ds_list_standard_score

Wikipedia:

In statistics, the standard score is the (signed) number of standard deviations an observation or datum is above the mean. Thus, a positive standard score indicates a datum above the mean, while a negative standard score indicates a datum below the mean. It is a dimensionless quantity obtained by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation.

The standard score of a raw score x is

$$\large z = {x- \mu \over \sigma}$$

where: $\mu$ is the mean of the population; $\sigma$ is the standard deviation of the population

ds_list_standard_score(list, pos): Returns the standard score (z-score) of the value at a position in a list.

COPY/// @func   ds_list_standard_score(list, pos)
///
/// @desc   Returns the standard score (z-score) of the value at a
///         position in a list. A standard score is the distance of
///         a value from the mean measured in standard deviations.
///         If the list is empty, undefined is returned.
///
/// @param  {list}      list        list data structure
/// @param  {real}      pos         position in the list
///
/// @return {real}      standard score
///
/// GMLscripts.com/license

function ds_list_standard_score(list, pos)
{
    var n = ds_list_size(list);
    if (n == 0) return undefined;

    var avg = 0;
    var sum = 0;

    for (var i=0; i<n; i++) avg += ds_list_find_value(list, i);
    avg /= n;
    for (var i=0; i<n; i++) sum += sqr(ds_list_find_value(list, i) - avg);

    return (ds_list_find_value(list, pos) - avg) / sqrt(sum / n);
}

Contributors: Quimp

GitHub: View · Commits · Blame · Raw