This guide will explain how to perform a Jarque-Bera test in Excel.
The Jarque-Bera test statistic can determine the normality of a given distribution.
Normality is the statistical property that checks if a distribution is spread according to a normal distribution. This type of distribution appears as a bell curve, with a symmetrical shape with most values falling close to the mean or central peak.
Many different statistical methods assume that the data is normally distributed. Because of this reason, practical statistics often require you to test your dataset for normality.
Statisticians who test normality perform calculations that will decide whether or not to reject the null hypothesis. This null hypothesis will state that the given distribution does not follow a normal distribution.
A quick way to check for normality is through the Jarque-Bera test. The test considers the skewness and kurtosis of the given population as a basis of normality.
The test statistic JB is defined as follows:
JB = (n/6) (S2 + ¼(K-3)2)
The value n refers to the number of observations, S refers to the sample skewness, and K refers to the sample kurtosis.
The test statistic is always positive. If the value of the test statistic moves away from 0, it indicates that the data does not follow a normal distribution. A test statistic closer to 0 indicates a higher chance of normality.
Before explaining how to perform the Jarque-Bera test, let’s look into a simple example of a use case where we may need to test for normality.
Suppose you want to test whether the IQ in a given population follows a normal distribution. Given a dataset of 1000 observations, how can we test for normality?
Excel provides the KURT
function to find the kurtosis of a sample and the SKEW
function to find the skewness of a sample. These functions will make it easier for users to conduct the Jarque-Bera test in a spreadsheet.
Now that we know when to use the Jarque-Bera test, let’s learn how to use it on an actual sample spreadsheet.
A Real Example of Using the Jarque-Bera Test in Excel.
The following section provides an example of how to perform the Jarque-Bera test. We will also explain the formulas and tools used in these examples.
First, let’s take a look at our sample data. We have 84 randomly selected observations arranged in a four-column table.
We’ll use the Jarque-Bera test statistic to determine whether the sample data follows a normal distribution. Afterwards, we’ll use a chi-square test to determine whether to accept the results of the JB test.
Do you want to take a closer look at our examples? You can make your own copy of the spreadsheet above using the link attached below.
If you’re ready to perform a Jarque-Bera test in Excel, head over to the next section to read our step-by-step breakdown on how to do it!
How to Perform a Jarque-Bera Test in Excel
This section will guide you through each step needed to test the normality of a distribution using the Jarque-Bera test. You’ll learn how to use the SKEW
and KURT
functions to find the Jarque-Bera test statistic. We’ll also explain how to calculate the test’s p-value.
Follow these steps to start using the Jarque-Bera test in Excel:
- First, we must find the value of n or the sample size of our data. We can determine the sample size using the
COUNT
function.
We’ll have to divide the value of n by 6 to follow the JB test statistic equation.
- Next, we’ll need to find the skewness of our sample data using the
SKEW
function. TheSKEW
function’s output will be raised to the power of 2.
- Next, we’ll find the kurtosis of the dataset using the
KURT
function.
- Evaluate the function by typing the Enter key.
In this example, we’ve determined that the sample data has a JB test statistic of 4.16.
- We can use the
CHISQ.DIST.RT
function to perform a chi-square test with two degrees of freedom.
These are all the steps needed to perform a Jarque Bera Test in Excel.
Frequently Asked Questions (FAQ)
Here are some frequently asked questions about the Jarque-Bera test:
- What are the downsides of the Jarque-Bera test?
The Jarque-Bera test works well for symmetric and long-tailed distributions. However, the test is less accurate when handling asymmetric or bimodal data. - In what situations is non-normality a problem?
Non-normality may be an indicator of a large number of outliers. Outliers may result in skewed data, making it difficult to create an accurate model.
This step-by-step guide should provide you with all the information you need to perform a Jarque-Bera test in Excel.
You should now understand why it is important to test for normality and how the skewness and kurtosis of a sample can be useful for testing.
The Jarque-Bera test is just one example of the many statistical functions you can use in your spreadsheets. Our website offers hundreds of other functions and methods to help you get more out of Microsoft Excel.
With so many other Excel functions available, you can find one appropriate for your use case.
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