'. + &mt('Press "Generate Statistics" when you are ready.'). + '
'. + &mt('It may take some time to update the student data '. + 'for the first analysis. Future analysis this session '. + ' will not have this delay.'). + '
'); return; + } elsif ($ENV{'form.statsfirstcall'} eq 'yes' || + exists($ENV{'form.UpdateCache'}) || + exists($ENV{'form.ClearCache'}) ) { + $r->print(''); + &Apache::lonstatistics::Gather_Student_Data($r); + } else { + $r->print(''); } + $r->rflush(); # - &Gather_Student_Data($r); - # + # This probably does not need to be done each time we are called, but + # it does not slow things down noticably. + &Apache::loncoursedata::populate_weight_table(); # - if ($output_mode eq 'html') { - $r->print("". - $ENV{'course.'.$ENV{'request.course.id'}.'.description'}. - "
\n"); - $r->print("".localtime(time)."
"); - $r->rflush(); - if ($show eq 'grouped') { - &output_html_grouped_by_sequence($r); - } elsif ($show eq 'ungrouped') { - &output_html_ungrouped($r); - } - } elsif ($output_mode eq 'excel') { - $r->print("Preparing Excel Spreadsheet
"); - &output_excel($r); - } elsif ($output_mode eq 'plot') { - if ($show eq 'deg of diff') { - &plot_statistics($r,'DoDiff'); - } elsif ($show eq 'per wrong') { - &plot_statistics($r,'%Wrng'); - } + if (exists($ENV{'form.Excel'})) { + &Excel_output($r); } else { - $r->print("Not implemented
"); + my $count = 0; + foreach my $seq (&Apache::lonstatistics::Sequences_with_Assess()) { + $count += $seq->{'num_assess'}; + } + if ($count > 10) { + $r->print(''. + &mt('Compiling statistics for [_1] problems',$count). + '
'); + if ($count > 30) { + $r->print(''.&mt('This will take some time.').'
'); + } + $r->rflush(); + } + # + my $sortby = $ENV{'form.sortby'}; + $sortby = 'container' if (! defined($sortby) || $sortby =~ /^\s*$/); + my $plot = $ENV{'form.plot'}; + if ($plot eq '' || $plot eq 'none') { + undef($plot); + } + if ($sortby eq 'container' && ! defined($plot)) { + &output_html_by_sequence($r); + } else { + if (defined($plot)) { + &make_plot($r,$plot); + } + &output_html_stats($r); + } } return; } -############################################### -############################################### - -=pod +########################################################## +########################################################## +## +## HTML output routines +## +########################################################## +########################################################## +sub output_html_by_sequence { + my ($r) = @_; + my $c = $r->connection(); + $r->print(&html_preamble()); + # + foreach my $seq (&Apache::lonstatistics::Sequences_with_Assess()) { + last if ($c->aborted); + next if ($seq->{'num_assess'} < 1); + $r->print("".$seq->{'title'}."
". + '| '."\n".
+ ' |
| '."\n".
+ ' |
". + $ENV{'course.'.$ENV{'request.course.id'}.'.description'}. + "
\n"; + my ($starttime,$endtime) = &Apache::lonstathelpers::get_time_limits(); + if (defined($starttime) || defined($endtime)) { + # Inform the user what the time limits on the data are. + $Str .= ''.&mt('Statistics on submissions from [_1] to [_2]', + &Apache::lonlocal::locallocaltime($starttime), + &Apache::lonlocal::locallocaltime($endtime) + ).'
'; + } + $Str .= "".&mt('Compiled on [_1]', + &Apache::lonlocal::locallocaltime(time))."
