simple-statistics/src/t_test_two_sample.js

import mean from "./mean";
import sampleVariance from "./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|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;