# The LearningOnline Network with CAPA
# (Publication Handler
#
# $Id: lonproblemstatistics.pm,v 1.27 2002/08/14 20:42:49 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 $jr;
sub InitializeProblemStatistics {
my ($cacheDB, $students, $courseID, $c, $r)=@_;
my %cache;
$jr = $r;
unless(tie(%cache,'GDBM_File',$cacheDB,&GDBM_READER(),0640)) {
$r->print('Unable to tie database.');
return ('ERROR', undef);
}
# Remove students who don't have the proper section.
my @sectionsSelected = split(':',$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 $lastStatus = (defined($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 ('ERROR', undef);
}
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 ('ERROR', undef); }
unless(tie(%cache,'GDBM_File',$cacheDB,&GDBM_READER(),0640)) {
$r->print('Unable to tie database.');
return ('ERROR', undef);
}
my ($problemData) = &ExtractStudentData(\%cache, $students);
&CalculateStatistics($problemData, \%cache);
untie(%cache);
unless(tie(%cache,'GDBM_File',$cacheDB,&GDBM_WRCREAT(),0640)) {
$r->print('Unable to tie database.');
return ('ERROR', undef);
}
foreach(keys(%$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 ('ERROR', undef);
}
}
my $orderedProblems = &SortProblems(\%cache,
$cache{'ProblemStatisticsSort'},
$cache{'SortProblems'},
$cache{'ProblemStatisticsAscend'});
return ('OK', $orderedProblems);
}
sub BuildProblemStatisticsPage {
my ($cacheDB, $students, $courseID, $c, $r)=@_;
my @Header = ("Homework Sets Order","#Stdnts","Tries","Mod",
"Mean","#YES","#yes","%Wrng","DoDiff",
"S.D.","Skew.","D.F.1st","D.F.2nd");
my $color=&setbgcolor(0);
my %cache;
unless(tie(%cache,'GDBM_File',$cacheDB,&GDBM_READER(),0640)) {
$r->print('Unable to tie database.');
return;
}
my $Ptr = '';
$Ptr .= '<table border="0" cellspacing="5"><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'});
my @sectionsSelected = split(':',$cache{'sectionsSelected'});
$Ptr .= &Apache::lonhtmlcommon::MultipleSectionSelect(\@sections,
\@sectionsSelected,
'Statistics');
$Ptr .= '</td></tr>'."\n";
$Ptr .= &ProblemStatisticsButtons($cache{'DisplayFormat'},
$cache{'DisplayLegend'},
$cache{'SortProblems'});
$Ptr .= '</table>';
if($cache{'DisplayLegend'} eq 'Show Legend') {
$Ptr .= &ProblemStatisticsLegend();
}
$r->print($Ptr);
$r->rflush();
untie(%cache);
my ($result, $orderedProblems) =
&InitializeProblemStatistics($cacheDB, $students, $courseID, $c, $r);
if($result ne 'OK') {
return;
}
unless(tie(%cache,'GDBM_File',$cacheDB,&GDBM_READER(),0640)) {
$r->print('Unable to tie database.');
return;
}
&BuildStatisticsTable(\%cache, $cache{'DisplayFormat'},
$cache{'SortProblems'}, $orderedProblems,
\@Header, $r, $color);
untie(%cache);
return;
}
sub BuildGraphicChart {
my ($graph,$cacheDB,$courseDescription,$students,$courseID,$r,$c)=@_;
my %cache;
