| ';
$Ptr .= '{'orderedSequences'})) {
@@ -437,11 +557,12 @@ sub ExtractStudentData {
}
}
+ my $studentTriesJoined = join(':::', @studentTries);
$problemData{$id.':sequenceTitle'} =
$cache->{$sequence.':title'};
$problemData{$id.':studentCount'} = $studentCount;
$problemData{$id.':totalTries'} = $totalTries;
- $problemData{$id.':studentTries'} = \@studentTries;
+ $problemData{$id.':studentTries'} = $studentTriesJoined;
$problemData{$id.':totalAwarded'} = $totalAwarded;
$problemData{$id.':correct'} = $correct;
$problemData{$id.':correctByOverride'} = $correctByOverride;
@@ -453,18 +574,51 @@ sub ExtractStudentData {
}
}
+ 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,$ascend)=@_;
+ my ($problemData,$sortBy,$sortProblems,$ascend)=@_;
my @problems = split(':::', $problemData->{'problemList'});
if($sortBy eq "Homework Sets Order") {
@@ -483,14 +637,47 @@ sub SortProblems {
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.") { $data = ''; }
+ elsif($sortBy eq "D.F.1st") { $data = ':discriminationFactor1'; }
+ elsif($sortBy eq "D.F.2nd") { $data = ':discriminationFactor2'; }
else { return \@problems; }
- my @orderedProblems =
- sort { $problemData->{$a.$data} <=> $problemData->{$b.$data} }
- @problems;
+ my %temp;
+ my @sequenceList=();
+ foreach(@problems) {
+ my ($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);
}
@@ -499,32 +686,36 @@ sub SortProblems {
}
sub CalculateStatistics {
- my ($data)=@_;
+ my ($data, $cache)=@_;
my @problems = split(':::', $data->{'problemList'});
foreach(@problems) {
# Mean
- $data->{$_.':mean'} = ($data->{$_.':studentCount'}) ?
+ my $mean = ($data->{$_.':studentCount'}) ?
($data->{$_.':totalTries'} / $data->{$_.':studentCount'}) : 0;
+ $data->{$_.':mean'} = sprintf("%.2f", $mean);
# %Wrong
- $data->{$_.':percentWrong'} = ($data->{$_.':studentCount'}) ?
+ my $pw = ($data->{$_.':studentCount'}) ?
(($data->{$_.':wrong'} / $data->{$_.':studentCount'}) * 100.0) :
100.0;
+ $data->{$_.':percentWrong'} = sprintf("%.1f", $pw);
# Degree of Difficulty
- $data->{$_.':degreeOfDifficulty'} = ($data->{$_.':totalTries'}) ?
+ my $dod = ($data->{$_.':totalTries'}) ?
(1 - (($data->{$_.':correct'} + $data->{$_.':correctByOverride'}) /
$data->{$_.':totalTries'})) : 0;
+ $data->{$_.':degreeOfDifficulty'} = sprintf("%.2f", $dod);
+
# Factor in mean
- my $studentTries = $data->{$_.':studentTries'};
- foreach(my $index=0; $index < scalar(@$studentTries); $index++) {
- $studentTries->[$index] -= $data->{$_.':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) {
+ foreach(@studentTries) {
my $squared = ($_ * $_);
my $cubed = ($squared * $_);
$sumSquared += $squared;
@@ -532,147 +723,73 @@ sub CalculateStatistics {
}
# Standard deviation
- $data->{$_.':standardDeviation'} = ($data->{$_.':studentCount'} - 1) ?
- ((sqrt($sumSquared)) / ($data->{$_.':studentCount'} - 1)) : 0;
+ my $standardDeviation;
+ if($data->{$_.':studentCount'} - 1 > 0) {
+ $standardDeviation = (sqrt($sumSquared)) /
+ ($data->{$_.':studentCount'} - 1);
+ } else {
+ $standardDeviation = 0.0;
+ }
+ $data->{$_.':standardDeviation'} = sprintf("%.1f", $standardDeviation);
# Skewness
- my $standardDeviation = $data->{$_.':standardDeviation'};
- $data->{$_.':skewness'} = ($data->{$_.':standardDeviation'}) ?
