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<?php
// This file is part of Moodle - http://moodle.org/
//
// Moodle 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 3 of the License, or
// (at your option) any later version.
//
// Moodle 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 Moodle. If not, see <http://www.gnu.org/licenses/>.
namespace quiz_statistics;
defined('MOODLE_INTERNAL') || die();
/**
* Class to calculate and also manage caching of quiz statistics.
*
* These quiz statistics calculations are described here :
*
* http://docs.moodle.org/dev/Quiz_statistics_calculations#Test_statistics
*
* @package quiz_statistics
* @copyright 2013 The Open University
* @author James Pratt me@jamiep.org
* @license http://www.gnu.org/copyleft/gpl.html GNU GPL v3 or later
*/
class calculator {
/**
* @var \core\progress\base
*/
protected $progress;
public function __construct(\core\progress\base $progress = null) {
if ($progress === null) {
$progress = new \core\progress\none();
}
$this->progress = $progress;
}
/**
* Compute the quiz statistics.
*
* @param int $quizid the quiz id.
* @param int $whichattempts which attempts to use, represented internally as one of the constants as used in
* $quiz->grademethod ie.
* QUIZ_GRADEAVERAGE, QUIZ_GRADEHIGHEST, QUIZ_ATTEMPTLAST or QUIZ_ATTEMPTFIRST
* we calculate stats based on which attempts would affect the grade for each student.
* @param \core\dml\sql_join $groupstudentsjoins Contains joins, wheres, params for students in this group.
* @param int $p number of positions (slots).
* @param float $sumofmarkvariance sum of mark variance, calculated as part of question statistics
* @return calculated $quizstats The statistics for overall attempt scores.
*/
public function calculate($quizid, $whichattempts, \core\dml\sql_join $groupstudentsjoins, $p, $sumofmarkvariance) {
$this->progress->start_progress('', 3);
$quizstats = new calculated($whichattempts);
$countsandaverages = $this->attempt_counts_and_averages($quizid, $groupstudentsjoins);
$this->progress->progress(1);
foreach ($countsandaverages as $propertyname => $value) {
$quizstats->{$propertyname} = $value;
}
$s = $quizstats->s();
if ($s != 0) {
// Recalculate sql again this time possibly including test for first attempt.
list($fromqa, $whereqa, $qaparams) =
quiz_statistics_attempts_sql($quizid, $groupstudentsjoins, $whichattempts);
$quizstats->median = $this->median($s, $fromqa, $whereqa, $qaparams);
$this->progress->progress(2);
if ($s > 1) {
$powers = $this->sum_of_powers_of_difference_to_mean($quizstats->avg(), $fromqa, $whereqa, $qaparams);
$this->progress->progress(3);
$quizstats->standarddeviation = sqrt($powers->power2 / ($s - 1));
// Skewness.
if ($s > 2) {
// See http://docs.moodle.org/dev/Quiz_item_analysis_calculations_in_practise#Skewness_and_Kurtosis.
$m2 = $powers->power2 / $s;
$m3 = $powers->power3 / $s;
$m4 = $powers->power4 / $s;
$k2 = $s * $m2 / ($s - 1);
$k3 = $s * $s * $m3 / (($s - 1) * ($s - 2));
if ($k2 != 0) {
$quizstats->skewness = $k3 / (pow($k2, 3 / 2));
// Kurtosis.
if ($s > 3) {
$k4 = $s * $s * ((($s + 1) * $m4) - (3 * ($s - 1) * $m2 * $m2)) / (($s - 1) * ($s - 2) * ($s - 3));
$quizstats->kurtosis = $k4 / ($k2 * $k2);
}
if ($p > 1) {
$quizstats->cic = (100 * $p / ($p - 1)) * (1 - ($sumofmarkvariance / $k2));
$quizstats->errorratio = 100 * sqrt(1 - ($quizstats->cic / 100));
$quizstats->standarderror = $quizstats->errorratio *
$quizstats->standarddeviation / 100;
}
}
}
}
$quizstats->cache(quiz_statistics_qubaids_condition($quizid, $groupstudentsjoins, $whichattempts));
}
$this->progress->end_progress();
return $quizstats;
}
/** @var integer Time after which statistics are automatically recomputed. */
const TIME_TO_CACHE = 900; // 15 minutes.
/**
* Load cached statistics from the database.
*
* @param $qubaids \qubaid_condition
* @return calculated The statistics for overall attempt scores or false if not cached.
*/
public function get_cached($qubaids) {
global $DB;
$timemodified = time() - self::TIME_TO_CACHE;
$fromdb = $DB->get_record_select('quiz_statistics', 'hashcode = ? AND timemodified > ?',
array($qubaids->get_hash_code(), $timemodified));
$stats = new calculated();
$stats->populate_from_record($fromdb);
return $stats;
}
/**
* Find time of non-expired statistics in the database.
*
* @param $qubaids \qubaid_condition
* @return integer|boolean Time of cached record that matches this qubaid_condition or false is non found.
