Levene's Test in Excel using QI Macros Add-in

Levene's Test for Non-normal Data and More Than Two Data Samples

Levene's Test compares two or more independent sets of test data. It helps determine if the variances are the same or different from each other. The Levene's Test is like the f test. However, the Levene's test is robust enough for non-normal data and handles more than two columns of data. QI Macros uses Median (Brown-Forsythe modification) instead of the Mean for calculations.

Note: Excel does not do a Levene's Test; QI Macros adds this functionality.

Levene's Test Example

If you're producing rubber made with two different recipes, you might want to know if the variances in tensile strengths are the same or different (Juran's QC Handbook 4th pg 23.74):

Conduct a test and enter the data into Excel.

example of levenes test data

Click and drag over the data to select it and click on QI Macros Menu, Statistical Tools, f and t Tests and then Levene's test for variance:

levenes test excel

QI Macros will perform the calculations and interpret the results for you.

levenes test results

Interpreting the Levene's Test Results Manually

  • The null hypothesis (H0) - variances are the same (variances are not different)
  • The alternate hypothesis (Ha) - variances are different
Hypothesis Test
p value Method p value < a Reject the null hypothesis
p value Method p value > a Cannot Reject the null hypothesis (Accept the null hypothesis)

Since Levene's p value > a ( 0.337> 0.05), we cannot reject the null hypothesis (accept the null hypothesis) that the variances are equal. 

While an F test works well on two-samples of normal data, it isn't robust enough to handle non-normal data or more than two samples. (Notice that Levene's p value differs from F Test's two-tailed value of 0.305; however both cause acceptance of null hypothesis.)

Levene's Test - ten sample example

Now, consider the following example of ten batches of gear diameters:

Levene's Test sample data

Levene's Test results /></p>
<p> Again the p-value 0.099 > 0.05, so we cannot reject the null hypothesis (accept the null hypothesis). Variances are the same from a batch to batch. 
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