totalTries'},
                       $cache->{$_.':maxTries'},
                       sprintf("%.2f", $cache->{$_.':mean'}),
                       $cache->{$_.':correct'},
                       $cache->{$_.':correctByOverride'},
                       sprintf("%.1f", $cache->{$_.':percentWrong'}),
                       sprintf("%.2f", $cache->{$_.':degreeOfDifficulty'}),
                       sprintf("%.1f", $cache->{$_.':standardDeviation'}),
                       sprintf("%.1f", $cache->{$_.':skewness'}),
                       sprintf("%.2f", $cache->{$_.':discriminationFactor1'}),
                       sprintf("%.2f", $cache->{$_.':discriminationFactor2'}),
                       0); # 0 is for discussion, need to figure out

        &TableRow($displayFormat,$tableData,$count,$r,$color);
        $count++;
    }
    if($cache->{'DisplayFormat'} ne 'Display CSV Format') {
        $r->print('</table>'."\n");
    }
    $r->print('</td></tr></table>');
#6666666
#	    $r->print('<br>'.$out.'&'.$DoD);
#            print (OUT $out.'@'.$DoD.'&');
#6666666

#6666666
#    close( OUT );
#666666
    return;
}

sub TableRow {
    my ($displayFormat,$Str,$RealIdx,$r,$color)=@_;
    my($ref,$title,$source,$StdNo,$TotalTries,$MxTries,$Avg,$YES,$Override,
       $Wrng,$DoD,$SD,$Sk,$_D1,$_D2,$DiscNo,$Prob)=split(/\&/,$Str);	
    my $Ptr;
    if($displayFormat eq 'Display CSV Format') {
        $Ptr="\n".'<br>'.
             "\n".'"'.$RealIdx.'",'.
             "\n".'"'.$title.'",'.
             "\n".'"'.$source.'",'.
             "\n".'"'.$StdNo.'",'.
             "\n".'"'.$TotalTries.'",'.
             "\n".'"'.$MxTries.'",'.
             "\n".'"'.$Avg.'",'.
             "\n".'"'.$YES.'",'.
             "\n".'"'.$Override.'",'.
             "\n".'"'.$Wrng.'",'.
             "\n".'"'.$DoD.'",'.
             "\n".'"'.$SD.'",'.
             "\n".'"'.$Sk.'",'.
             "\n".'"'.$_D1.'",'.
	     "\n".'"'.$_D2.'"'.
	     "\n".'"'.$DiscNo.'"';

        $r->print("\n".$Ptr);
    } else {
        $Ptr="\n".'<tr>'.
             "\n".'<td bgcolor="#ffffe6">'.$RealIdx.'</td>'.
             "\n".'<td bgcolor="#ffffe6">'.$ref.'</td>'.
             "\n".'<td bgcolor='.$color->{"yellow"}.'> '.$StdNo.'</td>'.
             "\n".'<td bgcolor='.$color->{"yellow"}.'>'.$TotalTries.'</td>'.
             "\n".'<td bgcolor='.$color->{"yellow"}.'>'.$MxTries.'</td>'.
             "\n".'<td bgcolor='.$color->{"gb"}.'>'.$Avg.'</td>'.
             "\n".'<td bgcolor='.$color->{"gb"}.'> '.$YES.'</td>'.
             "\n".'<td bgcolor='.$color->{"gb"}.'> '.$Override.'</td>'.
             "\n".'<td bgcolor='.$color->{"red"}.'> '.$Wrng.'</td>'.
             "\n".'<td bgcolor='.$color->{"red"}.'> '.$DoD.'</td>'.
             "\n".'<td bgcolor='.$color->{"green"}.'> '.$SD.'</td>'.
             "\n".'<td bgcolor='.$color->{"green"}.'> '.$Sk.'</td>'.
             "\n".'<td bgcolor='.$color->{"purple"}.'> '.$_D1.'</td>'.
	     "\n".'<td bgcolor='.$color->{"purple"}.'> '.$_D2.'</td>'.
             "\n".'<td bgcolor='.$color->{"yellow"}.'> '.$DiscNo.'</td>';
        $r->print("\n".$Ptr.'</tr>' );
    }

