simple-statistics/src/t_test.js

Simple Statistics

import mean from "./mean.js";
import standardDeviation from "./standard_deviation.js";

/**
 * This is to compute [a one-sample t-test](https://en.wikipedia.org/wiki/Student%27s_t-test#One-sample_t-test), comparing the mean
 * of a sample to a known value, x.
 *
 * in this case, we're trying to determine whether the
 * population mean is equal to the value that we know, which is `x`
 * here. 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.
 *
 * @param {Array<number>} x sample of one or more numbers
 * @param {number} expectedValue expected value of the population mean
 * @returns {number} value
 * @example
 * tTest([1, 2, 3, 4, 5, 6], 3.385).toFixed(2); // => '0.16'
 */
function tTest(x, expectedValue) {
    // The mean of the sample
    const sampleMean = mean(x);

    // The standard deviation of the sample
    const sd = standardDeviation(x);

    // Square root the length of the sample
    const rootN = Math.sqrt(x.length);

    // returning the t value
    return (sampleMean - expectedValue) / (sd / rootN);
}

export default tTest;