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   1  <?php
   2  // This file is part of Moodle - http://moodle.org/
   3  //
   4  // Moodle is free software: you can redistribute it and/or modify
   5  // it under the terms of the GNU General Public License as published by
   6  // the Free Software Foundation, either version 3 of the License, or
   7  // (at your option) any later version.
   8  //
   9  // Moodle is distributed in the hope that it will be useful,
  10  // but WITHOUT ANY WARRANTY; without even the implied warranty of
  11  // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  12  // GNU General Public License for more details.
  13  //
  14  // You should have received a copy of the GNU General Public License
  15  // along with Moodle.  If not, see <http://www.gnu.org/licenses/>.
  16  
  17  /**
  18   * Question statistics calculator class. Used in the quiz statistics report but also available for use elsewhere.
  19   *
  20   * @package    core
  21   * @subpackage questionbank
  22   * @copyright  2013 Open University
  23   * @author     Jamie Pratt <me@jamiep.org>
  24   * @license    http://www.gnu.org/copyleft/gpl.html GNU GPL v3 or later
  25   */
  26  
  27  namespace core_question\statistics\questions;
  28  defined('MOODLE_INTERNAL') || die();
  29  
  30  /**
  31   * This class has methods to compute the question statistics from the raw data.
  32   *
  33   * @copyright 2013 Open University
  34   * @author    Jamie Pratt <me@jamiep.org>
  35   * @license   http://www.gnu.org/copyleft/gpl.html GNU GPL v3 or later
  36   */
  37  class calculator {
  38  
  39      /**
  40       * @var all_calculated_for_qubaid_condition all the stats calculated for slots and sub-questions and variants of those
  41       *                                                  questions.
  42       */
  43      protected $stats;
  44  
  45      /**
  46       * @var float
  47       */
  48      protected $sumofmarkvariance = 0;
  49  
  50      /**
  51       * @var array[] keyed by a string representing the pool of questions that this random question draws from.
  52       *              string as returned from {@link \core_question\statistics\questions\calculated::random_selector_string}
  53       */
  54      protected $randomselectors = array();
  55  
  56      /**
  57       * @var \progress_trace
  58       */
  59      protected $progress;
  60  
  61      /**
  62       * @var string The class name of the class to instantiate to store statistics calculated.
  63       */
  64      protected $statscollectionclassname = '\core_question\statistics\questions\all_calculated_for_qubaid_condition';
  65  
  66      /**
  67       * Constructor.
  68       *
  69       * @param object[] questions to analyze, keyed by slot, also analyses sub questions for random questions.
  70       *                              we expect some extra fields - slot, maxmark and number on the full question data objects.
  71       * @param \core\progress\base|null $progress the element to send progress messages to, default is {@link \core\progress\none}.
  72       */
  73      public function __construct($questions, $progress = null) {
  74  
  75          if ($progress === null) {
  76              $progress = new \core\progress\none();
  77          }
  78          $this->progress = $progress;
  79          $this->stats = new $this->statscollectionclassname();
  80          foreach ($questions as $slot => $question) {
  81              $this->stats->initialise_for_slot($slot, $question);
  82              $this->stats->for_slot($slot)->randomguessscore = $this->get_random_guess_score($question);
  83          }
  84      }
  85  
  86      /**
  87       * Calculate the stats.
  88       *
  89       * @param \qubaid_condition $qubaids Which question usages to calculate the stats for?
  90       * @return all_calculated_for_qubaid_condition The calculated stats.
  91       */
  92      public function calculate($qubaids) {
  93  
  94          $this->progress->start_progress('', 6);
  95  
  96          list($lateststeps, $summarks) = $this->get_latest_steps($qubaids);
  97  
  98          if ($lateststeps) {
  99              $this->progress->start_progress('', count($lateststeps), 1);
 100              // Compute the statistics of position, and for random questions, work
 101              // out which questions appear in which positions.
 102              foreach ($lateststeps as $step) {
 103  
 104                  $this->progress->increment_progress();
 105  
 106                  $israndomquestion = ($step->questionid != $this->stats->for_slot($step->slot)->questionid);
 107                  $breakdownvariants = !$israndomquestion && $this->stats->for_slot($step->slot)->break_down_by_variant();
 108                  // If this is a variant we have not seen before create a place to store stats calculations for this variant.
