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(id,pos)

Returns the standard score (z-score) of the value at a given position in a given list.

COPY
/// ds_list_standard_score(id,pos)
//
//  Returns the standard score (z-score) of the 
//  value at a given position in a given list.
//
//      id          list data structure, real
//      pos         position in the list, real
//
/// gmlscripts.pro/license
{
    var n, avg, sum, i;
    n = ds_list_size(argument0);
    avg = 0;
    sum = 0;
 
    for (i=0; i<n; i+=1) avg += ds_list_find_value(argument0, i);
    avg /= n;
    for (i=0; i<n; i+=1) sum += sqr(ds_list_find_value(argument0, i) - avg);
 
    return (ds_list_find_value(argument0, argument1) - avg)/sqrt(sum/n);
}

Contributors: Quimp

Related: ds_list_add_list, ds_list_add_map, ds_list_cv, ds_list_flip, ds_list_geometric_mean, ds_list_load, ds_list_max, ds_list_mean, ds_list_median, ds_list_min, ds_list_pop_standard_deviation, ds_list_range, ds_list_save, ds_list_select_relative, ds_list_select_relative_wrap, ds_list_standard_deviation, ds_list_standard_score, ds_list_sum, ds_list_sum_squares, ds_list_variance, ds_list_vmr

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