James Pratt
445 lines
18 KiB
PHP
445 lines
18 KiB
PHP
<?php
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// This file is part of Moodle - http://moodle.org/
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//
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// Moodle is free software: you can redistribute it and/or modify
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// it under the terms of the GNU General Public License as published by
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// the Free Software Foundation, either version 3 of the License, or
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// (at your option) any later version.
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//
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// Moodle is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU General Public License
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// along with Moodle. If not, see <http://www.gnu.org/licenses/>.
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/**
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* Question statistics calculator class. Used in the quiz statistics report but also available for use elsewhere.
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*
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* @package core
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* @subpackage questionbank
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* @copyright 2013 Open University
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* @author Jamie Pratt <me@jamiep.org>
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* @license http://www.gnu.org/copyleft/gpl.html GNU GPL v3 or later
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*/
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namespace core_question\statistics\questions;
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defined('MOODLE_INTERNAL') || die();
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/**
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* This class has methods to compute the question statistics from the raw data.
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*
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* @copyright 2013 Open University
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* @author Jamie Pratt <me@jamiep.org>
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* @license http://www.gnu.org/copyleft/gpl.html GNU GPL v3 or later
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*/
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class calculator {
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/**
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* @var calculated[]
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*/
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public $questionstats = array();
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/**
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* @var calculated_for_subquestion[]
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*/
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public $subquestionstats = array();
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/**
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* @var float
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*/
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protected $sumofmarkvariance = 0;
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protected $randomselectors = array();
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/**
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* Constructor.
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*
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* @param object[] questions to analyze, keyed by slot, also analyses sub questions for random questions.
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* we expect some extra fields - slot, maxmark and number on the full question data objects.
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*/
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public function __construct($questions) {
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foreach ($questions as $slot => $question) {
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$this->questionstats[$slot] = new calculated();
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$this->questionstats[$slot]->questionid = $question->id;
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$this->questionstats[$slot]->question = $question;
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$this->questionstats[$slot]->slot = $slot;
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$this->questionstats[$slot]->positions = $question->number;
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$this->questionstats[$slot]->maxmark = $question->maxmark;
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$this->questionstats[$slot]->randomguessscore = $this->get_random_guess_score($question);
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}
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}
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/**
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* @param $qubaids \qubaid_condition
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* @return array containing two arrays calculated[] and calculated_for_subquestion[].
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*/
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public function calculate($qubaids) {
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set_time_limit(0);
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list($lateststeps, $summarks, $summarksavg) = $this->get_latest_steps($qubaids);
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if ($lateststeps) {
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// Compute the statistics of position, and for random questions, work
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// out which questions appear in which positions.
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foreach ($lateststeps as $step) {
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$this->initial_steps_walker($step, $this->questionstats[$step->slot], $summarks);
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// If this is a random question what is the real item being used?
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if ($step->questionid != $this->questionstats[$step->slot]->questionid) {
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if (!isset($this->subquestionstats[$step->questionid])) {
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$this->subquestionstats[$step->questionid] = new calculated_for_subquestion();
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$this->subquestionstats[$step->questionid]->questionid = $step->questionid;
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$this->subquestionstats[$step->questionid]->maxmark = $step->maxmark;
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} else if ($this->subquestionstats[$step->questionid]->maxmark != $step->maxmark) {
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$this->subquestionstats[$step->questionid]->differentweights = true;
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}
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$this->initial_steps_walker($step, $this->subquestionstats[$step->questionid], $summarks, false);
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$number = $this->questionstats[$step->slot]->question->number;
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$this->subquestionstats[$step->questionid]->usedin[$number] = $number;
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$randomselectorstring = $this->questionstats[$step->slot]->question->category. '/'
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.$this->questionstats[$step->slot]->question->questiontext;
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if (!isset($this->randomselectors[$randomselectorstring])) {
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$this->randomselectors[$randomselectorstring] = array();
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}
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$this->randomselectors[$randomselectorstring][$step->questionid] = $step->questionid;
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}
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}
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foreach ($this->randomselectors as $key => $notused) {
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ksort($this->randomselectors[$key]);
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}
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// Compute the statistics of question id, if we need any.