 109                  if ($breakdownvariants && is_null($this->stats->for_slot($step->slot , $step->variant))) {
 110                      $question = $this->stats->for_slot($step->slot)->question;
 111                      $this->stats->initialise_for_slot($step->slot, $question, $step->variant);
 112                      $this->stats->for_slot($step->slot, $step->variant)->randomguessscore =
 113                                                                                      $this->get_random_guess_score($question);
 114                  }
 115  
 116                  // Step data walker for main question.
 117                  $this->initial_steps_walker($step, $this->stats->for_slot($step->slot), $summarks, true, $breakdownvariants);
 118  
 119                  // If this is a random question do the calculations for sub question stats.
 120                  if ($israndomquestion) {
 121                      if (is_null($this->stats->for_subq($step->questionid))) {
 122                          $this->stats->initialise_for_subq($step);
 123                      } else if ($this->stats->for_subq($step->questionid)->maxmark != $step->maxmark) {
 124                          $this->stats->for_subq($step->questionid)->differentweights = true;
 125                      }
 126  
 127                      // If this is a variant of this subq we have not seen before create a place to store stats calculations for it.
 128                      if (is_null($this->stats->for_subq($step->questionid, $step->variant))) {
 129                          $this->stats->initialise_for_subq($step, $step->variant);
 130                      }
 131  
 132                      $this->initial_steps_walker($step, $this->stats->for_subq($step->questionid), $summarks, false);
 133  
 134                      // Extra stuff we need to do in this loop for subqs to keep track of where they need to be displayed later.
 135  
 136                      $number = $this->stats->for_slot($step->slot)->question->number;
 137                      $this->stats->for_subq($step->questionid)->usedin[$number] = $number;
 138  
 139                      // Keep track of which random questions are actually selected from each pool of questions that random
 140                      // questions are pulled from.
 141                      $randomselectorstring = $this->stats->for_slot($step->slot)->random_selector_string();
 142                      if (!isset($this->randomselectors[$randomselectorstring])) {
 143                          $this->randomselectors[$randomselectorstring] = array();
 144                      }
 145                      $this->randomselectors[$randomselectorstring][$step->questionid] = $step->questionid;
 146                  }
 147              }
 148              $this->progress->end_progress();
 149  
 150              foreach ($this->randomselectors as $key => $notused) {
 151                  ksort($this->randomselectors[$key]);
 152                  $this->randomselectors[$key] = implode(',', $this->randomselectors[$key]);
 153              }
 154  
 155              $this->stats->subquestions = question_load_questions($this->stats->get_all_subq_ids());
 156              // Compute the statistics for sub questions, if there are any.
 157              $this->progress->start_progress('', count($this->stats->subquestions), 1);
 158              foreach ($this->stats->subquestions as $qid => $subquestion) {
 159                  $this->progress->increment_progress();
 160                  $subquestion->maxmark = $this->stats->for_subq($qid)->maxmark;
 161                  $this->stats->for_subq($qid)->question = $subquestion;
 162                  $this->stats->for_subq($qid)->randomguessscore = $this->get_random_guess_score($subquestion);
 163  
 164                  if ($variants = $this->stats->for_subq($qid)->get_variants()) {
 165                      foreach ($variants as $variant) {
 166                          $this->stats->for_subq($qid, $variant)->question = $subquestion;
 167                          $this->stats->for_subq($qid, $variant)->randomguessscore = $this->get_random_guess_score($subquestion);
 168                      }
 169                      $this->stats->for_subq($qid)->sort_variants();
 170                  }
 171                  $this->initial_question_walker($this->stats->for_subq($qid));
 172  
 173                  if ($this->stats->for_subq($qid)->usedin) {
 174                      sort($this->stats->for_subq($qid)->usedin, SORT_NUMERIC);
 175                      $this->stats->for_subq($qid)->positions = implode(',', $this->stats->for_subq($qid)->usedin);
 176                  } else {
 177                      $this->stats->for_subq($qid)->positions = '';
 178                  }
 179              }
 180              $this->progress->end_progress();
 181  
 182              // Finish computing the averages, and put the sub-question data into the
 183              // corresponding questions.
 184  
 185              // This cannot be a foreach loop because we need to have both
 186              // $question and $nextquestion available, but apart from that it is
 187              // foreach ($this->questions as $qid => $question).