    return;
}

# For loading the colored table for display or un-colored for print
sub setbgcolor {
    my $PrintTable=shift;
    my %color;
    if ($PrintTable){
	$color{"gb"}="#FFFFFF";
	$color{"red"}="#FFFFFF";
	$color{"yellow"}="#FFFFFF";
	$color{"green"}="#FFFFFF";
	$color{"purple"}="#FFFFFF";
    } else {
	$color{"gb"}="#DDFFFF";
	$color{"red"}="#FFDDDD";
	$color{"yellow"}="#EEFFCC";
	$color{"green"}="#DDFFDD";
	$color{"purple"}="#FFDDFF";
    }

    return \%color;
}

sub ProblemStatisticsButtons {
    my ($displayFormat, $displayLegend)=@_;

    my $Ptr = '<tr><td></td><td align="left">';
    $Ptr .= '<input type="submit" name="DoDiffGraph" ';
    $Ptr .= 'value="DoDiff Graph" />'."\n";
    $Ptr .= '&nbsp;&nbsp;&nbsp;';
    $Ptr .= '<input type="submit" name="PercentWrongGraph" ';
    $Ptr .= 'value="%Wrong Graph" />'."\n";
    $Ptr .= '</td></tr><tr><td></td><td>'."\n";
    $Ptr .= '<input type="submit" name="DisplayLegend" ';
    if($displayLegend eq 'Show Legend') {
        $Ptr .= 'value="Hide Legend" />'."\n";
    } else {
        $Ptr .= 'value="Show Legend" />'."\n";
    }
    $Ptr .= '&nbsp;&nbsp;&nbsp;';
    $Ptr .= '<input type="submit" name="DisplayCSVFormat" ';
    if($displayFormat eq 'Display CSV Format') {
        $Ptr .= 'value="Display Table Format" />'."\n";
    } else {
        $Ptr .= 'value="Display CSV Format" />'."\n";
    }
    $Ptr .= '</td></tr>';

