/**
* Saves the mean/median of a question on a paper.
* @param int $paperID - The ID of the paper we are dealing with.
* @param array $q_medians - Array containing the statistics to be saved.
*/
public function save_median_question_marks($paperID, $q_medians)
{
$this->db->autocommit(false);
$result = $this->db->prepare("REPLACE INTO cache_median_question_marks (paperID, questionID, median, mean) VALUES (?, ?, ?, ?)");
foreach ($q_medians as $q_id => $median_array) {
$median = MathsUtils::median($median_array);
$mean = MathsUtils::mean($median_array);
$result->bind_param('iidd', $paperID, $q_id, $median, $mean);
$result->execute();
}
$result->close();
$this->db->commit();
$this->db->autocommit(true);
}
/**
* Creates an array of basic statistics on the cohort performance.
*/
public function generate_stats()
{
$configObject = Config::get_instance();
$percent_decimals = $configObject->get('percent_decimals');
// Generate summary statistics.
$this->set_user_no();
$mark_total = 0;
$percent_total = 0;
$this->stats['sum_of_marks'] = 0;
$this->stats['out_of_range'] = 0;
$this->stats['completed_no'] = 0;
$this->stats['failures'] = 0;
$this->stats['passes'] = 0;
$this->stats['honours'] = 0;
$this->stats['total_time'] = 0;
$this->stats['max_mark'] = 0;
$this->stats['min_mark'] = 9999;
$this->stats['max_percent'] = 0;
$this->stats['min_percent'] = 100;
$median_mark_array = array();
$median_percent_array = array();
$marks_data = array();
for ($i = 0; $i < $this->user_no; $i++) {
if (isset($this->user_results[$i]['percent']) and $this->user_results[$i]['questions'] >= $this->question_no and $this->user_results[$i]['visible']) {
$this->stats['completed_no']++;
$median_mark_array[] = round($this->user_results[$i]['mark'], $percent_decimals);
$median_percent_array[] = round($this->user_results[$i]['percent'], $percent_decimals);
$mark_total += round($this->user_results[$i]['mark'], $percent_decimals);
$percent_total += round($this->user_results[$i]['percent'], $percent_decimals);
// Round to the precision being displayed on screen.
}
if (isset($this->user_results[$i]['mark']) and $this->user_results[$i]['visible']) {
$tmp_mark = round($this->user_results[$i]['mark'], $percent_decimals);
$tmp_percent = round($this->user_results[$i]['percent'], $percent_decimals);
$marks_data[] = $tmp_percent;
if ($tmp_percent < $this->pass_mark) {
$this->stats['failures']++;
}
if ($tmp_percent < $this->stats['min_percent']) {
$this->stats['min_percent'] = $tmp_percent;
}
if ($tmp_percent > $this->stats['max_percent']) {
$this->stats['max_percent'] = $tmp_percent;
}
if ($tmp_percent >= $this->pass_mark and $tmp_percent < $this->distinction_mark) {
$this->stats['passes']++;
}
if ($tmp_percent >= $this->distinction_mark) {
$this->stats['honours']++;
}
if ($tmp_mark < $this->stats['min_mark']) {
$this->stats['min_mark'] = $tmp_mark;
}
if ($tmp_mark > $this->stats['max_mark']) {
$this->stats['max_mark'] = $tmp_mark;
}
$this->stats['sum_of_marks'] += $tmp_mark;
}
if ($this->user_results[$i]['visible']) {
$this->stats['total_time'] += $this->user_results[$i]['duration'];
} else {
$this->stats['out_of_range']++;
}
}
if ($this->stats['min_mark'] == 9999) {
$this->stats['min_mark'] = 0;
}
// Reset back to zero if still on default.
$this->stats['range'] = $this->stats['max_mark'] - $this->stats['min_mark'];
$this->stats['range_percent'] = $this->stats['max_percent'] - $this->stats['min_percent'];
// Calculate StdDev.
$xmean_total = 0;
$xmean_percent_total = 0;
for ($i = 0; $i < $this->user_no; $i++) {
if (isset($this->user_results[$i]['questions']) and $this->user_results[$i]['questions'] >= $this->question_no and $this->user_results[$i]['visible'] and $this->stats['completed_no'] > 0) {
$tmp_percent = round($this->user_results[$i]['percent'], $percent_decimals);
$xmean_total += ($this->user_results[$i]['mark'] - $mark_total / $this->stats['completed_no']) * ($this->user_results[$i]['mark'] - $mark_total / $this->stats['completed_no']);
$xmean_percent_total += ($tmp_percent - $percent_total / $this->stats['completed_no']) * ($tmp_percent - $percent_total / $this->stats['completed_no']);
}
}
if ($this->stats['completed_no'] > 1) {
$this->stats['stddev_mark'] = sqrt($xmean_total / ($this->stats['completed_no'] - 1));
$this->stats['stddev_percent'] = sqrt($xmean_percent_total / ($this->stats['completed_no'] - 1));
} else {
$this->stats['stddev_mark'] = 0;
$this->stats['stddev_percent'] = 0;
}
if ($this->stats['completed_no'] > 0) {
$this->stats['mean_mark'] = $mark_total / $this->stats['completed_no'];
$this->stats['mean_percent'] = $percent_total / $this->stats['completed_no'];
$this->stats['median_mark'] = MathsUtils::median($median_mark_array);
$this->stats['median_percent'] = MathsUtils::median($median_percent_array);
} else {
$this->stats['mean_mark'] = 0;
$this->stats['mean_percent'] = 0;
$this->stats['median_mark'] = 0;
$this->stats['median_percent'] = 0;
}
$this->stats['q1'] = MathsUtils::percentile($marks_data, 0.75);
$this->stats['q2'] = MathsUtils::percentile($marks_data, 0.5);
$this->stats['q3'] = MathsUtils::percentile($marks_data, 0.25);
for ($i = 1; $i < 10; $i++) {
$this->stats["decile{$i}"] = MathsUtils::percentile($marks_data, $i / 10);
}
}
