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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;