    return $Ptr;
}

sub ProblemStatisticsLegend {
    my $Ptr = '';
    $Ptr = '<table border="0">';
    $Ptr .= '<tr><td>';
    $Ptr .= '<b>#Stdnts</b></td>';
    $Ptr .= '<td>Total number of students attempted the problem.';
    $Ptr .= '</td></tr><tr><td>';
    $Ptr .= '<b>Tries</b></td>';
    $Ptr .= '<td>Total number of tries for solving the problem.';
    $Ptr .= '</td></tr><tr><td>';
    $Ptr .= '<b>Mod</b></td>';
    $Ptr .= '<td>Largest number of tries for solving the problem by a student.';
    $Ptr .= '</td></tr><tr><td>';
    $Ptr .= '<b>Mean</b></td>';
    $Ptr .= '<td>Average number of tries. [ Tries / #Stdnts ]';
    $Ptr .= '</td></tr><tr><td>';
    $Ptr .= '<b>#YES</b></td>';
    $Ptr .= '<td>Number of students solved the problem correctly.';
    $Ptr .= '</td></tr><tr><td>';
    $Ptr .= '<b>#yes</b></td>';
    $Ptr .= '<td>Number of students solved the problem by override.';
    $Ptr .= '</td></tr><tr><td>';
    $Ptr .= '<b>%Wrong</b></td>';
    $Ptr .= '<td>Percentage of students who tried to solve the problem ';
    $Ptr .= 'but is still incorrect. [ 100*((#Stdnts-(#YES+#yes))/#Stdnts) ]';
    $Ptr .= '</td></tr><tr><td>';
    $Ptr .= '<b>DoDiff</b></td>';
    $Ptr .= '<td>Degree of Difficulty of the problem.  ';
    $Ptr .= '[ 1 - ((#YES+#yes) / Tries) ]';
    $Ptr .= '</td></tr><tr><td>';
    $Ptr .= '<b>S.D.</b></td>';
    $Ptr .= '<td>Standard Deviation of the tries.  ';
    $Ptr .= '[ sqrt(sum((Xi - Mean)^2)) / (#Stdnts-1) ';
    $Ptr .= 'where Xi denotes every student\'s tries ]';
    $Ptr .= '</td></tr><tr><td>';
    $Ptr .= '<b>Skew.</b></td>';
    $Ptr .= '<td>Skewness of the students tries.';
    $Ptr .= '[(sqrt( sum((Xi - Mean)^3) / #Stdnts)) / (S.D.^3)]';
    $Ptr .= '</td></tr><tr><td>';
    $Ptr .= '<b>Dis.F.</b></td>';
    $Ptr .= '<td>Discrimination Factor: A Standard for evaluating the ';
    $Ptr .= 'problem according to a Criterion<br>';
    $Ptr .= '<b>[Applied Criterion in %27 Upper Students - ';
    $Ptr .= 'Applied the same Criterion in %27 Lower Students]</b><br>';
    $Ptr .= '<b>1st Criterion</b> for Sorting the Students: ';
    $Ptr .= '<b>Sum of Partial Credit Awarded / Total Number of Tries</b><br>';
    $Ptr .= '<b>2nd Criterion</b> for Sorting the Students: ';
    $Ptr .= '<b>Total number of Correct Answers / Total Number of Tries</b>';
    $Ptr .= '</td></tr>';
    $Ptr .= '<tr><td><b>Disc.</b></td>';
    $Ptr .= '<td>Number of Students had at least one discussion.';
    $Ptr .= '</td></tr></table>';

    return $Ptr;
}

#------- Processing upperlist and lowerlist according to each problem

sub ExtractStudentData {
    my ($cache, $students)=@_;

#$Apache::lonxml::debug=1;
#&Apache::lonhomework::showhash(%$cache);
#$Apache::lonxml::debug=0;

    my @problemList=();
    my %problemData;
    foreach my $sequence (split(':', $cache->{'orderedSequences'})) {
        foreach my $problemID (split(':', $cache->{$sequence.':problems'})) {
            foreach my $part (split(/\:/,$cache->{$sequence.':'.
                                                  $problemID.
                                                  ':parts'})) {
                my $id = $sequence.':'.$problemID.':'.$part;
                push(@problemList, $id);
                my $totalTries = 0;
                my $totalAwarded = 0;
                my $correct = 0;
                my $correctByOverride = 0;
                my $studentCount = 0;
                my $maxTries = 0;
                my $totalFirst = 0;
                my @studentTries=();
                foreach(@$students) {
                    my $code = $cache->{"$_:$problemID:$part:code"};

                    if(defined($cache->{$_.':error'}) || $code eq ' ' ||
                       $cache->{"$_:$problemID:NoVersion"} eq 'true') {
                        next;
                    }

                    $studentCount++;
                    my $tries =  $cache->{"$_:$problemID:$part:tries"};
                    if($maxTries < $tries) {
                        $maxTries = $tries;
                    }
                    $totalTries += $tries;
                    push(@studentTries, $tries);

                    my $awarded = $cache->{"$_:$problemID:$part:awarded"};
                    $totalAwarded += $awarded;

                    if($code eq '*') {
                        $correct++;
                        if($tries == 1) {
                            $totalFirst++;
                        }
                    } elsif($code eq '+') {
                        $correctByOverride++;
                    }
                }

