How to Perform a Normality Test in Google Sheets

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:

• H₀: The data is normally distributed.
• H_A: The data is not normally distributed.

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).

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 Google Sheets.

Step 1: Enter the Data

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

Step 2: Calculate the Test Statistic

Next, we will 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 formula:

=CHISQ.DIST.RT(JB test statistic, 2)

The following screenshot shows how to use this formula in practice:

The p-value of the test is 0.601244.

Recall that this Jarque-Bera normality test uses the following hypotheses:

• H₀: The data is normally distributed.
• H_A: The data is not normally distributed.

Since this p-value is not less than 0.05, we fail to reject the null hypothesis.

This means 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

The following tutorials explain how to perform other common tasks in Google Sheets:

How to Perform t-Tests in Google Sheets
How to Perform F-Tests in Google Sheets
How to Calculate Confidence Intervals in Google Sheets