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t_test_two_sample.js
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t_test_two_sample.js
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import mean from "./mean.js";
import sampleVariance from "./sample_variance.js";
/**
* 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 reject](https://en.wikipedia.org/wiki/Exclusion_of_the_null_hypothesis)
* 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|null} test result
*
* @example
* tTestTwoSample([1, 2, 3, 4], [3, 4, 5, 6], 0); // => -2.1908902300206643
*/
function tTestTwoSample(sampleX, sampleY, difference) {
const n = sampleX.length;
const 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;
}
const meanX = mean(sampleX);
const meanY = mean(sampleY);
const sampleVarianceX = sampleVariance(sampleX);
const sampleVarianceY = sampleVariance(sampleY);
if (
typeof meanX === "number" &&
typeof meanY === "number" &&
typeof sampleVarianceX === "number" &&
typeof sampleVarianceY === "number"
) {
const weightedVariance =
((n - 1) * sampleVarianceX + (m - 1) * sampleVarianceY) /
(n + m - 2);
return (
(meanX - meanY - difference) /
Math.sqrt(weightedVariance * (1 / n + 1 / m))
);
}
}
export default tTestTwoSample;