                $problemData{$id.':sequenceTitle'} = 
                    $cache->{$sequence.':title'};
                $problemData{$id.':studentCount'} = $studentCount;
                $problemData{$id.':totalTries'} = $totalTries;
                $problemData{$id.':studentTries'} = \@studentTries;
                $problemData{$id.':totalAwarded'} = $totalAwarded;
                $problemData{$id.':correct'} = $correct;
                $problemData{$id.':correctByOverride'} = $correctByOverride;
                $problemData{$id.':wrong'} = $studentCount - 
                                             ($correct + $correctByOverride);
                $problemData{$id.':maxTries'} = $maxTries;
                $problemData{$id.':totalFirst'} = $totalFirst;
            }
        }
    }

    my @upperStudents1=();
    my @lowerStudents1=();
    my @upperStudents2=();
    my @lowerStudents2=();
    my $upperCount = int(0.27*scalar(@$students));
    # Discriminant Factor criterion 1
    my $sortedStudents = &SortDivideByTries($students,$cache,':totalAwarded');

    for(my $i=0; $i<$upperCount; $i++) {
        push(@lowerStudents1, $sortedStudents->[$i]);
        push(@upperStudents1, $sortedStudents->[(scalar(@$students)-$i-1)]);
    }

    $problemData{'studentsUpperListCriterion1'}=join(':::', @upperStudents1);
    $problemData{'studentsLowerListCriterion1'}=join(':::', @lowerStudents1);

    # Discriminant Factor criterion 2
    $sortedStudents = &SortDivideByTries($students, $cache, ':totalSolved');

    for(my $i=0; $i<$upperCount; $i++) {
        push(@lowerStudents2, $sortedStudents->[$i]);
        push(@upperStudents2, $sortedStudents->[(scalar(@$students)-$i-1)]);
    }
    $problemData{'studentsUpperListCriterion2'}=join(':::', @upperStudents2);
    $problemData{'studentsLowerListCriterion2'}=join(':::', @lowerStudents2);

    $problemData{'problemList'} = join(':::', @problemList);
#                $Discussed=0;
#                if($Discuss->{"$name:$problem"}) {
#		    $TotDiscuss++;
#                    $Discussed=1;
#                }

    return \%problemData;
}

sub SortDivideByTries {
    my ($toSort, $data, $sortOn)=@_;
    my @orderedData = sort { ($data->{$a.':totalTries'}) ? 
                             ($data->{$a.$sortOn}/$data->{$a.':totalTries'}):0
                             <=>
                             ($data->{$b.':totalTries'}) ? 
                             ($data->{$b.$sortOn}/$data->{$b.':totalTries'}):0
                           } @$toSort;

    return \@orderedData;
}

sub SortProblems {
    my ($problemData,$sortBy,$ascend)=@_;

    my @problems = split(':::', $problemData->{'problemList'});
    if($sortBy eq "Homework Sets Order") {
        return \@problems;
    }

    my $data;

    if   ($sortBy eq "#Stdnts") { $data = ':studentCount'; }
    elsif($sortBy eq "Tries")   { $data = ':totalTries'; }
    elsif($sortBy eq "Mod")     { $data = ':maxTries'; }
    elsif($sortBy eq "Mean")    { $data = ':mean'; }
    elsif($sortBy eq "#YES")    { $data = ':correct'; }
    elsif($sortBy eq "#yes")    { $data = ':correctByOverride'; }
    elsif($sortBy eq "%Wrng")   { $data = ':percentWrong'; }
    elsif($sortBy eq "DoDiff")  { $data = ':degreeOfDifficulty'; }
    elsif($sortBy eq "S.D.")    { $data = ':standardDeviation'; }
    elsif($sortBy eq "Skew.")   { $data = ':skewness'; }
    elsif($sortBy eq "D.F.1st") { $data = ':discriminantFactor1'; }
    elsif($sortBy eq "D.F.2nd") { $data = ':discriminantFactor2'; }
    elsif($sortBy eq "Disc.")   { $data = ''; }
    else                        { return \@problems; }

    my @orderedProblems = 
        sort { $problemData->{$a.$data} <=> $problemData->{$b.$data} }
             @problems;
    if($ascend eq 'Descending') {
        @orderedProblems = reverse(@orderedProblems);
    }

    return \@orderedProblems;
}

sub CalculateStatistics {
    my ($data, $cache)=@_;

    my @problems = split(':::', $data->{'problemList'});
    foreach(@problems) {
        # Mean
        $data->{$_.':mean'} = ($data->{$_.':studentCount'}) ? 
            ($data->{$_.':totalTries'} / $data->{$_.':studentCount'}) : 0;