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$subquestions = question_load_questions(array_keys($this->subquestionstats));
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foreach ($subquestions as $qid => $subquestion) {
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$this->subquestionstats[$qid]->question = $subquestion;
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$this->subquestionstats[$qid]->question->maxmark = $this->subquestionstats[$qid]->maxmark;
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$this->subquestionstats[$qid]->randomguessscore = $this->get_random_guess_score($subquestion);
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$this->initial_question_walker($this->subquestionstats[$qid]);
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if ($this->subquestionstats[$qid]->differentweights) {
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// TODO output here really sucks, but throwing is too severe.
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global $OUTPUT;
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$name = $this->subquestionstats[$qid]->question->name;
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echo $OUTPUT->notification( get_string('erroritemappearsmorethanoncewithdifferentweight',
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'quiz_statistics', $name));
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}
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if ($this->subquestionstats[$qid]->usedin) {
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sort($this->subquestionstats[$qid]->usedin, SORT_NUMERIC);
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$this->subquestionstats[$qid]->positions = implode(',', $this->subquestionstats[$qid]->usedin);
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} else {
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$this->subquestionstats[$qid]->positions = '';
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}
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}
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// Finish computing the averages, and put the subquestion data into the
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// corresponding questions.
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// This cannot be a foreach loop because we need to have both
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// $question and $nextquestion available, but apart from that it is
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// foreach ($this->questions as $qid => $question).
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reset($this->questionstats);
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while (list($slot, $questionstat) = each($this->questionstats)) {
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$nextquestionstats = current($this->questionstats);
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$this->initial_question_walker($questionstat);
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if ($questionstat->question->qtype == 'random') {
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$randomselectorstring = $questionstat->question->category .'/'. $questionstat->question->questiontext;
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if ($nextquestionstats && $nextquestionstats->question->qtype == 'random') {
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$nextrandomselectorstring =
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$nextquestionstats->question->category .'/'. $nextquestionstats->question->questiontext;
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if ($randomselectorstring == $nextrandomselectorstring) {
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continue; // Next loop iteration.
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}
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}
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if (isset($this->randomselectors[$randomselectorstring])) {
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$questionstat->subquestions = implode(',', $this->randomselectors[$randomselectorstring]);
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}
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}
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}
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// Go through the records one more time.
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foreach ($lateststeps as $step) {
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$this->secondary_steps_walker($step, $this->questionstats[$step->slot], $summarks, $summarksavg);
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if ($this->questionstats[$step->slot]->subquestions) {
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$this->secondary_steps_walker($step, $this->subquestionstats[$step->questionid], $summarks, $summarksavg);
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}
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}
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$sumofcovariancewithoverallmark = 0;
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foreach ($this->questionstats as $questionstat) {
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$this->secondary_question_walker($questionstat);
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$this->sumofmarkvariance += $questionstat->markvariance;
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if ($questionstat->covariancewithoverallmark >= 0) {
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$sumofcovariancewithoverallmark += sqrt($questionstat->covariancewithoverallmark);
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}
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}
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foreach ($this->subquestionstats as $subquestionstat) {
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$this->secondary_question_walker($subquestionstat);
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}
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foreach ($this->questionstats as $questionstat) {
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if ($sumofcovariancewithoverallmark) {
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if ($questionstat->negcovar) {
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$questionstat->effectiveweight = null;
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} else {
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$questionstat->effectiveweight = 100 * sqrt($questionstat->covariancewithoverallmark) /
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$sumofcovariancewithoverallmark;
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}
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} else {
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$questionstat->effectiveweight = null;
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}
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}
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$this->cache_stats($qubaids);
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}
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return array($this->questionstats, $this->subquestionstats);
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}
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/**
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* Load cached statistics from the database.
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*
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* @param $qubaids \qubaid_condition
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* @return array containing two arrays calculated[] and calculated_for_subquestion[].
