text: /* @flow */
  
  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 /*: Array<number> */,
      sampleY /*: Array<number> */,
      difference /*: ?number */
  ) /*: ?number */ {
      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;
  