*/
public function get_last_calculated_time($qubaids) {
global $DB;
$timemodified = time() - self::TIME_TO_CACHE;
return $DB->get_field_select('quiz_statistics', 'timemodified', 'hashcode = ? AND timemodified > ?',
array($qubaids->get_hash_code(), $timemodified));
}
/**
* Given a particular quiz grading method return a lang string describing which attempts contribute to grade.
*
* Note internally we use the grading method constants to represent which attempts we are calculating statistics for, each
* grading method corresponds to different attempts for each user.
*
* @param int $whichattempts which attempts to use, represented internally as one of the constants as used in
* $quiz->grademethod ie.
* QUIZ_GRADEAVERAGE, QUIZ_GRADEHIGHEST, QUIZ_ATTEMPTLAST or QUIZ_ATTEMPTFIRST
* we calculate stats based on which attempts would affect the grade for each student.
* @return string the appropriate lang string to describe this option.
*/
public static function using_attempts_lang_string($whichattempts) {
return get_string(static::using_attempts_string_id($whichattempts), 'quiz_statistics');
}
/**
* Given a particular quiz grading method return a string id for use as a field name prefix in mdl_quiz_statistics or to
* fetch the appropriate language string describing which attempts contribute to grade.
*
* Note internally we use the grading method constants to represent which attempts we are calculating statistics for, each
* grading method corresponds to different attempts for each user.
*
* @param int $whichattempts which attempts to use, represented internally as one of the constants as used in
* $quiz->grademethod ie.
* QUIZ_GRADEAVERAGE, QUIZ_GRADEHIGHEST, QUIZ_ATTEMPTLAST or QUIZ_ATTEMPTFIRST
* we calculate stats based on which attempts would affect the grade for each student.
* @return string the string id for this option.
*/
public static function using_attempts_string_id($whichattempts) {
switch ($whichattempts) {
case QUIZ_ATTEMPTFIRST :
return 'firstattempts';
case QUIZ_GRADEHIGHEST :
return 'highestattempts';
case QUIZ_ATTEMPTLAST :
return 'lastattempts';
case QUIZ_GRADEAVERAGE :
return 'allattempts';
}
}
/**
* Calculating count and mean of marks for first and ALL attempts by students.
*
* See : http://docs.moodle.org/dev/Quiz_item_analysis_calculations_in_practise
* #Calculating_MEAN_of_grades_for_all_attempts_by_students
* @param int $quizid
* @param \core\dml\sql_join $groupstudentsjoins Contains joins, wheres, params for students in this group.
* @return \stdClass with properties with count and avg with prefixes firstattempts, highestattempts, etc.
*/
protected function attempt_counts_and_averages($quizid, \core\dml\sql_join $groupstudentsjoins) {
global $DB;
$attempttotals = new \stdClass();
foreach (array_keys(quiz_get_grading_options()) as $which) {
list($fromqa, $whereqa, $qaparams) = quiz_statistics_attempts_sql($quizid, $groupstudentsjoins, $which);
$fromdb = $DB->get_record_sql("SELECT COUNT(*) AS rcount, AVG(sumgrades) AS average FROM $fromqa WHERE $whereqa",
$qaparams);
$fieldprefix = static::using_attempts_string_id($which);
$attempttotals->{$fieldprefix.'avg'} = $fromdb->average;
$attempttotals->{$fieldprefix.'count'} = $fromdb->rcount;
}
return $attempttotals;
}
/**
* Median mark.
*
* http://docs.moodle.org/dev/Quiz_statistics_calculations#Median_Score
*
* @param $s integer count of attempts
* @param $fromqa string
* @param $whereqa string
* @param $qaparams string
* @return float
*/
protected function median($s, $fromqa, $whereqa, $qaparams) {
global $DB;
if ($s % 2 == 0) {
// An even number of attempts.
$limitoffset = $s / 2 - 1;
$limit = 2;
} else {
$limitoffset = floor($s / 2);
$limit = 1;
}
$sql = "SELECT quiza.id, quiza.sumgrades
FROM $fromqa
WHERE $whereqa
ORDER BY sumgrades";
$medianmarks = $DB->get_records_sql_menu($sql, $qaparams, $limitoffset, $limit);
return array_sum($medianmarks) / count($medianmarks);
}
/**
* Fetch the sum of squared, cubed and to the power 4 differences between sumgrade and it's mean.
*
* Explanation here : http://docs.moodle.org/dev/Quiz_item_analysis_calculations_in_practise
* #Calculating_Standard_Deviation.2C_Skewness_and_Kurtosis_of_grades_for_all_attempts_by_students
*
* @param $mean
* @param $fromqa
* @param $whereqa
* @param $qaparams
* @return object with properties power2, power3, power4
*/
protected function sum_of_powers_of_difference_to_mean($mean, $fromqa, $whereqa, $qaparams) {
global $DB;
$sql = "SELECT
SUM(POWER((quiza.sumgrades - $mean), 2)) AS power2,
SUM(POWER((quiza.sumgrades - $mean), 3)) AS power3,
SUM(POWER((quiza.sumgrades - $mean), 4)) AS power4
FROM $fromqa
WHERE $whereqa";
$params = array('mean1' => $mean, 'mean2' => $mean, 'mean3' => $mean) + $qaparams;
return $DB->get_record_sql($sql, $params, MUST_EXIST);
}
}