JarqueBera Test Calculator for Statistical Analysis

JarqueBera Test Calculator for Statistical Analysis calculator can be used to test if a sample of data has a distribution that is sufficiently close to the normal distribution. It is a goodness-of-fit test based on the sample skewness and kurtosis.

Input Parameters

Calculation Results

Calculation Formula

J = n/6 * [ (Σ(xi - x̄)²/n) / (s²) - 3 ]²

Where:
n = sample size
x̄ = sample mean
s² = sample variance
xi = individual data points

JarqueBera Test Calculator for Statistical Analysis Calculator Usage Guide

Learn how to use the JarqueBera Test Calculator for Statistical Analysis calculator and its working principles

How to Use the Calculator

  1. Enter your data in the text box, separated by commas. Ensure each value is a numeric number.
  2. Click the "Calculate" button to perform the Jarque-Bera test.
  3. The calculator will display the Jarque-Bera test statistic, p-value, sample skewness, and sample kurtosis.

Understanding the Results

The Jarque-Bera test is a statistical test for normality. The null hypothesis is that the data follows a normal distribution.

  • Test Statistic (J): Measures how much the sample distribution deviates from normality.
  • P-value: Indicates the probability of observing the test statistic under the null hypothesis. A small p-value (typically less than 0.05) suggests rejecting the null hypothesis, indicating the data is not normally distributed.
  • Skewness: Measures the asymmetry of the probability distribution. A skewness close to 0 indicates a symmetric distribution.
  • Kurtosis: Measures the "tailedness" of the probability distribution. A kurtosis close to 0 indicates a distribution with tails similar to a normal distribution.

Principle of the Jarque-Bera Test

The Jarque-Bera test is based on the fact that if a sample comes from a normal distribution, then the skewness should be close to 0 and the kurtosis should be close to 3. The test statistic is calculated by comparing the sample skewness and kurtosis to these theoretical values.

Limitations

The Jarque-Bera test has some limitations:

  • It becomes more powerful as the sample size increases.
  • It may not be reliable for small sample sizes.
  • It assumes that the data is continuous and normally distributed.