"; + return $Str; +} -=cut ############################################### ############################################### -sub output_html_grouped_by_sequence { - my ($r) = @_; - my $problem_num = 0; - #$r->print(&ProblemStatisticsLegend()); - my @Header = ("Title","Part","#Stdnts","Tries","Mod", - "Mean","#YES","#yes","%Wrng","DoDiff", - "S.D.","Skew.");#,"D.F.1st","D.F.2nd"); - # #FFFFE6 #EEFFCC #DDFFFF FFDDDD #DDFFDD #FFDDFF - foreach my $sequence (&Apache::lonstatistics::Sequences_with_Assess()) { - next if ($sequence->{'num_assess'}<1); - $r->print("".$sequence->{'title'}."
"); - $r->print(''."\n");
- $r->print('
|
'. + &mt('Unable to plot the requested statistic.'). + '
'); + return; + } # - my $sortby = undef; - foreach (@Header) { - if ($ENV{'form.sortby'} eq $_) { - $sortby = $_; + # Build up the data sets to plot + my @Labels; + my @Data; + my $max = 1; + foreach my $data (@StatsArray) { + push(@Labels,$data->{'problem_num'}); + push(@Data,$data->{$datafield}); + if ($data->{$datafield}>$max) { + $max = $data->{$datafield}; } } - if (! defined($sortby) || $sortby eq '') { - $sortby = 'Container'; - } - # If there is more than one sequence, list their titles - my @Sequences = &Apache::lonstatistics::Sequences_with_Assess(); - if (@Sequences > 1) { - unshift(@Header,"Container"); - $show_container = 1; + foreach (1,2,3,4,5,10,15,20,25,40,50,75,100,150,200,250,300,500,600,750, + 1000,1500,2000,2500,3000,3500,4000,5000,7500,10000,15000,20000) { + if ($max <= $_) { + $max = $_; + last; + } } - # - # If the option for showing the problem number is needed, push that - # on the list too - if (defined($option) && $option =~ /show probnum/) { - unshift(@Header,"P#"); + if ($max > 20000) { + $max = 10000*(int($max/10000)+1); } # - $r->print('| '."\n");
- $r->rflush();
- #
- # Compile the data
- my @Statsarray;
- foreach my $sequence (@Sequences) {
- next if ($sequence->{'num_assess'}<1);
- foreach my $resource (@{$sequence->{'contents'}}) {
- next if ($resource->{'type'} ne 'assessment');
- foreach my $part (@{$resource->{'parts'}}) {
- $problem_num++;
- my ($num,$tries,$mod,$mean,$Solved,$solved,$DegOfDiff,$STD,
- $SKEW) = &get_statistics($resource->{'symb'},$part);
- #
- $show_part = 1 if ($part ne '0');
- $part = ' ' if ($part == 0);
- #
- my $wrongpercent = 0;
- if (defined($num) && $num > 0) {
- $wrongpercent=int(10*100*($num-$Solved+$solved)/$num)/10;
- }
- push (@Statsarray,
- { 'sequence' => $sequence,
- 'resource' => $resource,
- 'Title' => $resource->{'title'},
- 'Part' => $part,
- '#Stdnts' => $num,
- 'Tries' => $tries,
- 'Mod' => $mod,
- 'Mean' => $mean,
- '#YES' => $Solved,
- '#yes' => $solved,
- '%Wrng' => $wrongpercent,
- 'DoDiff' => $DegOfDiff,
- 'S.D.' => $STD,
- 'Skew' => $SKEW,
- 'problem_num' => $problem_num,
- });
- }
+ $r->print(" ".&Apache::loncommon::DrawBarGraph($title, + 'Problem Number', + $yaxis, + $max, + undef, # colors + \@Labels, + \@Data)." \n"); + return; +} + +sub degrees_plot { + my ($r)=@_; + my $count = scalar(@StatsArray); + my $width = 50 + 10*$count; + $width = 300 if ($width < 300); + my $height = 300; + my $plot = ''; + my $ymax = 0; + my $ymin = 0; + my @Disc; my @Diff; my @Labels; + foreach my $data (@StatsArray) { + push(@Labels,$data->{'problem_num'}); + my $disc = $data->{'deg_of_disc'}; + my $diff = $data->{'deg_of_diff'}; + push(@Disc,$disc); + push(@Diff,$diff); + # + $ymin = $disc if ($ymin > $disc); + $ymin = $diff if ($ymin > $diff); + $ymax = $disc if ($ymax < $disc); + $ymax = $diff if ($ymax < $diff); + } + # + # Make sure we show relevant information. + if ($ymin < 0) { + if (abs($ymin) < 0.05) { + $ymin = 0; + } else { + $ymin = -1; } } - # - # Table Headers - $r->print('
|
'.&Apache::lonxml::xmlparse($r,'web',$plot).'
