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491 lines
21 KiB
491 lines
21 KiB
2 years ago
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<?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 all_calculated_for_qubaid_condition all the stats calculated for slots and sub-questions and variants of those
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* questions.
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*/
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protected $stats;
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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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/**
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* @var array[] keyed by a string representing the pool of questions that this random question draws from.
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* string as returned from {@link \core_question\statistics\questions\calculated::random_selector_string}
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*/
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protected $randomselectors = array();
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/**
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* @var \progress_trace
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*/
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protected $progress;
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/**
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* @var string The class name of the class to instantiate to store statistics calculated.
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*/
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protected $statscollectionclassname = '\core_question\statistics\questions\all_calculated_for_qubaid_condition';
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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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* @param \core\progress\base|null $progress the element to send progress messages to, default is {@link \core\progress\none}.
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*/
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public function __construct($questions, $progress = null) {
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if ($progress === null) {
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$progress = new \core\progress\none();
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}
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$this->progress = $progress;
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$this->stats = new $this->statscollectionclassname();
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foreach ($questions as $slot => $question) {
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$this->stats->initialise_for_slot($slot, $question);
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$this->stats->for_slot($slot)->randomguessscore = $this->get_random_guess_score($question);
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}
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}
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/**
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* Calculate the stats.
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*
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* @param \qubaid_condition $qubaids Which question usages to calculate the stats for?
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* @return all_calculated_for_qubaid_condition The calculated stats.
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*/
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public function calculate($qubaids) {
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$this->progress->start_progress('', 6);
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list($lateststeps, $summarks) = $this->get_latest_steps($qubaids);
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if ($lateststeps) {
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$this->progress->start_progress('', count($lateststeps), 1);
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// Compute the statistics of position, and for random questions, work
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// out which questions appear in which positions.
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foreach ($lateststeps as $step) {
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$this->progress->increment_progress();
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$israndomquestion = ($step->questionid != $this->stats->for_slot($step->slot)->questionid);
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$breakdownvariants = !$israndomquestion && $this->stats->for_slot($step->slot)->break_down_by_variant();
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// If this is a variant we have not seen before create a place to store stats calculations for this variant.
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if ($breakdownvariants && !$this->stats->has_slot($step->slot, $step->variant)) {
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$question = $this->stats->for_slot($step->slot)->question;
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$this->stats->initialise_for_slot($step->slot, $question, $step->variant);
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$this->stats->for_slot($step->slot, $step->variant)->randomguessscore =
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$this->get_random_guess_score($question);
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}
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// Step data walker for main question.
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$this->initial_steps_walker($step, $this->stats->for_slot($step->slot), $summarks, true, $breakdownvariants);
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// If this is a random question do the calculations for sub question stats.
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if ($israndomquestion) {
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if (!$this->stats->has_subq($step->questionid)) {
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$this->stats->initialise_for_subq($step);
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} else if ($this->stats->for_subq($step->questionid)->maxmark != $step->maxmark) {
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$this->stats->for_subq($step->questionid)->differentweights = true;
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}
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// If this is a variant of this subq we have not seen before create a place to store stats calculations for it.
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if (!$this->stats->has_subq($step->questionid, $step->variant)) {
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$this->stats->initialise_for_subq($step, $step->variant);
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}
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$this->initial_steps_walker($step, $this->stats->for_subq($step->questionid), $summarks, false);
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// Extra stuff we need to do in this loop for subqs to keep track of where they need to be displayed later.
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$number = $this->stats->for_slot($step->slot)->question->number;
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$this->stats->for_subq($step->questionid)->usedin[$number] = $number;
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// Keep track of which random questions are actually selected from each pool of questions that random
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// questions are pulled from.
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$randomselectorstring = $this->stats->for_slot($step->slot)->random_selector_string();
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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] = $step->questionid;
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}
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}
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$this->progress->end_progress();
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foreach ($this->randomselectors as $key => $notused) {
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ksort($this->randomselectors[$key]);
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$this->randomselectors[$key] = implode(',', $this->randomselectors[$key]);
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}
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$this->stats->subquestions = question_load_questions($this->stats->get_all_subq_ids());
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// Compute the statistics for sub questions, if there are any.
