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b1c97381b4
PHP before version 8.1 automatically converted to int if the function parameter (or array key) is expected to be int. PHP 8.1 shows notice in this case
496 lines
22 KiB
PHP
496 lines
22 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 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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$covariancewithoverallmark = $this->stats->for_slot($slot)->covariancewithoverallmark;
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if (null !== $covariancewithoverallmark && $covariancewithoverallmark >= 0) {
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$sumofcovariancewithoverallmark += sqrt($covariancewithoverallmark);
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}
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}
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$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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/**
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* Then loop through all questions for the first time.
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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 step data.
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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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if ($stats->s != 0) {
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$stats->markaverage = $stats->totalmarks / $stats->s;
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$stats->othermarkaverage = $stats->totalothermarks / $stats->s;
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$stats->summarksaverage = $stats->totalsummarks / $stats->s;
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} else {
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$stats->markaverage = 0;
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$stats->othermarkaverage = 0;
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$stats->summarksaverage = 0;
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}
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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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sort($stats->markarray, SORT_NUMERIC);
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sort($stats->othermarksarray, SORT_NUMERIC);
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// Here we have collected enough data to make the decision about which questions have variants whose stats we also want to
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// calculate. We delete the initialised structures where they are not needed.
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if (!$stats->get_variants() || !$stats->break_down_by_variant()) {
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$stats->clear_variants();
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}
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foreach ($stats->get_variants() as $variant) {
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$this->initial_question_walker($stats->variantstats[$variant]);
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}
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}
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/**
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* Loop through all last step data again.
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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 float[] $summarks of the sum of marks for each question usage, indexed by question usage id
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*/
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protected function secondary_steps_walker($step, $stats, $summarks) {
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$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] - $stats->summarksaverage;
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$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 * $overallmarkdifference;
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if (isset($stats->variantstats[$step->variant])) {
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$this->secondary_steps_walker($step, $stats->variantstats[$step->variant], $summarks);
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}
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}
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/**
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* And finally loop through all the questions again.
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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 /
|
|
$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;
|
|
}
|
|
}
|