        # %Wrong
        $data->{$_.':percentWrong'} = ($data->{$_.':studentCount'}) ?
            (($data->{$_.':wrong'} / $data->{$_.':studentCount'}) * 100.0) : 
            100.0;

        # Degree of Difficulty
        $data->{$_.':degreeOfDifficulty'} = ($data->{$_.':totalTries'}) ?
            (1 - (($data->{$_.':correct'} + $data->{$_.':correctByOverride'}) /
                  $data->{$_.':totalTries'})) : 0;

        # Factor in mean
        my $studentTries = $data->{$_.':studentTries'};
        foreach(my $index=0; $index < scalar(@$studentTries); $index++) {
            $studentTries->[$index] -= $data->{$_.':mean'};
        }
        my $sumSquared = 0;
        my $sumCubed = 0;
        foreach(@$studentTries) {
            my $squared = ($_ * $_);
            my $cubed = ($squared * $_);
            $sumSquared += $squared;
            $sumCubed += $cubed;
        }

        # Standard deviation
        $data->{$_.':standardDeviation'} = ($data->{$_.':studentCount'} - 1) ?
            ((sqrt($sumSquared)) / ($data->{$_.':studentCount'} - 1)) : 0;

        # Skewness
        my $standardDeviation = $data->{$_.':standardDeviation'};
        $data->{$_.':skewness'} = ($data->{$_.':standardDeviation'}) ?
            (((sqrt($sumSquared)) / $data->{$_.':studentCount'}) / 
             ($standardDeviation * $standardDeviation * $standardDeviation)) :
             0;

        # Discrimination Factor 1
        my ($sequence, $problem, $part) = split(':', $_);

        my @upper1 = split(':::', $data->{'studentsUpperListCriterion1'});
        my @lower1 = split(':::', $data->{'studentsLowerListCriterion1'});

        my $upper1Sum=0;
        foreach my $name (@upper1) {
            $upper1Sum += $cache->{"$name:$problem:$part:awarded"};
        }
        $upper1Sum = (scalar(@upper1)) ? ($upper1Sum/(scalar(@upper1))) : 0;

        my $lower1Sum=0;
        foreach my $name (@lower1) {
            $lower1Sum += $cache->{"$name:$problem:$part:awarded"};
        }
        $lower1Sum = (scalar(@lower1)) ? ($lower1Sum/(scalar(@lower1))) : 0;

        $data->{$_.':discriminationFactor1'} = $upper1Sum - $lower1Sum;

        # Discrimination Factor 2
        my @upper2 = split(':::', $data->{'studentsUpperListCriterion2'});
        my @lower2 = split(':::', $data->{'studentsLowerListCriterion2'});

        my $upper2Sum=0;
        foreach my $name (@upper2) {
            $upper2Sum += $cache->{"$name:$problem:$part:awarded"};
        }
        $upper2Sum = (scalar(@upper2)) ? ($upper2Sum/(scalar(@upper2))) : 0;

        my $lower2Sum=0;
        foreach my $name (@lower2) {
            $lower2Sum += $cache->{"$name:$problem:$part:awarded"};
        }
        $lower2Sum = (scalar(@lower2)) ? ($lower2Sum/(scalar(@lower2))) : 0;

        $data->{$_.':discriminationFactor2'} = $upper2Sum - $lower2Sum;
    }

    return;
}

#---- END Problem Statistics Web Page ----------------------------------------

1;
__END__