# The LearningOnline Network with CAPA
#
# $Id: lonproblemstatistics.pm,v 1.64 2004/01/28 14:38:40 matthew 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
#
###############################################
###############################################

=pod

=head1 NAME

lonproblemstatistics

=head1 SYNOPSIS

Routines to present problem statistics to instructors via tables,
Excel files, and plots.

=over 4

=cut

###############################################
###############################################

package Apache::lonproblemstatistics;

use strict;
use Apache::lonnet();
use Apache::loncommon();
use Apache::lonhtmlcommon;
use Apache::loncoursedata;
use Apache::lonstatistics;
use Apache::lonlocal;
use Spreadsheet::WriteExcel;

##
## Localization notes:
##
## in @Fields[0]->{'long_title'} is placed in Excel files and is used as the
## header for plots created with Graph.pm, both of which more than likely do
## not support localization.
##
my @Fields = (
           { name => 'problem_num',
             title => 'P#',
             align => 'right',
             color => '#FFFFE6' },
           { name   => 'container',
             title  => 'Sequence or Folder',
             align  => 'left',
             color  => '#FFFFE6',
             sortable => 'yes' },
           { name   => 'title',
             title  => 'Title',
             align  => 'left',
             color  => '#FFFFE6',
             special  => 'link',
             sortable => 'yes', },
           { name   => 'part', 
             title  => 'Part',
             align  => 'left',
             color  => '#FFFFE6',
             },
           { name   => 'num_students',
             title  => '#Stdnts',
             align  => 'right',
             color  => '#EEFFCC',
             format => '%d',
             sortable  => 'yes',
             graphable => 'yes',
             long_title => 'Number of Students Attempting Problem' },
           { name   => 'tries',
             title  => 'Tries',
             align  => 'right',
             color  => '#EEFFCC',
             format => '%d',
             sortable  => 'yes',
             graphable => 'yes',
             long_title => 'Total Number of Tries' },
           { name   => 'max_tries',
             title  => 'Max Tries',
             align  => 'right',
             color  => '#DDFFFF',
             format => '%d',
             sortable  => 'yes',
             graphable => 'yes',
             long_title => 'Maximum Number of Tries' },
           { name   => 'mean_tries',
             title  => 'Mean Tries',
             align  => 'right',
             color  => '#DDFFFF',
             format => '%5.2f',
             sortable  => 'yes',
             graphable => 'yes',
             long_title => 'Average Number of Tries' },
           { name   => 'std_tries',
             title  => 'S.D. tries',
             align  => 'right',
             color  => '#DDFFFF',
             format => '%5.2f',
             sortable  => 'yes',
             graphable => 'yes',
             long_title => 'Standard Deviation of Number of Tries' },
           { name   => 'skew_tries',
             title  => 'Skew Tries',
             align  => 'right',
             color  => '#DDFFFF',
             format => '%5.2f',
             sortable  => 'yes',
             graphable => 'yes',
             long_title => 'Skew of Number of Tries' },
           { name   => 'deg_of_diff',
             title  => 'DoDiff',
             align  => 'right',
             color  => '#DDFFFF',
             format => '%5.2f',
             sortable  => 'yes',
             graphable => 'yes',
             long_title => 'Degree of Difficulty'.
                           '[ 1 - ((#YES+#yes) / Tries) ]'},
           { name   => 'num_solved',
             title  => '#YES',
             align  => 'right',
             color  => '#FFDDDD',
             format => '%4.1f',#             format => '%d',
             sortable  => 'yes',
             graphable => 'yes',
             long_title => 'Number of Students able to Solve' },
           { name   => 'num_override',
             title  => '#yes',
             align  => 'right',
             color  => '#FFDDDD',
             format => '%4.1f',#             format => '%d',
             sortable  => 'yes',
             graphable => 'yes',
             long_title => 'Number of Students given Override' },
           { name   => 'per_wrong',
             title  => '%Wrng',
             align  => 'right',
             color  => '#FFFFE6',
             format => '%4.1f',
             sortable  => 'yes',
             graphable => 'yes',
             long_title => 'Percent of students whose final answer is wrong' },
);

###############################################
###############################################

=pod 

=item &CreateInterface()

Create the main intereface for the statistics page.  Allows the user to
select sections, maps, and output.