'.$/; + $r->print($plotresult); return; } +sub plot_dropdown { + my $current = ''; + # + if (defined($ENV{'form.plot'})) { + $current = $ENV{'form.plot'}; + } + # + my @Additional_Plots = ( + { graphable=>'yes', + name => 'degrees', + title => 'DoDisc and DoDiff' }, + { graphable=>'yes', + name => 'tries statistics', + title => 'Mean and S.D. of Tries' }); + # + my $Str= "\n".''."\n"; + return $Str; +} + ############################################### ############################################### - -=pod - -=item &output_excel() - -Presents the statistical data in an Excel 95 compatable spreadsheet file. - -=cut - +## +## Excel output routines +## ############################################### ############################################### -sub output_excel { +sub Excel_output { my ($r) = @_; + $r->print(''.&mt('Preparing Excel Spreadsheet').'
'); + ## + ## Compute the statistics + &compute_all_statistics($r); + my $c = $r->connection; + return if ($c->aborted()); + ## + ## Create the excel workbook my $filename = '/prtspool/'. $ENV{'user.name'}.'_'.$ENV{'user.domain'}.'_'. - time.'_'.rand(1000000000).'.xls'; - # - my $excel_workbook = undef; - my $excel_sheet = undef; - # - my $rows_output = 0; - my $cols_output = 0; + time.'_'.rand(1000000000).'.xls'; + my ($starttime,$endtime) = &Apache::lonstathelpers::get_time_limits(); # # Create sheet - $excel_workbook = Spreadsheet::WriteExcel->new('/home/httpd'.$filename); + my $excel_workbook = Spreadsheet::WriteExcel->new('/home/httpd'.$filename); # # Check for errors if (! defined($excel_workbook)) { $r->log_error("Error creating excel spreadsheet $filename: $!"); - $r->print("Problems creating new Excel file. ". + $r->print(&mt("Problems creating new Excel file. ". "This error has been logged. ". - "Please alert your LON-CAPA administrator"); - return ; + "Please alert your LON-CAPA administrator.")); + return 0; } # # The excel spreadsheet stores temporary data in files, then put them @@ -581,7 +810,12 @@ sub output_excel { if (length($sheetname) > 31) { $sheetname = substr($sheetname,0,31); } - $excel_sheet = $excel_workbook->addworksheet($sheetname); + my $excel_sheet = $excel_workbook->addworksheet( + &Apache::loncommon::clean_excel_name($sheetname)); + ## + ## Begin creating excel sheet + ## + my ($rows_output,$cols_output) = (0,0); # # Put the course description in the header $excel_sheet->write($rows_output,$cols_output++, @@ -608,6 +842,21 @@ sub output_excel { $excel_sheet->write($rows_output,$cols_output++,$sectionstring); $cols_output += scalar(@Sections); # + # Time restrictions + my $time_string; + if (defined($starttime)) { + # call localtime but not lonlocal:locallocaltime because excel probably + # cannot handle localized text. Probably. + $time_string .= 'Data collected from '.localtime($time_string); + if (defined($endtime)) { + $time_string .= ' to '.localtime($endtime); + } + $time_string .= '.'; + } elsif (defined($endtime)) { + # See note above about lonlocal:locallocaltime + $time_string .= 'Data collected before '.localtime($endtime).'