Reference Table
BY: Statistics Fundamentals Team
Reviewed By: Minsa A (Senior Statistics Editor)

Levene's Test Reference Table: F Critical Values for Variance Equality Testing

The Levene's Test reference table gives the F critical value needed to reject the null hypothesis of equal group variances. Look up Fcrit by numerator df (k−1) and denominator df (N−k) at α = 0.10, 0.05, and 0.01 — for 2 to 10 groups and sample sizes up to 200.

Levene's Test F Critical Value Lookup

F critical =
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What Is Levene's Test?

Levene's Test is a hypothesis test for homogeneity of variance — the assumption that two or more groups share the same population variance. Proposed by Howard Levene in 1960, it became the standard check before ANOVA and pooled-variance t-tests because it performs reliably even when the data are not normally distributed, unlike Bartlett's Test.

The test converts each observation into an absolute deviation from its group mean: Zij = |Yij − Ȳi.|. It then runs a one-way ANOVA on these Z values. If group variances are truly equal, the between-group variation in the Z values should be small relative to the within-group variation. The resulting F statistic is compared against the F critical value in this table.

Quick definition: Levene's Test asks: "Are the spreads of these groups similar enough that we can treat their variances as equal?" The F critical table provides the threshold. If the observed F from your software exceeds Fcrit, the answer is no — the groups have significantly different variances.

Levene's Test Reference Table (F Critical Values)

Select your significance level (α) using the tabs below. The table columns are numerator degrees of freedom df1 = k−1 (number of groups minus one). The rows are denominator degrees of freedom df2 = N−k (total sample size minus number of groups). Click any cell to load the F critical value into the lookup tool above.

df1 = k − 1 (numerator, groups minus one). df2 = N − k (denominator, total observations minus groups). Reject H₀ if observed Levene F ≥ Fcrit. Values computed from the F distribution. Click any cell to highlight and load it into the lookup tool above.

The Levene's Test Statistic Formula

The Levene statistic W is essentially a one-way ANOVA F statistic applied to the absolute deviations from group means. Here is the complete formula:

Step 1 — Absolute deviations:
Zij = |Yij − Ȳi.|

Step 2 — Levene statistic:
W = [(N − k) / (k − 1)] × [Σᵢ nᵢ (Z̄i. − Z̄..)²] / [Σᵢ Σⱼ (Zij − Z̄i.)²]
Symbol Meaning
Yij The j-th observation in group i
Ȳi. Mean of group i
Zij Absolute deviation of Yij from its group mean
Z̄i. Mean of the Zij values within group i
Z̄.. Grand mean of all Zij values
nᵢ Sample size of group i
N Total number of observations across all groups
k Number of groups

Under H₀ (all variances equal), W follows an F distribution with df1 = k−1 and df2 = N−k. Most researchers obtain the Levene statistic from software and compare it to the F critical value in this table, rather than computing W by hand. The p-value printed in software output reaches the same decision.

How to Use the Levene's Test Reference Table: Step by Step

Testing variance equality with the Levene reference table requires only four inputs: the number of groups k, the total sample size N, the observed F statistic from your software, and your chosen α.

Step 1 — State Hypotheses and Choose α

H₀: σ₁² = σ₂² = … = σk² (all population variances are equal — homogeneity of variance holds). H₁: At least one group variance differs. Set α before examining results. The conventional choice is α = 0.05, though some researchers use α = 0.10 because the test's primary purpose is identifying a potential problem with ANOVA, not a finding in itself.

Step 2 — Obtain the Levene Statistic from Software

Run Levene's Test in your statistical software. Record the observed F (or W) statistic from the output. Software packages report it as "Levene Statistic," "W," or "F."

R: car::leveneTest(y ~ group)
Python: scipy.stats.levene(group1, group2, ...)
SPSS: Analyze → Compare Means → One-Way ANOVA → Options → Homogeneity of variance
SAS: PROC ANOVA; MEANS group / HOVTEST=LEVENE;

Step 3 — Compute Degrees of Freedom

df1 (numerator) = k − 1, where k is the number of groups. df2 (denominator) = N − k, where N is the total sample size across all groups. For example, comparing 4 groups with 15 observations each gives N = 60, df1 = 3, df2 = 56.

df1 = k − 1     df2 = N − k

Step 4 — Look Up F Critical in the Table

Select the α tab matching your chosen significance level. Find the column for df1 and the row for df2 (or the next smaller df2 if your exact value is absent — this is the conservative choice). The cell value is Fcrit.

Step 5 — Decision Rule

If Observed F ≥ Fcrit → Reject H₀ → Variances are significantly unequal
If Observed F < Fcrit → Fail to reject H₀ → Equal variances assumption holds

Worked Example: Levene's Test Before One-Way ANOVA

Scenario: A psychologist measures anxiety scores for three treatment groups (CBT, medication, control), with 20 participants per group (N = 60). Before running ANOVA, she checks the homogeneity of variance assumption using Levene's Test. Her software reports a Levene statistic of F = 1.87. Is the equal variances assumption met at α = 0.05?

Solution — Step by Step

Step Action Result
1 State hypotheses H₀: σ₁² = σ₂² = σ₃²; H₁: variances differ; α = 0.05
2 Record observed Levene F Fobs = 1.87
3 Compute degrees of freedom df1 = k−1 = 3−1 = 2; df2 = N−k = 60−3 = 57
4 Look up Fcrit df1=2, df2≈57, α=0.05 → Fcrit ≈ 3.17
5 Compare Fobs vs Fcrit 1.87 < 3.17 → Fail to reject H₀

Interpretation

With Levene F(2, 57) = 1.87 < Fcrit = 3.17, we fail to reject H₀. The anxiety score variances across the three treatment groups are not significantly different at α = 0.05. The homogeneity of variance assumption for one-way ANOVA is met. The researcher can proceed with standard ANOVA without switching to a Welch correction.