 188              $slots = $this->stats->get_all_slots();
 189              $this->progress->start_progress('', count($slots), 1);
 190              while (list(, $slot) = each($slots)) {
 191                  $this->stats->for_slot($slot)->sort_variants();
 192                  $this->progress->increment_progress();
 193                  $nextslot = current($slots);
 194  
 195                  $this->initial_question_walker($this->stats->for_slot($slot));
 196  
 197                  // The rest of this loop is to finish working out where randomly selected question stats should be displayed.
 198                  if ($this->stats->for_slot($slot)->question->qtype == 'random') {
 199                      $randomselectorstring = $this->stats->for_slot($slot)->random_selector_string();
 200                      if ($nextslot &&  ($randomselectorstring == $this->stats->for_slot($nextslot)->random_selector_string())) {
 201                          continue; // Next loop iteration.
 202                      }
 203                      if (isset($this->randomselectors[$randomselectorstring])) {
 204                          $this->stats->for_slot($slot)->subquestions = $this->randomselectors[$randomselectorstring];
 205                      }
 206                  }
 207              }
 208              $this->progress->end_progress();
 209  
 210              // Go through the records one more time.
 211              $this->progress->start_progress('', count($lateststeps), 1);
 212              foreach ($lateststeps as $step) {
 213                  $this->progress->increment_progress();
 214                  $israndomquestion = ($this->stats->for_slot($step->slot)->question->qtype == 'random');
 215                  $this->secondary_steps_walker($step, $this->stats->for_slot($step->slot), $summarks);
 216  
 217                  if ($israndomquestion) {
 218                      $this->secondary_steps_walker($step, $this->stats->for_subq($step->questionid), $summarks);
 219                  }
 220              }
 221              $this->progress->end_progress();
 222  
 223              $slots = $this->stats->get_all_slots();
 224              $this->progress->start_progress('', count($slots), 1);
 225              $sumofcovariancewithoverallmark = 0;
 226              foreach ($this->stats->get_all_slots() as $slot) {
 227                  $this->progress->increment_progress();
 228                  $this->secondary_question_walker($this->stats->for_slot($slot));
 229  
 230                  $this->sumofmarkvariance += $this->stats->for_slot($slot)->markvariance;
 231  
 232                  if ($this->stats->for_slot($slot)->covariancewithoverallmark >= 0) {
 233                      $sumofcovariancewithoverallmark += sqrt($this->stats->for_slot($slot)->covariancewithoverallmark);
 234                  }
 235              }
 236              $this->progress->end_progress();
 237  
 238              $subqids = $this->stats->get_all_subq_ids();
 239              $this->progress->start_progress('', count($subqids), 1);
 240              foreach ($subqids as $subqid) {
 241                  $this->progress->increment_progress();
 242                  $this->secondary_question_walker($this->stats->for_subq($subqid));
 243              }
 244              $this->progress->end_progress();
 245  
 246              foreach ($this->stats->get_all_slots() as $slot) {
 247                  if ($sumofcovariancewithoverallmark) {
 248                      if ($this->stats->for_slot($slot)->negcovar) {
 249                          $this->stats->for_slot($slot)->effectiveweight = null;
 250                      } else {
 251                          $this->stats->for_slot($slot)->effectiveweight =
 252                                                          100 * sqrt($this->stats->for_slot($slot)->covariancewithoverallmark) /
 253                                                          $sumofcovariancewithoverallmark;
 254                      }
 255                  } else {
 256                      $this->stats->for_slot($slot)->effectiveweight = null;
 257                  }
 258              }
 259              $this->stats->cache($qubaids);
 260  
 261              // All finished.
 262              $this->progress->end_progress();
 263          }
 264          return $this->stats;
 265      }
 266  
 267      /**
 268       * Used when computing Coefficient of Internal Consistency by quiz statistics.
 269       *
 270       * @return float
 271       */
 272      public function get_sum_of_mark_variance() {
 273          return $this->sumofmarkvariance;
 274      }
 275  
 276      /**
 277       * Get the latest step data from the db, from which we will calculate stats.
 278       *
 279       * @param \qubaid_condition $qubaids Which question usages to get the latest steps for?