=cut

###############################################
###############################################
my @OutputOptions = 
    (
     { name  => 'problem statistics grouped by sequence',
       value => 'HTML problem statistics grouped',
       description => 'Output statistics for the problem parts.',
       mode => 'html',
       show => 'grouped',
     },
     { name  => 'problem statistics ungrouped',
       value => 'HTML problem statistics ungrouped',
       description => 'Output statistics for the problem parts.',
       mode => 'html',
       show => 'ungrouped',
     },
     { name  => 'problem statistics, Excel',
       value => 'Excel problem statistics',
       description => 'Output statistics for the problem parts '.
           'in an Excel workbook',
       mode => 'excel',
       show => 'all',
     },
     );

sub CreateInterface {
    my $Str = '';
    $Str .= '<h2>Overall Problem Statistics'.
        &Apache::loncommon::help_open_topic('Statistics_Overall_Key').
        '</h2>'."\n";
    $Str .= '<table cellspacing="5">'."\n";
    $Str .= '<tr>';
    $Str .= '<td align="center"><b>'.&mt('Sections').'</b></td>';
    $Str .= '<td align="center"><b>'.&mt('Enrollment Status').'</b></td>';
    $Str .= '<td align="center"><b>'.&mt('Sequences and Folders').'</b></td>';
    $Str .= '<td align="center"><b>'.&mt('Output').'</b></td>';
    $Str .= '</tr>'."\n";
    #
    $Str .= '<tr><td align="center">'."\n";
    $Str .= &Apache::lonstatistics::SectionSelect('Section','multiple',5);
    $Str .= '</td><td align="center">';
    $Str .= &Apache::lonhtmlcommon::StatusOptions(undef,undef,5);
    $Str .= '</td><td align="center">';
    #
    my $only_seq_with_assessments = sub { 
        my $s=shift;
        if ($s->{'num_assess'} < 1) { 
            return 0;
        } else { 
            return 1;
        }
    };
    $Str .= &Apache::lonstatistics::MapSelect('Maps','multiple,all',5,
                                              $only_seq_with_assessments);
    $Str .= '</td><td>'."\n";
    my ($html,$outputmode,$show) = 
        &Apache::lonstatistics::CreateAndParseOutputSelector(
                                            'statsoutputmode',
                                            'HTML problem statistics grouped',
                                            @OutputOptions);
    $Str .= $html;
    $Str .= '</td></tr>'."\n";
    $Str .= '</table>'."\n";
    $Str .= '<input type="submit" name="GenerateStatistics" value="'.
        &mt('Generate Statistics').'" />';
    $Str .= '&nbsp;'x5;
    $Str .= '<input type="submit" name="ClearCache" value="'.
        &mt('Clear Caches').'" />';
    $Str .= '&nbsp;'x5;
    return ($Str,$outputmode,$show);
}

###############################################
###############################################

=pod 

=item &BuildProblemStatisticsPage()

Main interface to problem statistics.

=cut

###############################################
###############################################
sub BuildProblemStatisticsPage {
    my ($r,$c)=@_;
    #
    my %Saveable_Parameters = ('Status' => 'scalar',
                               'statsoutputmode' => 'scalar',
                               'Section' => 'array',
                               'StudentData' => 'array',
                               'Maps' => 'array');
    &Apache::loncommon::store_course_settings('statistics',
                                              \%Saveable_Parameters);
    &Apache::loncommon::restore_course_settings('statistics',
                                                \%Saveable_Parameters);
    #
    &Apache::lonstatistics::PrepareClasslist();
    #
    my ($interface,$output_mode,$show) = &CreateInterface();
    $r->print($interface);
    $r->print('<input type="hidden" name="statsfirstcall" value="no" />');
    $r->print('<input type="hidden" name="sortby" value="'.$ENV{'form.sortby'}.
              '" />');
    $r->print('<input type="hidden" name="plot" value="" />');
    if (! exists($ENV{'form.statsfirstcall'})) {
        return;
    }
    #
    &Apache::lonstatistics::Gather_Student_Data($r);
    #
    #
    if ($output_mode eq 'html') {
        $r->print("<h2>".
                  $ENV{'course.'.$ENV{'request.course.id'}.'.description'}.
                  "</h2>\n");
        $r->print("<h3>".localtime(time)."</h3>");
        $r->rflush();
        if ($show eq 'grouped') {
            &output_html_grouped_by_sequence($r);
        } elsif ($show eq 'ungrouped') {
            &output_html_ungrouped($r);
        }
    } elsif ($output_mode eq 'excel') {
        $r->print('<h2>'.&mt('Preparing Excel Spreadsheet').'</h2>');
        &output_excel($r);
    } else {
        $r->print('<h1>'.&mt('Not implemented').'</h1>');
    }
    return;
}

###############################################
###############################################

=pod 

=item &output_html_grouped_by_sequence()

Presents the statistics data as an html table organized by the order
the assessments appear in the course.

