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 samples to be compared come from a population with the same variance. In this case, possible variance differences occur only by chance, since there are small differences in each sampling.

If the p-value for the Levene test is greater than .05, the variances are not significantly different from each other (i.e., the homogeneity assumption of the variance is met). If the p-value for the Levene test is less than .05, there is a significant difference between the variances.

• H₀: Groups have equal variances
• H₁: Groups have different variances

It is important to note that the mean values of the individual groups have no influence on the result-they may differ. A big advantage of Levene's test is that it is very stable against violations of the normal distribution. Therefore, Levene's test is used in many statistics programs.

Furthermore, variance equality can also be checked graphically, usually with a grouped box plot or with a scatterplot.

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 provides a valid assessment of whether group variances can be considered equal.

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 individual subjects 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.

With the help of the box plot you can visualize the result of the Levene test. The box plot shows clearly how much the examined variables scatter.

After the box plot you will now get the table with the Levene test statistics. In this table the significance is the most important value; if the significance is above 0.05 there is no difference between the variances of the samples.

Therefore you can easily calculate a Levene test for equality of variances. If the p-value or significance is less than 0.05, you can assume inhomogeneous variance based on the available data.

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%.

Thus the null hypothesis is maintained and there is no difference between the variances of the three groups. Thus, the three samples come from populations with the same variance.