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*/
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public function get_cached($qubaids) {
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global $DB;
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$timemodified = time() - self::TIME_TO_CACHE;
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$questionstatrecs = $DB->get_records_select('question_statistics', 'hashcode = ? AND timemodified > ?',
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array($qubaids->get_hash_code(), $timemodified));
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$questionids = array();
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foreach ($questionstatrecs as $fromdb) {
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if (!$fromdb->slot) {
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$questionids[] = $fromdb->questionid;
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}
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}
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$subquestions = question_load_questions($questionids);
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foreach ($questionstatrecs as $fromdb) {
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if ($fromdb->slot) {
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$this->questionstats[$fromdb->slot]->populate_from_record($fromdb);
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// Array created in constructor and populated from question.
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} else {
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$this->subquestionstats[$fromdb->questionid] = new calculated_for_subquestion();
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$this->subquestionstats[$fromdb->questionid]->populate_from_record($fromdb);
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$this->subquestionstats[$fromdb->questionid]->question = $subquestions[$fromdb->questionid];
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}
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}
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return array($this->questionstats, $this->subquestionstats);
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}
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/**
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* Find time of non-expired statistics in the database.
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*
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* @param $qubaids \qubaid_condition
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* @return integer|boolean Time of cached record that matches this qubaid_condition or false is non found.
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*/
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public function get_last_calculated_time($qubaids) {
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global $DB;
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$timemodified = time() - self::TIME_TO_CACHE;
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return $DB->get_field_select('question_statistics', 'timemodified', 'hashcode = ? AND timemodified > ?',
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array($qubaids->get_hash_code(), $timemodified), IGNORE_MULTIPLE);
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}
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/** @var integer Time after which statistics are automatically recomputed. */
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const TIME_TO_CACHE = 900; // 15 minutes.
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/**
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* Used when computing Coefficient of Internal Consistency by quiz statistics.
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*
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* @return float
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*/
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public function get_sum_of_mark_variance() {
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return $this->sumofmarkvariance;
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}
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/**
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* @param $qubaids \qubaid_condition
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* @return array with three items
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* - $lateststeps array of latest step data for the question usages
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* - $summarks array of total marks for each usage, indexed by usage id
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* - $summarksavg the average of the total marks over all the usages
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*/
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protected function get_latest_steps($qubaids) {
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$dm = new \question_engine_data_mapper();
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$fields = " qas.id,
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qa.questionusageid,
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qa.questionid,
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qa.slot,
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qa.maxmark,
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qas.fraction * qa.maxmark as mark";
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$lateststeps = $dm->load_questions_usages_latest_steps($qubaids, array_keys($this->questionstats), $fields);
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$summarks = array();
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if ($lateststeps) {
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foreach ($lateststeps as $step) {
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if (!isset($summarks[$step->questionusageid])) {
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$summarks[$step->questionusageid] = 0;
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}
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$summarks[$step->questionusageid] += $step->mark;
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}
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$summarksavg = array_sum($summarks) / count($summarks);
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} else {
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$summarksavg = null;
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}
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return array($lateststeps, $summarks, $summarksavg);
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}
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/**
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* Update $stats->totalmarks, $stats->markarray, $stats->totalothermarks
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* and $stats->othermarksarray to include another state.
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*
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* @param object $step the state to add to the statistics.
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* @param calculated $stats the question statistics we are accumulating.
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* @param array $summarks of the sum of marks for each question usage, indexed by question usage id
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* @param bool $positionstat whether this is a statistic of position of question.
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*/
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protected function initial_steps_walker($step, $stats, $summarks, $positionstat = true) {
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$stats->s++;
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$stats->totalmarks += $step->mark;
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$stats->markarray[] = $step->mark;
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if ($positionstat) {
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$stats->totalothermarks += $summarks[$step->questionusageid] - $step->mark;
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$stats->othermarksarray[] = $summarks[$step->questionusageid] - $step->mark;
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} else {
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$stats->totalothermarks += $summarks[$step->questionusageid];
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$stats->othermarksarray[] = $summarks[$step->questionusageid];
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}
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}
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/**
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* Perform some computations on the per-question statistics calculations after
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* we have been through all the states.
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*
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* @param calculated $stats question stats to update.