=cut

###############################################
###############################################
sub output_html_grouped_by_sequence {
    my ($r) = @_;
    my $problem_num = 0;
    #$r->print(&ProblemStatisticsLegend());
    foreach my $sequence (&Apache::lonstatistics::Sequences_with_Assess()) {
        next if ($sequence->{'num_assess'}<1);
        $r->print("<h3>".$sequence->{'title'}."</h3>");
        $r->print('<table border="0"><tr><td bgcolor="#777777">'."\n");
        $r->print('<table border="0" cellpadding="3">'."\n");
        $r->print('<tr bgcolor="#FFFFE6">');
        my $Str = &statistics_table_header('no container no plots');
        $r->print('<tr bgcolor="#FFFFE6">'.$Str."</tr>\n");
        foreach my $resource (@{$sequence->{'contents'}}) {
            next if ($resource->{'type'} ne 'assessment');
            foreach my $part (@{$resource->{'parts'}}) {
                $problem_num++;
                my $data = &get_statistics($sequence,$resource,$part,
                                           $problem_num);
                my $option = '';
                $r->print('<tr>'.&statistics_html_table_data($data,
                                                             'no container').
                          "</tr>\n");
            }
        }
        $r->print("</table>\n");
        $r->print("</td></tr></table>\n");
        $r->rflush();
    }
    #
    return;
}

###############################################
###############################################

=pod 

=item &output_html_ungrouped()

Presents the statistics data in a single html table which can be sorted by
different columns.

=cut

###############################################
###############################################
sub output_html_ungrouped {
    my ($r,$option) = @_;
    #
    if (exists($ENV{'form.plot'}) && $ENV{'form.plot'} ne '') {
        &plot_statistics($r,$ENV{'form.plot'});
    }
    #
    my $problem_num = 0;
    my $show_container = 0;
    my $show_part = 0;
    #$r->print(&ProblemStatisticsLegend());
    my $sortby = undef;
    foreach my $field (@Fields) {
        if ($ENV{'form.sortby'} eq $field->{'name'}) {
            $sortby = $field->{'name'};
        }
    }
    if (! defined($sortby) || $sortby eq '' || $sortby eq 'problem_num') {
        $sortby = 'container';
    }
    # If there is more than one sequence, list their titles
    my @Sequences = &Apache::lonstatistics::Sequences_with_Assess();
    if (@Sequences < 1) {
        $option .= ' no container';
    }
    #
    # 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 $data = &get_statistics($sequence,$resource,$part,
                                           $problem_num);
                $show_part = 1 if ($part ne '0');
                #
                push (@Statsarray,$data);
            }
        }
    }
    #
    # Sort the data
    my @OutputOrder;
    if ($sortby eq 'container') {
        @OutputOrder = @Statsarray;
    } else {
        # $sortby is already defined, so we can charge ahead
        if ($sortby =~ /^(title|part)$/i) {
            # Alpha comparison
            @OutputOrder = sort {
                lc($a->{$sortby}) cmp lc($b->{$sortby}) ||
                    lc($a->{'title'}) cmp lc($b->{'title'}) ||
                        lc($a->{'part'}) cmp lc($b->{'part'});
            } @Statsarray;
        } else {
            # Numerical comparison
            @OutputOrder = 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;
        }
    }
    $option .= 'no part' if (! $show_part);
    my $num_output = 0;
    #
    # output the headers
    $r->print('<table border="0"><tr><td bgcolor="#777777">'."\n");
    $r->print('<table border="0" cellpadding="3">'."\n");
    my $Str = &statistics_table_header($option.' sortable');
    $r->print('<tr bgcolor="#FFFFE6">'.$Str."</tr>\n");
    #
    foreach my $rowdata (@OutputOrder) {
        $num_output++;
        if ($num_output % 25 == 0) {
            $r->print("</table>\n</td></tr></table>\n");
            #
            $r->print('<table border="0"><tr><td bgcolor="#777777">'."\n");
            $r->print('<table border="0" cellpadding="3">'."\n");
            my $Str = &statistics_table_header($option.' sortable');
            $r->print('<tr bgcolor="#FFFFE6">'.$Str."</tr>\n");
            $r->rflush();
        }
        $r->print('<tr>'.&statistics_html_table_data($rowdata,$option).
                  "</tr>\n");
    }
    $r->print("</table>\n");
    $r->print("</td></tr></table>\n");
    $r->rflush();
    #
    return;
}

