Levene Test

TL;DR

Tests whether variances are equal across two or more groups.
Non-parametric: does not assume a specific distribution for the data.
Commonly used to check variance assumptions before applying parametric tests (e.g., t-test, ANOVA).

Definition

The Levene test is a statistical test used to assess the equality of variances across different groups or samples. It is a non-parametric test that does not assume a specific distribution of the data.

Explanation

To perform the Levene test, the researcher:

Collects data for the variable of interest for each group or sample.
Calculates the mean and standard deviation for each group, and the overall mean and standard deviation for the entire sample.
Computes the absolute deviation of each data point from its group mean, then squares these deviations to obtain the sum of squares within groups (SSW).
Computes the absolute deviation of each group mean from the overall mean, then squares these deviations to obtain the sum of squares between groups (SSB).
Divides SSW by the degrees of freedom within groups and divides SSB by the degrees of freedom between groups.
Uses these values to calculate the Levene test statistic and compares it to a critical value from a table of critical values for the Levene test.
If the Levene test statistic is greater than the critical value, the researcher concludes that variances are unequal across groups.

Examples

Medical treatment comparison

A study compares the effectiveness of two different treatments for a medical condition by collecting data on improvement in symptoms for each treatment group. The researcher uses the Levene test to determine whether the two groups have equal variances in their symptom improvement scores. If variances are unequal, the researcher can choose a test that accounts for unequal variances.

Job satisfaction survey

A survey measures job satisfaction among employees in different departments of a company. The researcher applies the Levene test to determine whether satisfaction levels have equal variances across departments. If variances are unequal, the researcher can use a more appropriate test that accounts for unequal variances.

Use cases

Testing the variance-equality assumption before applying parametric tests such as the t-test or ANOVA.
Applicable in various settings, for example medical studies and surveys.

Notes or pitfalls

The Levene test does not assume a specific data distribution (non-parametric).
If the test indicates unequal variances, select statistical methods that account for unequal variances rather than proceeding with methods that assume homogeneity of variance.

t-test
ANOVA