my $max = 0;
my ($result, undef) =
&InitializeProblemStatistics($cacheDB, $students, $courseID, $c, $r);
if($result ne 'OK') {
return;
}
unless(tie(%cache,'GDBM_File',$cacheDB,&GDBM_READER(),0640)) {
return 'Unable to tie database.';
}
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">';
$Str .= '<a href="/adm/statistics?reportSelected=';
$Str .= &Apache::lonnet::escape('Problem Statistics');
$Str .= '&ProblemStatisticsSort=';
$Str .= &Apache::lonnet::escape($_).'">'.$_.'</a> </th>'."\n";
}
$Str .= "\n".'</tr>'."\n";
return $Str;
}
sub BuildStatisticsTable {
my ($cache,$displayFormat,$sortProblems,$orderedProblems,$headings,
$r,$color)=@_;
my $count = 1;
my $currentSequence = -1;
foreach(@$orderedProblems) {
my ($sequence,$problem,$part)=split(':', $_);
if($cache->{'StatisticsMaps'} ne 'All Maps' &&
$cache->{'StatisticsMaps'} ne $cache->{$sequence.':title'}) {
next;
}
if($currentSequence == -1 ||
($sortProblems eq 'Sort Within Sequence' &&
$currentSequence != $sequence)) {
if($displayFormat ne 'Display CSV Format') {
if($currentSequence ne -1) {
$r->print('</table>');
$r->print('</td></tr></table><br>');
}
if($sortProblems eq 'Sort Within Sequence') {
$r->print('<b>'.$cache->{$sequence.':title'}.'</b>');
}
$r->print('<table border="0"><tr><td bgcolor="#777777">'."\n");
$r->print('<table border="0" cellpadding="3">'."\n");
$r->print(&CreateProblemStatisticsTableHeading($headings, $r));
} else {
if($sortProblems eq 'Sort Within Sequence') {
$r->print('"'.$cache->{$sequence.':title'}.'"');
}
$r->print('<br>');
}
$currentSequence = $sequence;
}
my $ref = '<a href="'.$cache->{$problem.':source'}.
'" target="_blank">'.$cache->{$problem.':title'}.'</a>';
my $title = $cache->{$problem.':title'};
if($part != 0) {
$title .= ' Part '.$part;
}
my $source = $cache->{$problem.':source'};
my $tableData = join('&', $ref, $title, $source,
$cache->{$_.':studentCount'},
$cache->{$_.':totalTries'},
$cache->{$_.':maxTries'},
$cache->{$_.':mean'},
$cache->{$_.':correct'},
$cache->{$_.':correctByOverride'},
$cache->{$_.':percentWrong'},
$cache->{$_.':degreeOfDifficulty'},
$cache->{$_.':standardDeviation'},
$cache->{$_.':skewness'},
$cache->{$_.':discriminationFactor1'},
$cache->{$_.':discriminationFactor2'});
&TableRow($displayFormat,$tableData,$count,$r,$color);
$count++;
}
if($displayFormat ne 'Display CSV Format') {
$r->print('</table>'."\n");
$r->print('</td></tr></table>');
} else {
$r->print('<br>');
}
return;
}
sub TableRow {
my ($displayFormat,$Str,$RealIdx,$r,$color)=@_;
my($ref,$title,$source,$StdNo,$TotalTries,$MxTries,$Avg,$YES,$Override,
$Wrng,$DoD,$SD,$Sk,$_D1,$_D2)=split(/\&/,$Str);
my $Ptr;
if($displayFormat eq 'Display CSV Format') {
$Ptr='"'.$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".
"<br>\n";
$r->print("\n".$Ptr);
} else {
$Ptr='<tr>'."\n".
