JavaScript Program for Bartlett’s Test Calculator

In this article, we are going to implement Bartlett’s test calculator in JavaScript. Bartlett’s test is a statistical test used to determine whether the variances of multiple groups are homogeneous and plays a crucial role in various fields of experimental research such as analysis of variance and hypothesis testing.

We built Bartlett’s test calculator using JavaScript to assess the homogeneity of variances between data groups. By implementing this calculator, we can efficiently perform the Bartlett test and gain valuable insights into the variance of our data.

Approach

In this approach, we take the input sample as a parameter, calculate the variance for each group, and then calculate the chi-squared statistics from the mathematical formula.

χ² = (N - k) * ln(Sp²) - Σ(ni - 1) * ln(si²)

Now that we are calculating degrees of freedom, it can be achieved by subtracting one from the total number of samples. Then we have to calculate the value by using the given mathematical formula.

const pValue = 1 - Math.pow(Math.E, -chiSquare / (2 * degreesOfFreedom));

At last we have to return the object formed by pValue , ChiSquare ,degreesOfFreedom to the main program.

Example: The above approach implemented in the given code.

Javascript

function bartlettsTest(...inputSample) {

    // Number of Samples
    const k = inputSample.length;
    const n = inputSample.map(
        (sampleData) => sampleData.length
    );

    // Sample calculatedMeans
    const calculatedMeans = inputSample.map(
        (sampleData) =>
            sampleData.reduce(
                (sum, value) =>
                    sum + value,
                0
            ) / sampleData.length
    );

    // Sample Variances
    const variances = inputSample.map(
        (sampleData, i) =>
            sampleData.reduce(
                (sum, value) =>
                    sum +
                    Math.pow(
                        value -
                            calculatedMeans[i],
                        2
                    ),
                0
            ) /
            (sampleData.length - 1)
    );

    // Overall mean
    const overallMean =
        calculatedMeans.reduce(
            (sum, mean, i) =>
                sum + (n[i] - 1) * mean,
            0
        ) /
        (n.reduce(
            (sum, value) => sum + value,
            0
        ) -
            k);

    // Chi-square statistic
    const chiSquare =
        (n.reduce(
            (sum, value) => sum + value,
            0
        ) -
            k) *
            Math.log(
                variances.reduce(
                    (
                        prod,
                        variance,
                        i
                    ) =>
                        prod *
                        Math.pow(
                            variance,
                            n[i] - 1
                        ),
                    1
                )
            ) -
        n.reduce(
            (sum, value) =>
                sum + (value - 1),
            0
        );

    // Degrees of freedom
    const degreesOfFreedom = k - 1;

    // P-value
    const pValue =
        1 -
        Math.pow(
            Math.E,
            -chiSquare /
                (2 * degreesOfFreedom)
        );

    return {
        chiSquare: chiSquare,
        degreesOfFreedom:
            degreesOfFreedom,
        pValue: pValue,
    };
}

// Example usage
const sampleData1 = [1, 2, 3, 4, 5];
const sampleData2 = [2, 3, 4, 5, 6];
const sampleData3 = [3, 4, 5, 6, 7];

const result = bartlettsTest(
    sampleData1,
    sampleData2,
    sampleData3
);
console.log(result);

Output

{
  chiSquare: 119.94586538987835,
  degreesOfFreedom: 2,
  pValue: 0.9999999999999052
}