What is the Jarque-Bera Test?

The Jarque-Bera test is a statistical test used to assess whether a given dataset follows a normal distribution based on its skewness and kurtosis. Its purpose is to determine if the data conforms to the assumptions of many statistical techniques that rely on the normality assumption, such as linear regression and t-tests. By testing for normality, the Jarque-Bera test helps ensure the validity of statistical analyses and the reliability of their results.

• Null Hypothesis (H0): The data is normally distributed.
• Alternative Hypothesis (H1): The data is not normally distributed.

After conducting the test, you will typically obtain a test statistic and its associated p-value. Here’s how to interpret the results:

• If the p-value is less than the chosen significance level (e.g., 0.05)
  • Reject the null hypothesis.
  • Conclude that the data are not normally distributed.
• If the p-value is greater than or equal to the significance level
  • Fail to reject the null hypothesis.
  • Conclude that there is not enough evidence to suggest that the data are not normally distributed.

A larger test statistic indicates a greater departure from normality.

• If p-value < significance level: Reject H0, conclude data are not normally distributed.
• If p-value ≥ significance level: Fail to reject H0, conclude there’s not enough evidence to suggest data are not normally distributed.

The test statistic for the Jarque-Bera test is computed based on the skewness and kurtosis of the dataset. Specifically, it uses the following formula:

[Tex]JB = \frac{n}{6} \left( S^2 + \frac{1}{4}(K – 3)^2 \right) [/Tex]

Where:

• n is the sample size.
• S is the skewness of the data.
• K is the kurtosis of the data.

Under the null hypothesis of normality, the test statistic JB asymptotically follows a chi-square distribution with two degrees of freedom (because there are two parameters estimated from the sample data: skewness and kurtosis).

To conduct the Jarque-Bera test, we compare the computed test statistic with the critical value from the chi-square distribution at a chosen significance level. If the test statistic is greater than the critical value, then we reject the null hypothesis, indicating that the data is not normally distributed.

Preparing the data properly before conducting the test

1. Accuracy of Results: Preparing the data properly helps ensure that the data accurately reflects the underlying phenomenon being studied. This includes verifying the correctness of data entries, addressing missing or erroneous values, and checking for outliers or anomalies.
2. Assumption of Normality: The Jarque-Bera test assumes that the data are drawn from a normal distribution. Therefore, it’s essential to confirm that this assumption holds true before conducting the test. Data preparation may involve transforming the data or identifying and addressing any violations of normality assumptions.
3. Quality of Inferences: The conclusions drawn from the Jarque-Bera test can influence subsequent analyses or decisions. Proper data preparation helps mitigate potential biases or errors in these inferences, ensuring that they are accurate and reliable.
4. Validity of Statistical Analyses: Many statistical methods and models rely on the normality assumption. If the data violate this assumption, the results of subsequent analyses may be invalid or misleading. Proper data preparation helps ensure that the data conform to the assumptions required by the statistical techniques being applied.
5. Robustness of Findings: Well-prepared data contribute to the robustness of research findings. By addressing potential issues in the data before conducting the Jarque-Bera test, researchers can have greater confidence in the reliability and generalizability of their results.

In this article, we will discuss What is the Jarque-Bera Test and how we perform the Jarque-Bera Test in R Programming Language.