'<td bgcolor="#ffffe6">'.$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";
$r->print($Ptr.'</tr>'."\n");
}
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, $sortProblems)=@_;
my $Ptr = '<tr><td></td><td align="left">';
$Ptr .= '<input type="submit" name="DoDiffGraph" ';
$Ptr .= 'value="Degree of Difficulty" />'."\n";
$Ptr .= '</td><td align="left">';
$Ptr .= '<input type="submit" name="PercentWrongGraph" ';
$Ptr .= 'value="Percent Wrong" />'."\n";
$Ptr .= '</td></tr><tr><td></td><td>'."\n";
$Ptr .= '<input type="submit" name="SortProblems" ';
if($sortProblems eq 'Sort All Problems') {
$Ptr .= 'value="Sort Within Sequence" />'."\n";
} else {
$Ptr .= 'value="Sort All Problems" />'."\n";
}
$Ptr .= '</td><td align="left">';
$Ptr .= '<input type="submit" name="DisplayLegend" ';
if($displayLegend eq 'Show Legend') {
$Ptr .= 'value="Hide Legend" />'."\n";
} else {
$Ptr .= 'value="Show Legend" />'."\n";
}
$Ptr .= '</td><td align="left">';
$Ptr .= '<input type="submit" name="DisplayCSVFormat" ';
if($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 $Ptr;
}
sub ExtractStudentData {
my ($cache, $students)=@_;
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++;
}
}
my $studentTriesJoined = join(':::', @studentTries);
$problemData{$id.':sequenceTitle'} =
$cache->{$sequence.':title'};
$problemData{$id.':studentCount'} = $studentCount;
$problemData{$id.':totalTries'} = $totalTries;
$problemData{$id.':studentTries'} = $studentTriesJoined;
$problemData{$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);
$problemData{'problemList'} = join(':::', @problemList);
return \%problemData;
}
sub SortDivideByTries {
my ($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,$sortProblems,$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") { $data = ':discriminationFactor1'; }
elsif($sortBy eq "D.F.2nd") { $data = ':discriminationFactor2'; }
else { return \@problems; }
my %temp;
my @sequenceList=();
foreach(@problems) {
my ($sequence) = split(':', $_);
my @array=();
my $tempArray;
if(defined($temp{$sequence})) {
$tempArray = $temp{$sequence};
} else {
push(@sequenceList, $sequence);
$tempArray = \@array;
$temp{$sequence} = $tempArray;
}
push(@$tempArray, $_);
}
my @orderedProblems;
if($sortProblems eq "Sort Within Sequence") {
foreach(keys(%temp)) {
my $tempArray = $temp{$_};
my @tempOrder =
sort { $problemData->{$a.$data} <=> $problemData->{$b.$data} }
@$tempArray;
$temp{$_} = \@tempOrder;
}
foreach(@sequenceList) {
my $tempArray = $temp{$_};
@orderedProblems = (@orderedProblems, @$tempArray);
}
} else {
@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
my $mean = ($data->{$_.':studentCount'}) ?
($data->{$_.':totalTries'} / $data->{$_.':studentCount'}) : 0;
$data->{$_.':mean'} = sprintf("%.2f", $mean);
# %Wrong
my $pw = ($data->{$_.':studentCount'}) ?
(($data->{$_.':wrong'} / $data->{$_.':studentCount'}) * 100.0) :
100.0;
$data->{$_.':percentWrong'} = sprintf("%.1f", $pw);
# Degree of Difficulty
my $dod = ($data->{$_.':totalTries'}) ?
(1 - (($data->{$_.':correct'} + $data->{$_.':correctByOverride'}) /
$data->{$_.':totalTries'})) : 0;
$data->{$_.':degreeOfDifficulty'} = sprintf("%.2f", $dod);
# Factor in mean
my @studentTries = split(':::', $data->{$_.':studentTries'});
foreach(my $index=0; $index < scalar(@studentTries); $index++) {
$studentTries[$index] -= $mean;
}
my $sumSquared = 0;
my $sumCubed = 0;
foreach(@studentTries) {
my $squared = ($_ * $_);
my $cubed = ($squared * $_);
$sumSquared += $squared;
$sumCubed += $cubed;
}
# Standard deviation
my $standardDeviation;
if($data->{$_.':studentCount'} - 1 > 0) {
$standardDeviation = (sqrt($sumSquared)) /
($data->{$_.':studentCount'} - 1);
} else {
$standardDeviation = 0.0;
}
$data->{$_.':standardDeviation'} = sprintf("%.1f", $standardDeviation);
# Skewness
my $skew;
if($standardDeviation > 0.0999 && $data->{$_.':studentCount'} > 0) {
$skew = (((sqrt($sumSquared)) / $data->{$_.':studentCount'}) /
($standardDeviation *
$standardDeviation *
$standardDeviation));
} else {
$skew = 0.0;
}
$data->{$_.':skewness'} = sprintf("%.1f", $skew);
# Discrimination Factor 1
my ($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;
my $df1 = $upper1Sum - $lower1Sum;
$data->{$_.':discriminationFactor1'} = sprintf("%.2f", $df1);
# 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;
my $df2 = $upper2Sum - $lower2Sum;
$data->{$_.':discriminationFactor2'} = sprintf("%.2f", $df2);
}
return;
}
#---- END Problem Statistics Web Page ----------------------------------------
1;
__END__
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