###############################################
###############################################

=pod 

=item &output_excel()

Presents the statistical data in an Excel 95 compatable spreadsheet file.

=cut

###############################################
###############################################
sub output_excel {
    my ($r) = @_;
    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;
    #
    # Create sheet
    $excel_workbook = Spreadsheet::WriteExcel->new('/home/httpd'.$filename);
    #
    # Check for errors
    if (! defined($excel_workbook)) {
        $r->log_error("Error creating excel spreadsheet $filename: $!");
        $r->print(&mt("Problems creating new Excel file.  ".
                  "This error has been logged.  ".
                  "Please alert your LON-CAPA administrator."));
        return ;
    }
    #
    # The excel spreadsheet stores temporary data in files, then put them
    # together.  If needed we should be able to disable this (memory only).
    # The temporary directory must be specified before calling 'addworksheet'.
    # File::Temp is used to determine the temporary directory.
    $excel_workbook->set_tempdir($Apache::lonnet::tmpdir);
    #
    # Add a worksheet
    my $sheetname = $ENV{'course.'.$ENV{'request.course.id'}.'.description'};
    if (length($sheetname) > 31) {
        $sheetname = substr($sheetname,0,31);
    }
    $excel_sheet = $excel_workbook->addworksheet(
                       &Apache::loncommon::clean_excel_name($sheetname)
                                                 );
    #
    # Put the course description in the header
    $excel_sheet->write($rows_output,$cols_output++,
                   $ENV{'course.'.$ENV{'request.course.id'}.'.description'});
    $cols_output += 3;
    #
    # Put a description of the sections listed
    my $sectionstring = '';
    my @Sections = @Apache::lonstatistics::SelectedSections;
    if (scalar(@Sections) > 1) {
        if (scalar(@Sections) > 2) {
            my $last = pop(@Sections);
            $sectionstring = "Sections ".join(', ',@Sections).', and '.$last;
        } else {
            $sectionstring = "Sections ".join(' and ',@Sections);
        }
    } else {
        if ($Sections[0] eq 'all') {
            $sectionstring = "All sections";
        } else {
            $sectionstring = "Section ".$Sections[0];
        }
    }
    $excel_sheet->write($rows_output,$cols_output++,$sectionstring);
    $cols_output += scalar(@Sections);
    #
    # Put the date in there too
    $excel_sheet->write($rows_output,$cols_output++,
                        'Compiled on '.localtime(time));
    #
    $rows_output++; 
    $cols_output=0;
    #
    # Long Headersheaders
    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++;
    $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++;
    #
    # Write the data
    my $problem_num=0;
    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;
                $problem_num++;
                my $data = &get_statistics($sequence,$resource,$part,
                                           $problem_num);
                #
                if (!defined($part) || $part eq '') {
                    $part = ' ';
                }
                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
    $r->print('<br />'.
              '<a href="'.$filename.'">'.
              &mt('Your Excel Spreadsheet').'</a>'."\n");
    $r->rflush();
    return;
}

###############################################
###############################################

=pod 

=item &statistics_html_table_data()

Help function used to format the rows for HTML table output.

