# Seeking a statistical javascript function to return p-value from a z-score

I need to convert z-scores to percentile. I found reference to a function in the jStat library that I could use (jstat.ztest), but the jStat documentation seems to be ahead of the available library because there is no such function in the currently available version of the library.

I think there is a more recent version of the library on GitHub, which may include the ztest function, but I am a linux novice and could not figure out how to build the library from the instructions. I spent most of a day learning about git bash and cygwin trying to build the library; I finally decided I'd be better off asking here.

So, could anyone point me toward a javascript function that would do what I need? Alternatively, could anyone point me toward a built version of the jStat library with ztest function included?

I found this in a forum online and it works like a charm.

``````function GetZPercent(z)
{
//z == number of standard deviations from the mean

//if z is greater than 6.5 standard deviations from the mean
//the number of significant digits will be outside of a reasonable
//range
if ( z < -6.5)
return 0.0;
if( z > 6.5)
return 1.0;

var factK = 1;
var sum = 0;
var term = 1;
var k = 0;
var loopStop = Math.exp(-23);
while(Math.abs(term) > loopStop)
{
term = .3989422804 * Math.pow(-1,k) * Math.pow(z,k) / (2 * k + 1) / Math.pow(2,k) * Math.pow(z,k+1) / factK;
sum += term;
k++;
factK *= k;

}
sum += 0.5;

return sum;
}
``````

And I don't need to include a large library just for the one function.

Just editing the code from Paul's answer for a two-sided t-test

``````function GetZPercent(z)
{
//z == number of standard deviations from the mean

//if z is greater than 6.5 standard deviations from the mean
//the number of significant digits will be outside of a reasonable
//range
if ( z < -6.5)
return 0.0;
if( z > 6.5)
return 1.0;

if (z > 0) { z = -z;}

var factK = 1;
var sum = 0;
var term = 1;
var k = 0;
var loopStop = Math.exp(-23);
while(Math.abs(term) > loopStop)
{
term = .3989422804 * Math.pow(-1,k) * Math.pow(z,k) / (2 * k + 1) / Math.pow(2,k) * Math.pow(z,k+1) / factK;
sum += term;
k++;
factK *= k;

}
sum += 0.5;

return (2*sum);
}
``````

This seems like such a simple ask but I had a hard time tracking down a library that does this instead of copying some random code snippet. Best I can tell this will calculate z-score from a percentage using the simple-statistics library.

I took their documentation about cumulativestdnormalprobability and backed into the following algorithm. Feels like there should be an easier way but who knows.

https://simplestatistics.org/docs/#cumulativestdnormalprobability

``````const z_score = inverseErrorFunction((percentile_value - 0.5) / 0.5) * Math.sqrt(2);
``````