.'; + } + # # Put the date in there too $excel_sheet->write($rows_output,$cols_output++, 'Compiled on '.localtime(time)); @@ -615,242 +864,235 @@ sub output_excel { $rows_output++; $cols_output=0; # - # Add the headers - my @Header = ("Container","Title","Part","#Stdnts","Tries","Mod", - "Mean","#YES","#yes","%Wrng","DoDiff", - "S.D.","Skew.");#,"D.F.1st","D.F.2nd"); - foreach (@Header) { - $excel_sheet->write($rows_output,$cols_output++,$_); + # Long Headers + foreach my $field (@Fields) { + next if ($field->{'name'} eq 'problem_num'); + if (exists($field->{'long_title'})) { + $excel_sheet->write($rows_output,$cols_output++, + $field->{'long_title'}); + } else { + $excel_sheet->write($rows_output,$cols_output++,''); + } } $rows_output++; - # - # Write the data - foreach my $sequence (&Apache::lonstatistics::Sequences_with_Assess()) { - next if ($sequence->{'num_assess'}<1); - foreach my $resource (@{$sequence->{'contents'}}) { - next if ($resource->{'type'} ne 'assessment'); - foreach my $part (@{$resource->{'parts'}}) { - $cols_output=0; - my ($num,$tries,$mod,$mean,$Solved,$solved,$DegOfDiff,$STD, - $SKEW) = &get_statistics($resource->{'symb'},$part); - # - if (!defined($part) || $part eq '') { - $part = ' '; - } - my $wrongpercent = 0; - if (defined($num) && $num > 0) { - $wrongpercent=int(10*100*($num-$Solved+$solved)/$num)/10; - } - foreach ($sequence->{'title'},$resource->{'title'},$part, - $num,$tries,$mod,$mean,$Solved,$solved,$wrongpercent, - $DegOfDiff,$STD,$SKEW) { - $excel_sheet->write($rows_output,$cols_output++,$_); - } - $rows_output++; - } + $cols_output=0; + # Brief headers + foreach my $field (@Fields) { + next if ($field->{'name'} eq 'problem_num'); + # Use english for excel as I am not sure how well excel handles + # other character sets.... + $excel_sheet->write($rows_output,$cols_output++,$field->{'title'}); + } + $rows_output++; + foreach my $data (@StatsArray) { + $cols_output=0; + foreach my $field (@Fields) { + next if ($field->{'name'} eq 'problem_num'); + $excel_sheet->write($rows_output,$cols_output++, + $data->{$field->{'name'}}); } + $rows_output++; } # - # Write the excel file $excel_workbook->close(); + # # Tell the user where to get their excel file $r->print(''. - 'Your Excel spreadsheet.'."\n"); + ''. + &mt('Your Excel Spreadsheet').''."\n"); $r->rflush(); return; } -############################################### -############################################### +################################################## +################################################## +## +## Statistics Gathering and Manipulation Routines +## +################################################## +################################################## +sub compute_statistics_on_sequence { + my ($seq) = @_; + my @Data; + foreach my $res (@{$seq->{'contents'}}) { + next if ($res->{'type'} ne 'assessment'); + foreach my $part (@{$res->{'parts'}}) { + # + # This is where all the work happens + my $data = &get_statistics($seq,$res,$part,scalar(@StatsArray)+1); + push (@Data,$data); + push (@StatsArray,$data); + } + } + return @Data; +} -=pod +sub compute_all_statistics { + my ($r) = @_; + if (@StatsArray > 0) { + # Assume we have already computed the statistics + return; + } + my $c = $r->connection; + foreach my $seq (&Apache::lonstatistics::Sequences_with_Assess()) { + last if ($c->aborted); + next if ($seq->{'num_assess'} < 1); + &compute_statistics_on_sequence($seq); + } +} -=item &statistics_html_table_data() +sub