 280       * @return array with two items
 281       *              - $lateststeps array of latest step data for the question usages
 282       *              - $summarks    array of total marks for each usage, indexed by usage id
 283       */
 284      protected function get_latest_steps($qubaids) {
 285          $dm = new \question_engine_data_mapper();
 286  
 287          $fields = "    qas.id,
 288      qa.questionusageid,
 289      qa.questionid,
 290      qa.variant,
 291      qa.slot,
 292      qa.maxmark,
 293      qas.fraction * qa.maxmark as mark";
 294  
 295          $lateststeps = $dm->load_questions_usages_latest_steps($qubaids, $this->stats->get_all_slots(), $fields);
 296          $summarks = array();
 297          if ($lateststeps) {
 298              foreach ($lateststeps as $step) {
 299                  if (!isset($summarks[$step->questionusageid])) {
 300                      $summarks[$step->questionusageid] = 0;
 301                  }
 302                  $summarks[$step->questionusageid] += $step->mark;
 303              }
 304          }
 305  
 306          return array($lateststeps, $summarks);
 307      }
 308  
 309      /**
 310       * Calculating the stats is a four step process.
 311       *
 312       * We loop through all 'last step' data first.
 313       *
 314       * Update $stats->totalmarks, $stats->markarray, $stats->totalothermarks
 315       * and $stats->othermarksarray to include another state.
 316       *
 317       * @param object     $step         the state to add to the statistics.
 318       * @param calculated $stats        the question statistics we are accumulating.
 319       * @param array      $summarks     of the sum of marks for each question usage, indexed by question usage id
 320       * @param bool       $positionstat whether this is a statistic of position of question.
 321       * @param bool       $dovariantalso do we also want to do the same calculations for this variant?
 322       */
 323      protected function initial_steps_walker($step, $stats, $summarks, $positionstat = true, $dovariantalso = true) {
 324          $stats->s++;
 325          $stats->totalmarks += $step->mark;
 326          $stats->markarray[] = $step->mark;
 327  
 328          if ($positionstat) {
 329              $stats->totalothermarks += $summarks[$step->questionusageid] - $step->mark;
 330              $stats->othermarksarray[] = $summarks[$step->questionusageid] - $step->mark;
 331  
 332          } else {
 333              $stats->totalothermarks += $summarks[$step->questionusageid];
 334              $stats->othermarksarray[] = $summarks[$step->questionusageid];
 335          }
 336          if ($dovariantalso) {
 337              $this->initial_steps_walker($step, $stats->variantstats[$step->variant], $summarks, $positionstat, false);
 338          }
 339      }
 340  
 341      /**
 342       * Then loop through all questions for the first time.
 343       *
 344       * Perform some computations on the per-question statistics calculations after
 345       * we have been through all the step data.
 346       *
 347       * @param calculated $stats question stats to update.
 348       */
 349      protected function initial_question_walker($stats) {
 350          $stats->markaverage = $stats->totalmarks / $stats->s;
 351  
 352          if ($stats->maxmark != 0) {
 353              $stats->facility = $stats->markaverage / $stats->maxmark;
 354          } else {
 355              $stats->facility = null;
 356          }
 357  
 358          $stats->othermarkaverage = $stats->totalothermarks / $stats->s;
 359  
 360          $stats->summarksaverage = $stats->totalsummarks / $stats->s;
 361  
 362          sort($stats->markarray, SORT_NUMERIC);
 363          sort($stats->othermarksarray, SORT_NUMERIC);
 364  
 365          // Here we have collected enough data to make the decision about which questions have variants whose stats we also want to
 366          // calculate. We delete the initialised structures where they are not needed.
 367          if (!$stats->get_variants() || !$stats->break_down_by_variant()) {
 368              $stats->clear_variants();
 369          }
 370  
 371          foreach ($stats->get_variants() as $variant) {
 372              $this->initial_question_walker($stats->variantstats[$variant]);
 373          }
 374      }
 375  
 376      /**
 377       * Loop through all last step data again.
 378       *
 379       * Now we know the averages, accumulate the date needed to compute the higher
 380       * moments of the question scores.
 381       *
 382       * @param object $step        the state to add to the statistics.
 383       * @param calculated $stats       the question statistics we are accumulating.
