  # ds_list_standard_score

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
///

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