# The LearningOnline Network with CAPA
# (Publication Handler
#
# $Id: lonproblemstatistics.pm,v 1.23 2002/08/13 15:05:13 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;
}
my $Ptr = '';
$Ptr .= '
' );
}
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 = '
';
$Ptr .= '';
$Ptr .= '
';
$Ptr .= '#Stdnts
';
$Ptr .= '
Total number of students attempted the problem.';
$Ptr .= '
';
$Ptr .= 'Tries
';
$Ptr .= '
Total number of tries for solving the problem.';
$Ptr .= '
';
$Ptr .= 'Mod
';
$Ptr .= '
Largest number of tries for solving the problem by a student.';
$Ptr .= '
';
$Ptr .= 'Mean
';
$Ptr .= '
Average number of tries. [ Tries / #Stdnts ]';
$Ptr .= '
';
$Ptr .= '#YES
';
$Ptr .= '
Number of students solved the problem correctly.';
$Ptr .= '
';
$Ptr .= '#yes
';
$Ptr .= '
Number of students solved the problem by override.';
$Ptr .= '
';
$Ptr .= '%Wrong
';
$Ptr .= '
Percentage of students who tried to solve the problem ';
$Ptr .= 'but is still incorrect. [ 100*((#Stdnts-(#YES+#yes))/#Stdnts) ]';
$Ptr .= '
';
$Ptr .= 'DoDiff
';
$Ptr .= '
Degree of Difficulty of the problem. ';
$Ptr .= '[ 1 - ((#YES+#yes) / Tries) ]';
$Ptr .= '
';
$Ptr .= 'S.D.
';
$Ptr .= '
Standard Deviation of the tries. ';
$Ptr .= '[ sqrt(sum((Xi - Mean)^2)) / (#Stdnts-1) ';
$Ptr .= 'where Xi denotes every student\'s tries ]';
$Ptr .= '
';
$Ptr .= 'Skew.
';
$Ptr .= '
Skewness of the students tries.';
$Ptr .= '[(sqrt( sum((Xi - Mean)^3) / #Stdnts)) / (S.D.^3)]';
$Ptr .= '
';
$Ptr .= 'Dis.F.
';
$Ptr .= '
Discrimination Factor: A Standard for evaluating the ';
$Ptr .= 'problem according to a Criterion ';
$Ptr .= '[Applied Criterion in %27 Upper Students - ';
$Ptr .= 'Applied the same Criterion in %27 Lower Students] ';
$Ptr .= '1st Criterion for Sorting the Students: ';
$Ptr .= 'Sum of Partial Credit Awarded / Total Number of Tries ';
$Ptr .= '2nd Criterion for Sorting the Students: ';
$Ptr .= 'Total number of Correct Answers / Total Number of Tries';
$Ptr .= '
';
$Ptr .= '
Disc.
';
$Ptr .= '
Number of Students had at least one discussion.';
$Ptr .= '
';
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;
}
}
}
$problemData{'problemList'} = join(':::', @problemList);
# $Discussed=0;
# if($Discuss->{"$name:$problem"}) {
# $TotDiscuss++;
# $Discussed=1;
# }
return \%problemData;
}
sub SortProblems {
my ($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)=@_;
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
$data->{$_.':discriminationFactor1'} = 0;
# Discrimination Factor 2
$data->{$_.':discriminationFactor2'} = 0;
}
return;
}
sub ProcessDiscriminant {
my ($List) = @_;
my @sortedList = sort (@$List);
my $Count = scalar @sortedList;
my $Problem;
my @Dis;
my $Slvd=0;
my $tmp;
my $Sum1=0;
my $Sum2=0;
my $nIndex=0;
my $nStudent=0;
my %Proc=undef;
while ($nIndex<$Count) {
# $jr->print(" $nIndex) $sortedList[$nIndex]");
($Problem,$tmp)=split(/\=/,$sortedList[$nIndex]);
@Dis=split(/\+/,$tmp);
my $Temp = $Problem;
do {
$nIndex++;
$nStudent++;
$Sum1 += $Dis[0];
$Sum2 += $Dis[1];
($Problem,$tmp)=split(/\=/,$sortedList[$nIndex]);
@Dis=split(/\+/,$tmp);
} while ( $Problem eq $Temp && $nIndex < $Count );
$Proc{$Temp}=($Sum1/$nStudent).':'.($Sum2/$nStudent);
# $jr->print(" $nIndex) $Temp --> ($nStudent) $Proc{$Temp}");
$Sum1=0;
$Sum2=0;
$nStudent=0;
}
return %Proc;
}
#------- Creating Discimination factor
sub Discriminant {
my ($discriminant)=@_;
my @discriminantKeys=keys(%$discriminant);
my $Count = scalar @discriminantKeys;
my $UpCnt = int(0.27*$Count);
my $low=0;
my $up=$Count-$UpCnt;
my @UpList=();
my @LowList=();
$Count=0;
foreach my $key (sort(@discriminantKeys)) {
$Count++;
if($low < $UpCnt || $Count > $up) {
$low++;
my $str=$discriminant->{$key};
foreach(split(/\&/,$str)){
if($_) {
if($low<$UpCnt) { push(@LowList,$_); }
else { push(@UpList,$_); }
}
}
}
}
my %DisUp = &ProcessDiscriminant(\@UpList);
my %DisLow = &ProcessDiscriminant(\@LowList);
return (\%DisUp, \%DisLow);
}
#---- END Problem Statistics Web Page ----------------------------------------
#---- Problem Statistics Graph Web Page --------------------------------------
# ------------------------------------------- Prepare data for Graphical chart
sub BuildGraphicChart {
my ($graph,$cacheDB,$courseDescription,$r)=@_;
my %cache;
my $max = 0;
unless(tie(%cache,'GDBM_File',$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 = $#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(''."\n");
$r->print('');
$r->print('