Levene’s Test is used to determine whether two or more groups have equal variances. This is a widely used test in statistics because many statistical tests use the assumption that groups have equal variances.
This tutorial explains how to perform Levene’s Test in Excel.
Example: Levene’s Test in Excel
Researchers want to know if three different fertilizers lead to different levels of plant growth. They randomly select 30 different plants and split them into three groups of 10, applying a different fertilizer to each group. At the end of one month they measure the height of each plant.
Before they conduct a statistical test to determine if there is a difference in plant growth between the groups, they first want to perform Levene’s Test to determine whether or not the three groups have equal variances.
Use the following steps to perform Levene’s Test in Excel.
Step 1: Enter the data.
Enter the following data, which shows the total growth (in inches) for each of the 10 plants in each group:
Step 2: Calculate the mean of each group.
Next, calculate the mean of each group using the AVERAGE() function:
Step 3: Calculate the absolute residuals.
Next, calculate the absolute residuals for each group. The following screenshot shows the formula to use to calculate the residual of the first observation in the first group:
Copy this formula to all remaining cells:
Step 4: Perform a One-Way ANOVA.
Excel doesn’t have a built-in function to perform Levene’s Test, but a workaround is to perform a one-way ANOVA on the absolute residuals. If the p-value from the ANOVA is less than some significance level (.e.g 0.05), this indicates that the three groups do not have equal variances.
To perform a one-way ANOVA, go to the Data tab and click on Data Analysis. If you don’t see this option, then you need to first install the free Analysis ToolPak.
Once you click on Data Analysis, a new window will pop up. Select Anova: Single Factor and click OK.
For Input Range, choose the cells where the absolute residuals are located. For Output Range, choose a cell where you would like the results of the one-way ANOVA to appear. Then click OK.
The results of the one-way ANOVA will automatically appear:
We can see that the p-value of the one-way ANOVA is 0.591251. Because this value is not less than 0.05, we fail to reject the null hypothesis. In other words, we don’t have sufficient evidence to say that the variance between the three groups is different.
Thanks a lot! saved me so much time.
Thank you so much, Zach, for all of your assistance. I tell my students to look to STATOLOGY anytime they need user-friendly STAT support.
Keep the great, friendly work up!
Don’t you use the absolute difference of the MEDIAN and not the MEAN ??
Thank you very much, that was very helpful for my data analysis for my master thesis!!
thanks for your explination
You are very welcome! Keep us posted on your progress.
I have three parameters, with three parameters in four replicates in two years.
The experiment was a split-plot design, with four replicates over two years.
How can I use Levene’s test to show non-significance between years, and therefore use the two-year mean?
Please send an example of the statistical analysis in an Excel file.
This is important, and I hope you can help me quickly.
Hi Khaled…Good question — and just to be clear upfront, I can’t provide spreadsheets directly. But I can walk you through how to approach this.
Since you have a split-plot design with replicates across two years, what you want to check is whether the variance between years is significantly different. Levene’s test is useful here because it tests the equality of variances.
Here’s how you’d do it conceptually:
1. Organize your data so that you have a column for the response variable and a column indicating the year.
2. Apply Levene’s test with “year” as the grouping factor. Most stats packages (like R, SAS, SPSS, or Python’s `scipy.stats.levene`) let you specify groups like this.
3. Interpret the result:
* If the p-value is greater than your significance threshold (often 0.05), you fail to reject the null hypothesis of equal variances. That means there’s no significant difference in variance between years, so you can justify pooling data and reporting the two-year mean.
* If the test is significant, then you’d need to consider each year separately in your analysis.
The main idea is: Levene’s test doesn’t directly tell you “use the two-year mean,” but it reassures you that combining years won’t violate the assumption of equal variances.