sort_data { + my ($sortkey) = @_; + return if (! @StatsArray); + # + # Sort the data + my $sortby = undef; + foreach my $field (@Fields) { + if ($sortkey eq $field->{'name'}) { + $sortby = $field->{'name'}; + } + } + if (! defined($sortby) || $sortby eq '' || $sortby eq 'problem_num') { + $sortby = 'container'; + } + if ($sortby ne 'container') { + # $sortby is already defined, so we can charge ahead + if ($sortby =~ /^(title|part)$/i) { + # Alpha comparison + @StatsArray = sort { + lc($a->{$sortby}) cmp lc($b->{$sortby}) || + lc($a->{'title'}) cmp lc($b->{'title'}) || + lc($a->{'part'}) cmp lc($b->{'part'}); + } @StatsArray; + } else { + # Numerical comparison + @StatsArray = sort { + my $retvalue = 0; + if ($b->{$sortby} eq 'nan') { + if ($a->{$sortby} ne 'nan') { + $retvalue = -1; + } else { + $retvalue = 0; + } + } + if ($a->{$sortby} eq 'nan') { + if ($b->{$sortby} ne 'nan') { + $retvalue = 1; + } + } + if ($retvalue eq '0') { + $retvalue = $b->{$sortby} <=> $a->{$sortby} || + lc($a->{'title'}) <=> lc($b->{'title'}) || + lc($a->{'part'}) <=> lc($b->{'part'}); + } + $retvalue; + } @StatsArray; + } + } + # + # Renumber the data set + my $count; + foreach my $data (@StatsArray) { + $data->{'problem_num'} = ++$count; + } + return; +} -Help function used to format the rows for HTML table output. +######################################################## +######################################################## -=cut +=pod -############################################### -############################################### -sub statistics_html_table_data { - my ($resource,$part,$num,$tries,$mod,$mean,$Solved,$solved,$wrongpercent, - $DegOfDiff,$STD,$SKEW,$options) = @_; - my $row = ''; - $row .= '
".&DrawGraph(\@Data,$title,'Problem Number',$yaxis, - $Max)."
\n"); + my $data = &Apache::loncoursedata::get_problem_statistics + (\@Apache::lonstatistics::SelectedSections, + $Apache::lonstatistics::enrollment_status, + $symb,$part,$courseid,$starttime,$endtime); + $data->{'part'} = $part; + $data->{'problem_num'} = $problem_num; + $data->{'container'} = $sequence->{'title'}; + $data->{'title'} = $resource->{'title'}; + $data->{'title.link'} = $resource->{'src'}.'?symb='. + &Apache::lonnet::escape($resource->{'symb'}); # - # Print out the data - $ENV{'form.sortby'} = 'Contents'; - &output_html_ungrouped($r,'show probnum'); - return; + $data->{'deg_of_disc'} = &compute_discrimination_factor($resource,$part,$sequence); + return $data; } + ############################################### ############################################### -=pod +=pod + +=item &compute_discrimination_factor() -=item &DrawGraph() +Inputs: $Resource, $Sequence + +Returns: integer between -1 and 1 =cut ############################################### ############################################### -sub DrawGraph { - my ($values,$title,$xaxis,$yaxis,$Max)=@_; - $title = '' if (! defined($title)); - $xaxis = '' if (! defined($xaxis)); - $yaxis = '' if (! defined($yaxis)); - # - my $sendValues = join(',', @$values); - my $sendCount = scalar(@$values); - if ( $Max > 1 ) { - if ($Max % 10) { - if ( int($Max) < $Max ) { - $Max++; - $Max = int($Max); - } - } - } else { - $Max = 1; - } - my @GData = ($title,$xaxis,$yaxis,$Max,$sendCount,$sendValues); - return ').')