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*/
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protected function initial_question_walker($stats) {
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$stats->markaverage = $stats->totalmarks / $stats->s;
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if ($stats->maxmark != 0) {
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$stats->facility = $stats->markaverage / $stats->maxmark;
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} else {
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$stats->facility = null;
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}
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$stats->othermarkaverage = $stats->totalothermarks / $stats->s;
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sort($stats->markarray, SORT_NUMERIC);
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sort($stats->othermarksarray, SORT_NUMERIC);
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}
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/**
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* Now we know the averages, accumulate the date needed to compute the higher
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* moments of the question scores.
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*
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* @param object $step the state to add to the statistics.
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* @param calculated $stats the question statistics we are accumulating.
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* @param array $summarks of the sum of marks for each question usage, indexed by question usage id
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* @param float $summarksavg the average sum of marks for all question usages
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*/
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protected function secondary_steps_walker($step, $stats, $summarks, $summarksavg) {
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$markdifference = $step->mark - $stats->markaverage;
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if ($stats->subquestion) {
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$othermarkdifference = $summarks[$step->questionusageid] - $stats->othermarkaverage;
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} else {
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$othermarkdifference = $summarks[$step->questionusageid] - $step->mark - $stats->othermarkaverage;
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}
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$overallmarkdifference = $summarks[$step->questionusageid] - $summarksavg;
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$sortedmarkdifference = array_shift($stats->markarray) - $stats->markaverage;
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$sortedothermarkdifference = array_shift($stats->othermarksarray) - $stats->othermarkaverage;
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$stats->markvariancesum += pow($markdifference, 2);
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$stats->othermarkvariancesum += pow($othermarkdifference, 2);
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$stats->covariancesum += $markdifference * $othermarkdifference;
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$stats->covariancemaxsum += $sortedmarkdifference * $sortedothermarkdifference;
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$stats->covariancewithoverallmarksum += $markdifference * $overallmarkdifference;
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}
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/**
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* Perform more per-question statistics calculations.
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*
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* @param calculated $stats question stats to update.
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*/
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protected function secondary_question_walker($stats) {
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if ($stats->s > 1) {
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$stats->markvariance = $stats->markvariancesum / ($stats->s - 1);
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$stats->othermarkvariance = $stats->othermarkvariancesum / ($stats->s - 1);
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$stats->covariance = $stats->covariancesum / ($stats->s - 1);
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$stats->covariancemax = $stats->covariancemaxsum / ($stats->s - 1);
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$stats->covariancewithoverallmark = $stats->covariancewithoverallmarksum /
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($stats->s - 1);
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$stats->sd = sqrt($stats->markvariancesum / ($stats->s - 1));
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if ($stats->covariancewithoverallmark >= 0) {
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$stats->negcovar = 0;
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} else {
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$stats->negcovar = 1;
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}
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} else {
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$stats->markvariance = null;
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$stats->othermarkvariance = null;
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$stats->covariance = null;
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$stats->covariancemax = null;
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$stats->covariancewithoverallmark = null;
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$stats->sd = null;
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$stats->negcovar = 0;
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}
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if ($stats->markvariance * $stats->othermarkvariance) {
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$stats->discriminationindex = 100 * $stats->covariance /
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sqrt($stats->markvariance * $stats->othermarkvariance);
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} else {
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$stats->discriminationindex = null;
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}
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if ($stats->covariancemax) {
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$stats->discriminativeefficiency = 100 * $stats->covariance /
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$stats->covariancemax;
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} else {
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$stats->discriminativeefficiency = null;
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}
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}
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/**
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* @param object $questiondata
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* @return number the random guess score for this question.
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*/
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protected function get_random_guess_score($questiondata) {
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return \question_bank::get_qtype(
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$questiondata->qtype, false)->get_random_guess_score($questiondata);
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}
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/**
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* @param $qubaids \qubaid_condition
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*/
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protected function cache_stats($qubaids) {
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foreach ($this->questionstats as $questionstat) {
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$questionstat->cache($qubaids);
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}
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foreach ($this->subquestionstats as $subquestionstat) {
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$subquestionstat->cache($qubaids);
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}
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}
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}
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