- (((sqrt($sumSquared)) / $data->{$_.':studentCount'}) /
- ($standardDeviation * $standardDeviation * $standardDeviation)) :
- 0;
+ my $skew;
+ if($standardDeviation > 0.0999 && $data->{$_.':studentCount'} > 0) {
+ $skew = (((sqrt($sumSquared)) / $data->{$_.':studentCount'}) /
+ ($standardDeviation *
+ $standardDeviation *
+ $standardDeviation));
+ } else {
+ $skew = 0.0;
+ }
- # Discrimination Factor 1
- $data->{$_.':discriminationFactor1'} = 0;
+ $data->{$_.':skewness'} = sprintf("%.1f", $skew);
- # Discrimination Factor 2
- $data->{$_.':discriminationFactor2'} = 0;
- }
+ # Discrimination Factor 1
+ my ($sequence, $problem, $part) = split(':', $_);
- return;
-}
+ my @upper1 = split(':::', $data->{'studentsUpperListCriterion1'});
+ my @lower1 = split(':::', $data->{'studentsLowerListCriterion1'});
-sub ProcessDiscriminant {
- my ($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 $upper1Sum=0;
+ foreach my $name (@upper1) {
+ $upper1Sum += $cache->{"$name:$problem:$part:awarded"};
}
- }
- my %DisUp = &ProcessDiscriminant(\@UpList);
- my %DisLow = &ProcessDiscriminant(\@LowList);
-
- return (\%DisUp, \%DisLow);
-}
-
-#---- END Problem Statistics Web Page ----------------------------------------
+ $upper1Sum = (scalar(@upper1)) ? ($upper1Sum/(scalar(@upper1))) : 0;
-#---- Problem Statistics Graph Web Page --------------------------------------
+ my $lower1Sum=0;
+ foreach my $name (@lower1) {
+ $lower1Sum += $cache->{"$name:$problem:$part:awarded"};
+ }
+ $lower1Sum = (scalar(@lower1)) ? ($lower1Sum/(scalar(@lower1))) : 0;
-# ------------------------------------------- Prepare data for Graphical chart
+ my $df1 = $upper1Sum - $lower1Sum;
+ $data->{$_.':discriminationFactor1'} = sprintf("%.2f", $df1);
-sub BuildGraphicChart {
- my ($ylab,$r,$cacheDB)=@_;
- my %cache;
- my $Col;
- my $data='';
- my $count = 0;
- my $Max = 0;
+ # Discrimination Factor 2
+ my @upper2 = split(':::', $data->{'studentsUpperListCriterion2'});
+ my @lower2 = split(':::', $data->{'studentsLowerListCriterion2'});
- unless(tie(%cache,'GDBM_File',$cacheDB,&GDBM_READER(),0640)) {
- return 'Unable to tie database.';
- }
-
- my $p_count = $cache{'ProblemCount'};
+ my $upper2Sum=0;
+ foreach my $name (@upper2) {
+ $upper2Sum += $cache->{"$name:$problem:$part:awarded"};
+ }
+ $upper2Sum = (scalar(@upper2)) ? ($upper2Sum/(scalar(@upper2))) : 0;
- for ( my $k=0; $k<$p_count;$k++) {
- my @Temp=split(/\:/,$cache{'GraphGif:'.$k});
- my $inf = $Temp[$Col];
- if ( $Max < $inf ) {$Max = $inf;}
- $data .= $inf.',';
- $count++;
- }
- untie(%cache);
-# $r->print("
count=$p_count >>data= $data");
+ my $lower2Sum=0;
+ foreach my $name (@lower2) {
+ $lower2Sum += $cache->{"$name:$problem:$part:awarded"};
+ }
+ $lower2Sum = (scalar(@lower2)) ? ($lower2Sum/(scalar(@lower2))) : 0;
- if ( $Max > 1 ) {
- $Max += (10 - $Max % 10);
- $Max = int($Max);
- } else { $Max = 1; }
-
- my $cid=$ENV{'request.course.id'};
-
- if ( $ylab eq 'DoDiff Graph' ) {
- $ylab = 'Degree-of-Difficulty';
- $Col = 0;
- } else {
- $ylab = 'Wrong-Percentage';
- $Col = 1;
+ my $df2 = $upper2Sum - $lower2Sum;
+ $data->{$_.':discriminationFactor2'} = sprintf("%.2f", $df2);
}
- my $Course = $ENV{'course.'.$cid.'.description'};
- $Course =~ s/\ /"_"/eg;
- my $GData=$Course.'&'.'Problems#'.'&'.$ylab.'&'.
- $Max.'&'.$count.'&'.$data;
-
- $r->print(' ');
return;
}
+#---- END Problem Statistics Web Page ----------------------------------------
+
1;
__END__
|
).
+ ')
');
+ $r->print('