';
-}
-
-sub get_statistics {
- my ($symb,$part) = @_;
- #
- my $courseid = $ENV{'request.course.id'};
- #
- my $students = \@Apache::lonstatistics::Students;
- if ($Apache::lonstatistics::SelectedSections[0] eq 'all') {
- $students = undef;
- }
- my @Results = &Apache::loncoursedata::get_problem_statistics
- ($students,$symb,$part,$courseid);
- return @Results;
+sub compute_discrimination_factor {
+ my ($resource,$part,$sequence) = @_;
+ my @Resources;
+ foreach my $res (@{$sequence->{'contents'}}) {
+ next if ($res->{'symb'} eq $resource->{'symb'});
+ push (@Resources,$res->{'symb'});
+ }
+ #
+ # rank
+ my $ranking =
+ &Apache::loncoursedata::rank_students_by_scores_on_resources
+ (\@Resources,
+ \@Apache::lonstatistics::SelectedSections,
+ $Apache::lonstatistics::enrollment_status,undef);
+ #
+ # compute their percent scores on the problems in the sequence,
+ my $number_to_grab = int(scalar(@{$ranking})/4);
+ my $num_students = scalar(@{$ranking});
+ my @BottomSet = map { $_->[&Apache::loncoursedata::RNK_student()];
+ } @{$ranking}[0..$number_to_grab];
+ my @TopSet =
+ map {
+ $_->[&Apache::loncoursedata::RNK_student()];
+ } @{$ranking}[($num_students-$number_to_grab)..($num_students-1)];
+ my ($bottom_sum,$bottom_max) =
+ &Apache::loncoursedata::get_sum_of_scores($resource,$part,\@BottomSet);
+ my ($top_sum,$top_max) =
+ &Apache::loncoursedata::get_sum_of_scores($resource,$part,\@TopSet);
+ my $deg_of_disc;
+ if ($top_max == 0 || $bottom_max==0) {
+ $deg_of_disc = 'nan';
+ } else {
+ $deg_of_disc = ($top_sum/$top_max) - ($bottom_sum/$bottom_max);
+ }
+ #&Apache::lonnet::logthis(' '.$top_sum.'/'.$top_max.
+ # ' - '.$bottom_sum.'/'.$bottom_max);
+ return $deg_of_disc;
}
###############################################
@@ -858,68 +1100,170 @@ sub get_statistics {
=pod
-=item &ProblemStatisticsLegend()
+=item ProblemStatisticsLegend
+
+=over 4
+
+=item #Stdnts
+Total number of students attempted the problem.
+
+=item Tries
+Total number of tries for solving the problem.
+
+=item Max Tries
+Largest number of tries for solving the problem by a student.
+
+=item Mean
+Average number of tries. [ Tries / #Stdnts ]
+
+=item #YES
+Number of students solved the problem correctly.
+
+=item #yes
+Number of students solved the problem by override.
+
+=item %Wrong
+Percentage of students who tried to solve the problem
+but is still incorrect. [ 100*((#Stdnts-(#YES+#yes))/#Stdnts) ]
+
+=item DoDiff
+Degree of Difficulty of the problem.
+[ 1 - ((#YES+#yes) / Tries) ]
+
+=item S.D.
+Standard Deviation of the tries.
+[ sqrt(sum((Xi - Mean)^2)) / (#Stdnts-1)
+where Xi denotes every student\'s tries ]
+
+=item Skew.
+Skewness of the students tries.
+[(sqrt( sum((Xi - Mean)^3) / #Stdnts)) / (S.D.^3)]
+
+=item Dis.F.
+Discrimination Factor: A Standard for evaluating the
+problem according to a Criterion+ +=item [Criterion to group students into %27 Upper Students - +and %27 Lower Students] +1st Criterion for Sorting the Students: +Sum of Partial Credit Awarded / Total Number of Tries +2nd Criterion for Sorting the Students: +Total number of Correct Answers / Total Number of Tries + +=item Disc. +Number of Students had at least one discussion. + +=back =cut -############################################### -############################################### -sub ProblemStatisticsLegend { - my $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 .= '[Criterion to group students into %27 Upper Students - '; - $Ptr .= 'and %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 .= ' |
| Disc. | '; - $Ptr .= 'Number of Students had at least one discussion.'; - $Ptr .= ' |