NAME
    Statistics::Contingency - Calculate precision, recall, F1, accuracy, etc.

SYNOPSIS
     use Statistics::Contingency;
     my $s = new Statistics::Contingency(categories => \@all_categories);
 
     while (...something...) {
       ...
       $s->add_result($assigned_categories, $correct_categories);
     }
 
     print "Micro F1: ", $s->micro_F1, "\n"; # Access a single statistic
     print $s->stats_table; # Show several stats in table form

DESCRIPTION
    The "Statistics::Contingency" class helps you calculate several useful
    statistical measures based on 2x2 "contingency tables". I use these measures
    to help judge the results of automatic text categorization experiments, but
    they are useful in other situations as well.

    The general usage flow is to tally a whole bunch of results in the
    "Statistics::Contingency" object, then query that object to obtain the
    measures you are interested in. When all results have been collected, you
    can get a report on accuracy, precision, recall, F1, and so on, with both
    macro-averaging and micro-averaging over categories.

  Macro vs. Micro Statistics

    All of the statistics offered by this module can be calculated for each
    category and then averaged, or can be calculated over all decisions and then
    averaged. The former is called macro-averaging (specifically,
    macro-averaging with respect to category), and the latter is called
    micro-averaging. The two procedures bias the results differently -
    micro-averaging tends to over-emphasize the performance on the largest
    categories, while macro-averaging over-emphasizes the performance on the
    smallest. It's often best to look at both of them to get a good idea of how
    your data distributes across categories.

  Statistics available

    All of the statistics are calculated based on a so-called "contingency
    table", which looks like this:

                  Correct=Y   Correct=N
                +-----------+-----------+
     Assigned=Y |     a     |     b     |
                +-----------+-----------+
     Assigned=N |     c     |     d     |
                +-----------+-----------+

    a, b, c, and d are counts that reflect how the assigned categories matched
    the correct categories. Depending on whether a macro-statistic or a
    micro-statistic is being calculated, these numbers will be tallied
    per-category or for the entire result set.

    The following statistics are available:

    * accuracy
        This measures the portion of all decisions that were correct decisions.
        It is defined as "(a+d)/(a+b+c+d)". It falls in the range from 0 to 1,
        with 1 being the best score.

        Note that macro-accuracy and micro-accuracy will always give the same
        number.

    * error
        This measures the portion of all decisions that were incorrect
        decisions. It is defined as "(b+c)/(a+b+c+d)". It falls in the range
        from 0 to 1, with 0 being the best score.

        Note that macro-error and micro-error will always give the same number.

    * precision
        This measures the portion of the assigned categories that were correct.
        It is defined as "a/(a+b)". It falls in the range from 0 to 1, with 1
        being the best score.

    * recall
        This measures the portion of the correct categories that were assigned.
        It is defined as "a/(a+c)". It falls in the range from 0 to 1, with 1
        being the best score.

    * F1
        This measures an even combination of precision and recall. It is defined
        as "2*p*r/(p+r)". In terms of a, b, and c, it may be expressed as
        "2a/(2a+b+c)". It falls in the range from 0 to 1, with 1 being the best
        score.

    The F1 measure is often the only simple measure that is worth trying to
    maximize on its own - consider the fact that you can get a perfect precision
    score by always assigning zero categories, or a perfect recall score by
    always assigning every category. A truly smart system will assign the
    correct categories and only the correct categories, maximizing precision and
    recall at the same time, and therefore maximizing the F1 score.

    Sometimes it's worth trying to maximize the accuracy score, but accuracy
    (and its counterpart error) are considered fairly crude scores that don't
    give much information about the performance of a categorizer.

METHODS
    The general execution flow when using this class is to create a
    "Statistics::Contingency" object, add a bunch of results to it, and then
    report on the results.

    * $e = Statistics::Contingency->new()
        Returns a new "Statistics::Contingency" object. Expects a "categories"
        parameter specifying the entire set of categories that may be assigned
        during this experiment. Also accepts a "verbose" parameter - if true,
        some diagnostic status information will be displayed when certain
        actions are performed.

    * $e->add_result($assigned_categories, $correct_categories, $name)
        Adds a new result to the experiment. The lists of assigned and correct
        categories can be given as an array of category names (strings), as a
        hash whose keys are the category names and whose values are anything
        logically true, or as a single string if there is only one category.

        If you've already got the lists in hash form, this will be the fastest
        way to pass them. Otherwise, the current implementation will convert
        them to hash form internally in order to make its calculations
        efficient.

        The "$name" parameter is an optional name for this result. It will only
        be used in error messages or debugging/progress output.

        In the current implementation, we only store the contingency tables per
        category, as well as a table for the entire result set. This means that
        you can't recover information about any particular single result from
        the "Statistics::Contingency" object.

    * $e->micro_accuracy
        Returns the micro-averaged accuracy for the data set.

    * $e->micro_error
        Returns the micro-averaged error for the data set.

    * $e->micro_precision
        Returns the micro-averaged precision for the data set.

    * $e->micro_recall
        Returns the micro-averaged recall for the data set.

    * $e->micro_F1
        Returns the micro-averaged F1 for the data set.

    * $e->macro_accuracy
        Returns the macro-averaged accuracy for the data set.

    * $e->macro_error
        Returns the macro-averaged error for the data set.

    * $e->macro_precision
        Returns the macro-averaged precision for the data set.

    * $e->macro_recall
        Returns the macro-averaged recall for the data set.

    * $e->macro_F1
        Returns the macro-averaged F1 for the data set.

    * $e->stats_table
        Returns a string combining several statistics in one graphic table.
        Since accuracy is 1 minus error, we only report error since it takes
        less space to print. An optional argument specifies the number of
        significant digits to show in the data - the default is 3 significant
        digits.

    * $e->category_stats
        Returns a hash reference whose keys are the names of each category, and
        whose values contain the various statistical measures (accuracy, error,
        precision, recall, or F1) about each category as a hash reference. For
        example, to print a single statistic:

         print $e->category_stats->{sports}{recall}, "\n";

        Or to print certain statistics for all categtories:

         my $stats = $e->category_stats;
         while (my ($cat, $value) = each %$stats) {
           print "Category '$cat': \n";
           print "  Accuracy: $value->{accuracy}\n";
           print "  Precision: $value->{precision}\n";
           print "  F1: $value->{F1}\n";
         }

AUTHOR
    Ken Williams <kenw@ee.usyd.edu.au>

COPYRIGHT
    Copyright 2002 Ken Williams. All rights reserved.

    This distribution is free software; you can redistribute it and/or modify it
    under the same terms as Perl itself.