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$this->progress->start_progress('', count($this->stats->subquestions), 1);
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foreach ($this->stats->subquestions as $qid => $subquestion) {
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$this->progress->increment_progress();
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$subquestion->maxmark = $this->stats->for_subq($qid)->maxmark;
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$this->stats->for_subq($qid)->question = $subquestion;
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$this->stats->for_subq($qid)->randomguessscore = $this->get_random_guess_score($subquestion);
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if ($variants = $this->stats->for_subq($qid)->get_variants()) {
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foreach ($variants as $variant) {
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$this->stats->for_subq($qid, $variant)->question = $subquestion;
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$this->stats->for_subq($qid, $variant)->randomguessscore = $this->get_random_guess_score($subquestion);
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}
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$this->stats->for_subq($qid)->sort_variants();
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}
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$this->initial_question_walker($this->stats->for_subq($qid));
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if ($this->stats->for_subq($qid)->usedin) {
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sort($this->stats->for_subq($qid)->usedin, SORT_NUMERIC);
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$this->stats->for_subq($qid)->positions = implode(',', $this->stats->for_subq($qid)->usedin);
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} else {
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$this->stats->for_subq($qid)->positions = '';
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}
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}
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$this->progress->end_progress();
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// Finish computing the averages, and put the sub-question data into the
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// corresponding questions.
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$slots = $this->stats->get_all_slots();
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$totalnumberofslots = count($slots);
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$maxindex = $totalnumberofslots - 1;
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$this->progress->start_progress('', $totalnumberofslots, 1);
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foreach ($slots as $index => $slot) {
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$this->stats->for_slot($slot)->sort_variants();
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$this->progress->increment_progress();
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$nextslotindex = $index + 1;
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$nextslot = ($nextslotindex > $maxindex) ? false : $slots[$nextslotindex];
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$this->initial_question_walker($this->stats->for_slot($slot));
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// The rest of this loop is to finish working out where randomly selected question stats should be displayed.
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if ($this->stats->for_slot($slot)->question->qtype == 'random') {
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$randomselectorstring = $this->stats->for_slot($slot)->random_selector_string();
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if ($nextslot && ($randomselectorstring == $this->stats->for_slot($nextslot)->random_selector_string())) {
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continue; // Next loop iteration.
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}
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if (isset($this->randomselectors[$randomselectorstring])) {
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$this->stats->for_slot($slot)->subquestions = $this->randomselectors[$randomselectorstring];
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}
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}
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}
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$this->progress->end_progress();
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// Go through the records one more time.
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$this->progress->start_progress('', count($lateststeps), 1);
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foreach ($lateststeps as $step) {
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$this->progress->increment_progress();
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$israndomquestion = ($this->stats->for_slot($step->slot)->question->qtype == 'random');
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$this->secondary_steps_walker($step, $this->stats->for_slot($step->slot), $summarks);
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if ($israndomquestion) {
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$this->secondary_steps_walker($step, $this->stats->for_subq($step->questionid), $summarks);
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}
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}
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$this->progress->end_progress();
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$slots = $this->stats->get_all_slots();
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$this->progress->start_progress('', count($slots), 1);
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$sumofcovariancewithoverallmark = 0;
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foreach ($this->stats->get_all_slots() as $slot) {
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$this->progress->increment_progress();
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$this->secondary_question_walker($this->stats->for_slot($slot));
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$this->sumofmarkvariance += $this->stats->for_slot($slot)->markvariance;
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if ($this->stats->for_slot($slot)->covariancewithoverallmark >= 0) {
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$sumofcovariancewithoverallmark += sqrt($this->stats->for_slot($slot)->covariancewithoverallmark);
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}
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}
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$this->progress->end_progress();
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$subqids = $this->stats->get_all_subq_ids();
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$this->progress->start_progress('', count($subqids), 1);
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foreach ($subqids as $subqid) {
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$this->progress->increment_progress();
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$this->secondary_question_walker($this->stats->for_subq($subqid));
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}
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$this->progress->end_progress();
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foreach ($this->stats->get_all_slots() as $slot) {
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if ($sumofcovariancewithoverallmark) {
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if ($this->stats->for_slot($slot)->negcovar) {
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$this->stats->for_slot($slot)->effectiveweight = null;
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} else {
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$this->stats->for_slot($slot)->effectiveweight =
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100 * sqrt($this->stats->for_slot($slot)->covariancewithoverallmark) /
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$sumofcovariancewithoverallmark;
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}
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} else {
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$this->stats->for_slot($slot)->effectiveweight = null;
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}
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}
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$this->stats->cache($qubaids);
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// All finished.
