Levene's Test

Robust test for equality of variances across multiple groups.

Test Overview

What it tests:

Whether k populations have equal variances (homogeneity of variance assumption).

How it works:

Computes absolute deviations from group medians (or means) and performs ANOVA on these deviations.

Advantages:

• • Robust to non-normality
• • Works with multiple groups
• • Less sensitive to outliers
• • Widely available in software

When to Use:

• • Before ANOVA analysis
• • Non-normal data
• • Multiple group comparisons
• • Presence of outliers

W Statistic & Test Variants

Test Statistic:

Levene's test transforms each observation into an absolute deviation from its group center, then runs a one-way ANOVA on those deviations.

Transformed observation

Xij

= j-th observation in group i

= mean (or median) of group i

Levene's W statistic

= total number of observations

= number of groups

= number of observations in group i

= mean of Zij within group i

= grand mean of all Zij

Test Variants:

• • Median-based: Most robust, recommended (Brown-Forsythe modification)
• • Mean-based: More powerful with normal data
• • Trimmed mean: Compromise between robustness and power

Key Assumptions

• • Observations are independent within and across groups
• • Groups are random samples from their respective populations
• • W statistic is referred to an F-distribution with (k-1, N-k) degrees of freedom

Reading the Levene's Equal-Variance Plot

Example Result & Interpretation

Three groups (A, B, C) of measurements are tested for equal variances. Absolute deviations from each group's median are computed, then an ANOVA is run on those deviations to obtain the W statistic and its p-value.

Interpretation:

• • p < 0.05: Variances are not equal (reject homogeneity of variance)
• • p ≥ 0.05: Assumption of equal variances holds; safe to proceed with ANOVA/t-test
• • Larger W with small p indicates stronger evidence of unequal spread
• • If variances differ, consider Welch's ANOVA or a variance-stabilizing transformation

sixsigmacenter.com Implementation Guide

The Distribution Characterization module automatically computes group deviations, runs the ANOVA on those deviations, and reports the W statistic, degrees of freedom, and p-value.

Analysis Workflow

• Upload group data in separate columns
• Platform computes each group's median and absolute deviations
• One-way ANOVA is run on the deviations to compute W and its p-value
• Result is reported alongside a recommendation for the appropriate variance-comparison follow-up

Example Data Layout for Levene's Test

Multiple groups for testing equality of variances. Use separate columns for each group. Sample Size Recommendation: Minimum 5-10 observations per group, with balanced group sizes preferred for optimal test performance.

This is how your spreadsheet or CSV file should be structured before you upload it. Match the column names, keep one row per observation, and leave the analysis to the platform.