Levene Test

What is the Levene Test?

Many statistical testing procedures require equal variance in the samples. How can we check whether the variances are homogeneous, i.e. whether there is equality of variance? This is where the Levene test helps. The Levene test checks whether several groups have the same variance in the population.

Levene's test is therefore used to test the null hypothesis that the populations from which the groups were sampled have the same variance. Even if the population variances are equal, the sample variances will usually differ somewhat because of random sampling.

If the p-value for the Levene test is greater than .05, there is not enough evidence to conclude that the population variances differ. If the p-value is less than .05, there is evidence that at least one population variance differs. A non-significant result does not prove that the variances are exactly equal.

• H₀: The population variances are equal across groups.
• H₁: At least one population variance differs.

It is important to note that the mean values of the individual groups have no influence on the result; they may differ. A major advantage of Levene's test is that it is more robust to departures from normality than some other variance tests. The original test uses deviations from each group mean. A common variant, often called the Brown-Forsythe test, uses deviations from each group median and is generally more robust when distributions are skewed or contain outliers.

Variability can also be compared graphically with a grouped box plot. Such a plot is useful as a visual check, but it does not replace the formal test.

Assumptions for the Levene test

The Levene test has two basic assumptions:

• independent observations
• the test variable has metric scale level

First, the observations must be independent, meaning that the values in one group are not influenced by or related to the values in another group or to repeated measurements from the same individuals.

Second, the variable being tested should be measured on a metric scale, so that meaningful distances between values exist.

When these assumptions are met, Levene's test assesses whether the data provide evidence that the group variances differ.

Levene Test Example

In this fictitious example, you conducted a survey among students to find out how many cups of coffee they drink per week. Now you want to know whether the variances of the three fields of study are the same and calculate a Levene test for this.

To calculate the Levene test, simply copy the upper table into the table in the Statistics Calculator and then click on Hypothesis tests. Now you just need to select the three variables Math, History, and Psychology and an ANOVA will be calculated. Here you will also find a calculated Levene test.

As a result you get two tables and a box plot. The first table describes the variables descriptively and you can read the standard deviation of each variable.

The box plot helps you compare the spread of the three groups visually.

After the box plot you will now get the table with the Levene test statistics. In this table, the p-value is the most important value. If it is above 0.05, the test has not found sufficient evidence that the population variances differ.

Therefore you can easily calculate a Levene test for equality of variances. If the p-value is less than 0.05, the available data provide evidence of unequal population variances. For comparisons of means, a method that does not assume equal variances, such as Welch's t-test or Welch's ANOVA, may then be appropriate.

Interpreting the Levene Test

The degree of freedom df1 is obtained by calculating the number of groups minus 1, the degree of freedom df2 is obtained by calculating the number of cases minus the number of groups. In this example the significance of 0.153 is greater than the defined significance level of 5%.

The null hypothesis is therefore not rejected. The result does not provide sufficient evidence that the population variances differ, but it does not prove that they are exactly equal.