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$this->progress->end_progress();
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}
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return $this->stats;
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}
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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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* Get the latest step data from the db, from which we will calculate stats.
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*
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* @param \qubaid_condition $qubaids Which question usages to get the latest steps for?
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* @return array with two items
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* - $lateststeps array of latest step data for the question usages
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* - $summarks array of total marks for each usage, indexed by usage id
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*/
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protected function get_latest_steps($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.variant,
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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, $this->stats->get_all_slots(), $fields);
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$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] += $step->mark;
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}
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}
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return array($lateststeps, $summarks);
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}
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/**
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* Calculating the stats is a four step process.
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*
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* We loop through all 'last step' data first.
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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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* @param bool $dovariantalso do we also want to do the same calculations for this variant?
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*/
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protected function initial_steps_walker($step, $stats, $summarks, $positionstat = true, $dovariantalso = true) {
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$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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if ($dovariantalso) {
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$this->initial_steps_walker($step, $stats->variantstats[$step->variant], $summarks, $positionstat, false);
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}
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}
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|
||
|
|
/**
|
||
|
|
* Then loop through all questions for the first time.
|
||
|
|
*
|
||
|
|
* Perform some computations on the per-question statistics calculations after
|
||
|
|
* we have been through all the step data.
|
||
|
|
*
|
||
|
|
* @param calculated $stats question stats to update.
|
||
|
|
*/
|
||
|
|
protected function initial_question_walker($stats) {
|
||
|
|
$stats->markaverage = $stats->totalmarks / $stats->s;
|
||
|
|
|
||
|
|
if ($stats->maxmark != 0) {
|
||
|
|
$stats->facility = $stats->markaverage / $stats->maxmark;
|
||
|
|
} else {
|
||
|
|
$stats->facility = null;
|
||
|
|
}
|
||
|
|
|
||
|
|
$stats->othermarkaverage = $stats->totalothermarks / $stats->s;
|
||
|
|
|
||
|
|
$stats->summarksaverage = $stats->totalsummarks / $stats->s;
|
||
|
|
|
||
|
|
sort($stats->markarray, SORT_NUMERIC);
|
||
|
|
sort($stats->othermarksarray, SORT_NUMERIC);
|
||
|
|
|
||
|
|
// Here we have collected enough data to make the decision about which questions have variants whose stats we also want to
|
||
|
|
// calculate. We delete the initialised structures where they are not needed.
|
||
|
|
if (!$stats->get_variants() || !$stats->break_down_by_variant()) {
|
||
|
|
$stats->clear_variants();
|
||
|
|
}
|
||
|
|
|
||
|
|
foreach ($stats->get_variants() as $variant) {
|
||
|
|
$this->initial_question_walker($stats->variantstats[$variant]);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Loop through all last step data again.
|
||
|
|
*
|
||
|
|
* Now we know the averages, accumulate the date needed to compute the higher
|
||
|
|
* moments of the question scores.
|
||
|
|
*
|
||
|
|
* @param object $step the state to add to the statistics.
|
||
|
|
* @param calculated $stats the question statistics we are accumulating.
|
||
|
|
* @param float[] $summarks of the sum of marks for each question usage, indexed by question usage id
|
||
|
|
*/
|
||
|
|
protected function secondary_steps_walker($step, $stats, $summarks) {
|
||
|
|
$markdifference = $step->mark - $stats->markaverage;
|
||
|
|
if ($stats->subquestion) {
|
||
|
|
$othermarkdifference = $summarks[$step->questionusageid] - $stats->othermarkaverage;
|
||
|
|
} else {
|
||
|
|
$othermarkdifference = $summarks[$step->questionusageid] - $step->mark - $stats->othermarkaverage;
|
||
|
|
}
|
||
|
|
$overallmarkdifference = $summarks[$step->questionusageid] - $stats->summarksaverage;
|
||
|
|
|
||
|
|
$sortedmarkdifference = array_shift($stats->markarray) - $stats->markaverage;
|
||
|
|
$sortedothermarkdifference = array_shift($stats->othermarksarray) - $stats->othermarkaverage;
|
||
|
|
|
||
|
|
$stats->markvariancesum += pow($markdifference, 2);
|
||
|
|
$stats->othermarkvariancesum += pow($othermarkdifference, 2);
|
||
|
|
$stats->covariancesum += $markdifference * $othermarkdifference;
|
||
|
|
$stats->covariancemaxsum += $sortedmarkdifference * $sortedothermarkdifference;
|
||
|
|
$stats->covariancewithoverallmarksum += $markdifference * $overallmarkdifference;
|
||
|
|
|
||
|
|
if (isset($stats->variantstats[$step->variant])) {
|
||
|
|
$this->secondary_steps_walker($step, $stats->variantstats[$step->variant], $summarks);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* And finally loop through all the questions again.
