'use strict';

/* @flow */

var mean = require('./mean');

var sampleVariance = require('./sample_variance');

/**

* This is to compute [two sample t-test](http://en.wikipedia.org/wiki/Student's_t-test).

* Tests whether "mean(X)-mean(Y) = difference", (

* in the most common case, we often have `difference == 0` to test if two samples

* are likely to be taken from populations with the same mean value) with

* no prior knowledge on standard deviations of both samples

* other than the fact that they have the same standard deviation.

*

* Usually the results here are used to look up a

* [p-value](http://en.wikipedia.org/wiki/P-value), which, for

* a certain level of significance, will let you determine that the

* null hypothesis can or cannot be rejected.

*

* `diff` can be omitted if it equals 0.

*

* [This is used to confirm or deny](http://www.monarchlab.org/Lab/Research/Stats/2SampleT.aspx)

* a null hypothesis that the two populations that have been sampled into

* `sampleX` and `sampleY` are equal to each other.

*

* @param {Array<number>} sampleX a sample as an array of numbers

* @param {Array<number>} sampleY a sample as an array of numbers

* @param {number} [difference=0]

* @returns {number} test result

* @example

* ss.tTestTwoSample([1, 2, 3, 4], [3, 4, 5, 6], 0); //= -2.1908902300206643

*/

function tTestTwoSample(

sampleX/*: Array<number> */,

sampleY/*: Array<number> */,

difference/*: number */) {

var n = sampleX.length,

m = sampleY.length;

// If either sample doesn't actually have any values, we can't

// compute this at all, so we return `null`.

if (!n || !m) { return null; }

// default difference (mu) is zero

if (!difference) {

difference = 0;

}

var meanX = mean(sampleX),

meanY = mean(sampleY),

sampleVarianceX = sampleVariance(sampleX),

sampleVarianceY = sampleVariance(sampleY);

if (typeof meanX === 'number' &&

typeof meanY === 'number' &&

typeof sampleVarianceX === 'number' &&

typeof sampleVarianceY === 'number') {

var weightedVariance = ((n - 1) * sampleVarianceX +

(m - 1) * sampleVarianceY) / (n + m - 2);

return (meanX - meanY - difference) /

Math.sqrt(weightedVariance * (1 / n + 1 / m));

}

}

module.exports = tTestTwoSample;