=cut

###############################################
###############################################
sub statistics_html_table_data {
    my ($data,$options) = @_;
    my $row = '';
    foreach my $field (@Fields) {
        next if ($options =~ /no $field->{'name'}/);
        $row .= '<td bgcolor="'.$field->{'color'}.'"';
        if (exists($field->{'align'})) {
            $row .= ' align="'.$field->{'align'}.'"';
            }
        $row .= '>';
        if (exists($field->{'special'}) && $field->{'special'} eq 'link') {
            $row .= '<a href="'.$data->{$field->{'name'}.'.link'}.'">';
        }
        if (exists($field->{'format'})) {
            $row .= sprintf($field->{'format'},$data->{$field->{'name'}});
        } else {
            $row .= $data->{$field->{'name'}};
        }
        if (exists($field->{'special'}) && $field->{'special'} eq 'link') {
            $row.= '</a>';
        }
        $row .= '</td>';
    }
    return $row;
}

sub statistics_table_header {
    my ($options) = @_;
    my $header_row;
    foreach my $field (@Fields) {
        next if ($options =~ /no $field->{'name'}/);
        $header_row .= '<th>';
        if ($options =~ /sortable/ && 
            exists($field->{'sortable'}) && $field->{'sortable'} eq 'yes') {
            $header_row .= '<a href="javascript:'.
                'document.Statistics.sortby.value='."'".$field->{'name'}."'".
                    ';document.Statistics.submit();">';
        }
        $header_row .= &mt($field->{'title'});
        if ($options =~ /sortable/) {
            $header_row.= '</a>';
        }
        if ($options !~ /no plots/        && 
            exists($field->{'graphable'}) && 
            $field->{'graphable'} eq 'yes') {
            $header_row.=' (';
            $header_row .= '<a href="javascript:'.
                "document.Statistics.plot.value='$field->{'name'}'".
                    ';document.Statistics.submit();">';
            $header_row .= &mt('plot').'</a>)';
        }
        $header_row .= '</th>';
    }
    return $header_row;
}

###############################################
###############################################

=pod 

=item &plot_statistics()

=cut

###############################################
###############################################
sub plot_statistics {
    my ($r,$datafield) = @_;
    my @Data;
    #
    #
    my $sortfield = undef;
    my $title = undef;
    foreach my $field (@Fields) {
        if ($datafield eq $field->{'name'} &&
            exists($field->{'graphable'}) && $field->{'graphable'} eq 'yes') {
            $sortfield = $field->{'name'};
            $title = $field->{'long_title'};
        }
    }
    return if (! defined($sortfield) || $sortfield eq '');
    #
    my $Max = 0;
    my $problem_num = 0;
    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'}}) {
                my $problem_number++;
                my $data = &get_statistics($sequence,$resource,$part,
                                           $problem_num);
                my $value = $data->{$sortfield};
                $Max = $value if ($Max < $value);
                push (@Data,$value);
            }
        }
    }
    #
    # Print out plot request
    my $yaxis = '';
    if ($sortfield eq 'per_wrong') {
        $yaxis = 'Percent';
    }
    #
    # Determine appropriate value for $Max
    if ($sortfield eq 'deg_of_diff') {
        if ($Max > 0.5) {
            $Max = 1;
        } elsif ($Max > 0.2) {
            $Max = 0.5;
        } elsif ($Max > 0.1) {
            $Max = 0.2;
        }
    } elsif ($sortfield eq 'per_wrong') {
        if ($Max > 50) {
            $Max = 100;
        } elsif ($Max > 25) {
            $Max = 50;
        } elsif ($Max > 20) {
            $Max = 25;
        } elsif ($Max > 10) {
            $Max = 20;
        } elsif ($Max > 5) {
            $Max = 10;
        } else {
            $Max = 5;
        }
    }
    
    $r->print("<p>".&Apache::loncommon::DrawBarGraph($title,
                                                     'Problem Number',
                                                     $yaxis,
                                                     $Max,
                                                     undef,
                                                     \@Data)."</p>\n");
    #
    # Print out the data
    $ENV{'form.sortby'} = 'Contents';
#    &output_html_ungrouped($r);
    return;
}

sub get_statistics {
    my ($sequence,$resource,$part,$problem_num) = @_;
    #
    my $symb = $resource->{'symb'};
    my $courseid = $ENV{'request.course.id'};
    #
    my $students = \@Apache::lonstatistics::Students;
    if ($Apache::lonstatistics::SelectedSections[0] eq 'all') {
        $students = undef;
    }
    my $data = &Apache::loncoursedata::get_problem_statistics
                        ($students,$symb,$part,$courseid);
    $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'});
    #
    return $data;
}

###############################################
###############################################

=pod 

=item &ProblemStatisticsLegend()

HELP  This needs to be localized, or at least generated automatically.

=cut

###############################################
###############################################
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>Max Tries</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>[Criterion to group students into %27 Upper Students - ';
    $Ptr .= 'and %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;
}

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

1;
__END__