|
||
|
|
*
|
||
|
|
* Perform more per-question statistics calculations.
|
||
|
|
*
|
||
|
|
* @param calculated $stats question stats to update.
|
||
|
|
*/
|
||
|
|
protected function secondary_question_walker($stats) {
|
||
|
|
if ($stats->s > 1) {
|
||
|
|
$stats->markvariance = $stats->markvariancesum / ($stats->s - 1);
|
||
|
|
$stats->othermarkvariance = $stats->othermarkvariancesum / ($stats->s - 1);
|
||
|
|
$stats->covariance = $stats->covariancesum / ($stats->s - 1);
|
||
|
|
$stats->covariancemax = $stats->covariancemaxsum / ($stats->s - 1);
|
||
|
|
$stats->covariancewithoverallmark = $stats->covariancewithoverallmarksum /
|
||
|
|
($stats->s - 1);
|
||
|
|
$stats->sd = sqrt($stats->markvariancesum / ($stats->s - 1));
|
||
|
|
|
||
|
|
if ($stats->covariancewithoverallmark >= 0) {
|
||
|
|
$stats->negcovar = 0;
|
||
|
|
} else {
|
||
|
|
$stats->negcovar = 1;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
$stats->markvariance = null;
|
||
|
|
$stats->othermarkvariance = null;
|
||
|
|
$stats->covariance = null;
|
||
|
|
$stats->covariancemax = null;
|
||
|
|
$stats->covariancewithoverallmark = null;
|
||
|
|
$stats->sd = null;
|
||
|
|
$stats->negcovar = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
if ($stats->markvariance * $stats->othermarkvariance) {
|
||
|
|
$stats->discriminationindex = 100 * $stats->covariance /
|
||
|
|
sqrt($stats->markvariance * $stats->othermarkvariance);
|
||
|
|
} else {
|
||
|
|
$stats->discriminationindex = null;
|
||
|
|
}
|
||
|
|
|
||
|
|
if ($stats->covariancemax) {
|
||
|
|
$stats->discriminativeefficiency = 100 * $stats->covariance /
|
||
|
|
$stats->covariancemax;
|
||
|
|
} else {
|
||
|
|
$stats->discriminativeefficiency = null;
|
||
|
|
}
|
||
|
|
|
||
|
|
foreach ($stats->variantstats as $variantstat) {
|
||
|
|
$this->secondary_question_walker($variantstat);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Given the question data find the average grade that random guesses would get.
|
||
|
|
*
|
||
|
|
* @param object $questiondata the full question object.
|
||
|
|
* @return float the random guess score for this question.
|
||
|
|
*/
|
||
|
|
protected function get_random_guess_score($questiondata) {
|
||
|
|
return \question_bank::get_qtype(
|
||
|
|
$questiondata->qtype, false)->get_random_guess_score($questiondata);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Find time of non-expired statistics in the database.
|
||
|
|
*
|
||
|
|
* @param \qubaid_condition $qubaids Which question usages to look for?
|
||
|
|
* @return int|bool Time of cached record that matches this qubaid_condition or false is non found.
|
||
|
|
*/
|
||
|
|
public function get_last_calculated_time($qubaids) {
|
||
|
|
return $this->stats->get_last_calculated_time($qubaids);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Load cached statistics from the database.
|
||
|
|
*
|
||
|
|
* @param \qubaid_condition $qubaids Which question usages to load the cached stats for?
|
||
|
|
* @return all_calculated_for_qubaid_condition The cached stats.
|
||
|
|
*/
|
||
|
|
public function get_cached($qubaids) {
|
||
|
|
$this->stats->get_cached($qubaids);
|
||
|
|
return $this->stats;
|
||
|
|
}
|
||
|
|
}
|