Levene's Test
Hypothesis Testing
The Robust Alternative to the F-Test
Levene's test checks for equal variances across groups without assuming normality, making it more reliable than the F-test in practice. It is the standard method for verifying homoscedasticity before ANOVA.
- ANOVA Preparation β Checking assumptions before running analysis of variance
- Quality Engineering β Assessing process stability across multiple production lines
- Psychology Research β Verifying variance homogeneity in experimental designs
When normality is uncertain, Levene's test provides reliable variance checking.
Levene's test checks whether k groups have equal population variances (homoscedasticity). Unlike the F-test, it doesn't assume normality.
Python Implementation
Visualization
# Visualize variance differences
fig, ax = plt.subplots(figsize=(8, 5))
ax.boxplot([group_a, group_b, group_c], labels=['Group A', 'Group B', 'Group C'],
patch_artist=True)
ax.set_title(f"Group Variance Comparison\nLevene's: W={stat:.3f}, p={p:.4f}")
ax.set_ylabel('Values')
for i, (g, label) in enumerate(zip([group_a, group_b, group_c], ['A','B','C']), 1):
ax.text(i, g.max()+0.5, f'SD={g.std(ddof=1):.2f}', ha='center', fontsize=9)
plt.tight_layout()
plt.savefig('levenes_test.png', dpi=150)
plt.show()