 384       * @param float[]  $summarks    of the sum of marks for each question usage, indexed by question usage id
 385       */
 386      protected function secondary_steps_walker($step, $stats, $summarks) {
 387          $markdifference = $step->mark - $stats->markaverage;
 388          if ($stats->subquestion) {
 389              $othermarkdifference = $summarks[$step->questionusageid] - $stats->othermarkaverage;
 390          } else {
 391              $othermarkdifference = $summarks[$step->questionusageid] - $step->mark - $stats->othermarkaverage;
 392          }
 393          $overallmarkdifference = $summarks[$step->questionusageid] - $stats->summarksaverage;
 394  
 395          $sortedmarkdifference = array_shift($stats->markarray) - $stats->markaverage;
 396          $sortedothermarkdifference = array_shift($stats->othermarksarray) - $stats->othermarkaverage;
 397  
 398          $stats->markvariancesum += pow($markdifference, 2);
 399          $stats->othermarkvariancesum += pow($othermarkdifference, 2);
 400          $stats->covariancesum += $markdifference * $othermarkdifference;
 401          $stats->covariancemaxsum += $sortedmarkdifference * $sortedothermarkdifference;
 402          $stats->covariancewithoverallmarksum += $markdifference * $overallmarkdifference;
 403  
 404          if (isset($stats->variantstats[$step->variant])) {
 405              $this->secondary_steps_walker($step, $stats->variantstats[$step->variant], $summarks);
 406          }
 407      }
 408  
 409      /**
 410       * And finally loop through all the questions again.
 411       *
 412       * Perform more per-question statistics calculations.
 413       *
 414       * @param calculated $stats question stats to update.
 415       */
 416      protected function secondary_question_walker($stats) {
 417          if ($stats->s > 1) {
 418              $stats->markvariance = $stats->markvariancesum / ($stats->s - 1);
 419              $stats->othermarkvariance = $stats->othermarkvariancesum / ($stats->s - 1);
 420              $stats->covariance = $stats->covariancesum / ($stats->s - 1);
 421              $stats->covariancemax = $stats->covariancemaxsum / ($stats->s - 1);
 422              $stats->covariancewithoverallmark = $stats->covariancewithoverallmarksum /
 423                  ($stats->s - 1);
 424              $stats->sd = sqrt($stats->markvariancesum / ($stats->s - 1));
 425  
 426              if ($stats->covariancewithoverallmark >= 0) {
 427                  $stats->negcovar = 0;
 428              } else {
 429                  $stats->negcovar = 1;
 430              }
 431          } else {
 432              $stats->markvariance = null;
 433              $stats->othermarkvariance = null;
 434              $stats->covariance = null;
 435              $stats->covariancemax = null;
 436              $stats->covariancewithoverallmark = null;
 437              $stats->sd = null;
 438              $stats->negcovar = 0;
 439          }
 440  
 441          if ($stats->markvariance * $stats->othermarkvariance) {
 442              $stats->discriminationindex = 100 * $stats->covariance /
 443                  sqrt($stats->markvariance * $stats->othermarkvariance);
 444          } else {
 445              $stats->discriminationindex = null;
 446          }
 447  
 448          if ($stats->covariancemax) {
 449              $stats->discriminativeefficiency = 100 * $stats->covariance /
 450                  $stats->covariancemax;
 451          } else {
 452              $stats->discriminativeefficiency = null;
 453          }
 454  
 455          foreach ($stats->variantstats as $variantstat) {
 456              $this->secondary_question_walker($variantstat);
 457          }
 458      }
 459  
 460      /**
 461       * Given the question data find the average grade that random guesses would get.
 462       *
 463       * @param object $questiondata the full question object.
 464       * @return float the random guess score for this question.
 465       */
 466      protected function get_random_guess_score($questiondata) {
 467          return \question_bank::get_qtype(
 468              $questiondata->qtype, false)->get_random_guess_score($questiondata);
 469      }
 470  
 471      /**
 472       * Find time of non-expired statistics in the database.
 473       *
 474       * @param \qubaid_condition $qubaids Which question usages to look for?
 475       * @return int|bool Time of cached record that matches this qubaid_condition or false is non found.
 476       */
 477      public function get_last_calculated_time($qubaids) {
 478          return $this->stats->get_last_calculated_time($qubaids);
 479      }
 480  
 481      /**
 482       * Load cached statistics from the database.
 483       *
 484       * @param \qubaid_condition $qubaids Which question usages to load the cached stats for?
 485       * @return all_calculated_for_qubaid_condition The cached stats.
 486       */
 487      public function get_cached($qubaids) {
 488          $this->stats->get_cached($qubaids);
 489          return $this->stats;
 490      }
 491  }