The Jarque-Bera test is a goodness-of-fit test that determines whether or not sample data have skewness and kurtosis that matches a normal distribution.
The test statistic of the Jarque-Bera test is always a positive number and if it’s far from zero, it indicates that the sample data do not have a normal distribution.
The test statistic JB is defined as:
JB =(n/6) * (S2 + (C2/4))
where:
- n: the number of observations in the sample
- S: the sample skewness
- C: the sample kurtosis
Under the null hypothesis of normality, JB ~ X2(2)
This tutorial explains how to conduct a Jarque-Bera test in Excel.
Jarque-Bera test in Excel
Use the following steps to perform a Jarque-Bera test for a given dataset in Excel.
Step 1: Input the data.
First, input the dataset into one column:
Step 2: Calculate the Jarque-Bera Test Statistic.
Next, calculate the JB test statistic. Column F shows the formulas used:
Step 3: Calculate the p-value of the test.
Recall that under the null hypothesis of normality, the test statistic JB follows a Chi-Square distribution with 2 degrees of freedom. Thus, to find the p-value for the test we will use the following function in Excel: =CHISQ.DIST.RT(JB test statistic, 2)
The p-value of the test is 0.5921. Since this p-value is not less than 0.05, we fail to reject the null hypothesis. We don’t have sufficient evidence to say that the dataset is not normally distributed.
plz correct test statistic for Jarque-Bera Test Statistic.
It should be
JB =(n/6) * (S^2 + ((C-3)^2/4))
In fact, the KURT function of Excel is the “Excess Kurtosis”, and not the Kurtosis. The Excess Kurtosis is exactly the Kurtosis minus 3 (note that 3 is the Kurtosis value for a normal distribution). So, the formulation presented by Zack is correct.