Many statistical tests make the assumption that the values in a dataset are normally distributed.

One of the easiest ways to test this assumption is to perform a **Jarque-Bera test**, which is a goodness-of-fit test that determines whether or not sample data have skewness and kurtosis that matches a normal distribution.

This test uses the following hypotheses:

H_{0}: The data is normally distributed.

H_{A}: The data is *not* normally distributed.

The test statistic * JB *is defined as:

* JB * =(n/6) * (S

^{2}+ (C

^{2}/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 ~ *X^{2}(2).

If the p-value that corresponds to the test statistic is less than some significance level (e.g. α = .05), then we can reject the null hypothesis and conclude that the data is not normally distributed.

This tutorial provides a step-by-step example of how to perform a Jarque-Bera test for a given dataset in Excel.

**Step 1: Create the Data**

First, let’s create a fake dataset with 15 values:

**Step 2: Calculate the Test Statistic**

Next, calculate the JB test statistic. Column E shows the formulas used:

The test statistic turns out to be **1.0175**.

**Step 3: Calculate the P-Value**

Under the null hypothesis of normality, the test statistic JB follows a Chi-Square distribution with 2 degrees of freedom.

So, 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 **0.601244**. 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.

In other words, we can assume that the data is normally distributed.

**Additional Resources**

How to Create a Q-Q Plot in Excel

How to Perform a Chi-Square Goodness of Fit Test in Excel

is Chi Square for categorical data though?

Aren’t you forgetting to subtract “3” from the kurtosis in the JB test statistic calculation?

i.e. JB=(n/6) * (S^2 + ((C-3)^2) / 4 )

Does the result from this correlate with results from statistical software like R, SPSS, SAS, SigmaPlot? I guess it does not. Then it would be meaningless to follow your technique. Any clarification you may have in this querry would be appreciated. Thank you.

Hello Zach, thank you for posting but, according to Wikipedia,

JB = n/6*(S^2+((K-3)^2)/4))

what do you think?

The JB goodness of fit is designed for sample sizes > 2000.

How much confidence can be put into statistic with smaller sample sizes?

I believe the ‘K-3’ issue relates to the author’s use of Excel’s KURT() function. This calculates excess kurtosis which is 3 less than kurtosis. Therefore there is no need to deduct 3 when calculating the JB test value.

I appreciate the tutorial. It was inspiration for me to create a normality test procedure based on an Excel form. I added a histogram and normal plot overlay for visualization using variable binning based on 3.5 SD. I am surprised at the comments. I don’t believe the author should have to prove the validity of the test method. There are a number of journal articles that address this: https://www.tandfonline.com/doi/full/10.1080/00949655.2010.520163

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