/**
* Compute the quiz statistics.
*
* @param int $quizid the quiz id.
* @param int $whichattempts which attempts to use, represented internally as one of the constants as used in
* $quiz->grademethod ie.
* QUIZ_GRADEAVERAGE, QUIZ_GRADEHIGHEST, QUIZ_ATTEMPTLAST or QUIZ_ATTEMPTFIRST
* we calculate stats based on which attempts would affect the grade for each student.
* @param array $groupstudents students in this group.
* @param int $p number of positions (slots).
* @param float $sumofmarkvariance sum of mark variance, calculated as part of question statistics
* @return quiz_statistics_calculated $quizstats The statistics for overall attempt scores.
*/
public function calculate($quizid, $whichattempts, $groupstudents, $p, $sumofmarkvariance)
{
$quizstats = new quiz_statistics_calculated($whichattempts);
$countsandaverages = $this->attempt_counts_and_averages($quizid, $groupstudents);
foreach ($countsandaverages as $propertyname => $value) {
$quizstats->{$propertyname} = $value;
}
$s = $quizstats->s();
if ($s == 0) {
return $quizstats;
}
// Recalculate sql again this time possibly including test for first attempt.
list($fromqa, $whereqa, $qaparams) = quiz_statistics_attempts_sql($quizid, $groupstudents, $whichattempts);
$quizstats->median = $this->median($s, $fromqa, $whereqa, $qaparams);
if ($s > 1) {
$powers = $this->sum_of_powers_of_difference_to_mean($quizstats->avg(), $fromqa, $whereqa, $qaparams);
$quizstats->standarddeviation = sqrt($powers->power2 / ($s - 1));
// Skewness.
if ($s > 2) {
// See http://docs.moodle.org/dev/Quiz_item_analysis_calculations_in_practise#Skewness_and_Kurtosis.
$m2 = $powers->power2 / $s;
$m3 = $powers->power3 / $s;
$m4 = $powers->power4 / $s;
$k2 = $s * $m2 / ($s - 1);
$k3 = $s * $s * $m3 / (($s - 1) * ($s - 2));
if ($k2 != 0) {
$quizstats->skewness = $k3 / pow($k2, 3 / 2);
// Kurtosis.
if ($s > 3) {
$k4 = $s * $s * (($s + 1) * $m4 - 3 * ($s - 1) * $m2 * $m2) / (($s - 1) * ($s - 2) * ($s - 3));
$quizstats->kurtosis = $k4 / ($k2 * $k2);
}
if ($p > 1) {
$quizstats->cic = 100 * $p / ($p - 1) * (1 - $sumofmarkvariance / $k2);
$quizstats->errorratio = 100 * sqrt(1 - $quizstats->cic / 100);
$quizstats->standarderror = $quizstats->errorratio * $quizstats->standarddeviation / 100;
}
}
}
}
$quizstats->cache(quiz_statistics_qubaids_condition($quizid, $groupstudents, $whichattempts));
return $quizstats;
}