What to Do When Levene's Test Is Significant

A significant Levene's Test (F ≥ Fcrit) means the data provide evidence that group variances differ. This does not stop the analysis — it changes which test to use. The table below outlines each option.

Original Design: ANOVA

Switch to Welch's ANOVA (also called the Welch F-test or one-way ANOVA with Welch correction). It adjusts the degrees of freedom to account for unequal variances. Available in R via oneway.test(y ~ group) and in SPSS's Robust Tests of Equality of Means.

Original Design: Two-Sample t-Test

Switch to the Welch two-sample t-test, which uses separate variance estimates for each group. In R, t.test(x, y, var.equal=FALSE). This is the default in most software. See the two-sample t-test guide for details.

Non-Parametric Alternative

If both normality and equal variance assumptions are violated, consider the Kruskal-Wallis test (non-parametric equivalent to one-way ANOVA) or the Mann-Whitney U test for two groups. These tests rank the data and require neither normality nor equal variances.

Illustrative F Critical Values at α = 0.05

This table shows how the F critical value changes with the number of groups (df1) and total sample size (df2) at α = 0.05. Larger samples produce lower thresholds, making it easier to detect unequal variances.

Design k (groups) N (total) df1 df2 Fcrit (α=0.05)
Two independent groups, small sample 2 20 1 18 4.41
Two independent groups, medium sample 2 60 1 58 4.00
Three groups (classic ANOVA check) 3 45 2 42 3.22
Four groups, clinical trial 4 80 3 76 2.73
Five groups, large education study 5 150 4 145 2.43

Fcrit values at α = 0.05 from the F distribution. As df2 increases (larger N), Fcrit decreases because larger samples give more precise variance estimates.

Applied Examples Across Research Fields

Levene's Test appears across disciplines wherever comparing group means is the goal. These scenarios show the range of practical applications and how the table lookup works in context.

Clinical Trial: Drug Dosage Response

Researchers compare blood pressure reduction across 3 dosage groups (low, medium, high) with n = 25 per group (N = 75). Before ANOVA, Levene's Test gives F = 2.14. With df1 = 2 and df2 = 72, Fcrit at α = 0.05 ≈ 3.12. Since 2.14 < 3.12, variances are equal. Standard one-way ANOVA proceeds. See hypothesis testing for the next steps.

Education Research: Teaching Method Comparison

A study compares exam score spreads across 4 classroom teaching methods with unequal group sizes (n = 18, 22, 15, 25; N = 80). Levene's F = 4.86 with df1 = 3, df2 = 76. Fcrit at α = 0.05 ≈ 2.73. Since 4.86 > 2.73, the test is significant — one or more groups have different variance. Welch's ANOVA replaces standard ANOVA here.

Manufacturing Quality Control

A quality engineer tests whether five production lines have equal process variability (measured by component thickness in mm), with n = 30 per line (N = 150). Levene's F = 1.32 with df1 = 4, df2 = 145. Fcrit at α = 0.05 ≈ 2.43. The variances are equal; ANOVA is appropriate for comparing mean thickness across lines.

Psychology: Treatment Group Variability

Two therapy approaches (CBT vs mindfulness) are compared on symptom reduction scores, with n = 35 per group (N = 70). Before the pooled-variance t-test, Levene's F = 5.71 with df1 = 1, df2 = 68. Fcrit at α = 0.05 ≈ 3.98. Since 5.71 > 3.98, the Welch t-test (unequal variances) applies instead of the pooled test. Learn more about the two-sample t-test.

Levene's Test vs Bartlett's Test vs Brown-Forsythe Test

Three tests commonly check for variance equality. Choosing between them depends on the distribution of your data and how sensitive you want the test to be.

Test Null Hypothesis Basis Normality Requirement Recommended When
Levene's Test (mean-based) H₀: all group variances equal ANOVA on |Y − group mean| Robust to moderate departures from normality Default choice; balanced and unbalanced designs; most software default
Brown-Forsythe Test (median-based) H₀: all group variances equal ANOVA on |Y − group median| More robust to non-normality, especially skewed data Skewed distributions; heavy-tailed data; when means are outlier-sensitive
Bartlett's Test H₀: all group variances equal Log-likelihood ratio; χ² distribution Sensitive to non-normality — inflated Type I error if data are not normal Data are confirmed normal; maximum power needed under normality
F-Max Test (Hartley) H₀: largest variance = smallest variance Ratio of max to min variance Requires normality and equal sample sizes Balanced designs with normal data; quick preliminary check

Practical guidance: Levene's Test is the best general-purpose choice. Use the Brown-Forsythe variant when your data are skewed or contain outliers. Bartlett's Test is theoretically more powerful under normality, but its sensitivity to non-normality makes it risky in most applied work. Both the Levene and Brown-Forsythe tests use the same F critical value table — only the test statistic differs.

Assumptions of Levene's Test

Levene's Test itself rests on a set of conditions. When these are met, the F statistic follows the F distribution assumed by the table above.

Independence of Observations

Each observation must come from a different, independent subject. Repeated measures, clustered data, or matched pairs violate this assumption. For repeated measures designs, use specialized variance tests for correlated groups.

Continuous or Ordinal Data

Levene's Test requires variables measured on at least an ordinal scale. It is typically applied to continuous data (interval or ratio). It should not be used with nominal categorical outcomes.

Two or More Distinct Groups

The grouping variable must define two or more non-overlapping groups. The test is most informative when groups differ on a factor you intend to compare with ANOVA or a t-test. For two groups, df1 = 1; for three groups, df1 = 2.

Robustness to Non-Normality (a strength)

Unlike Bartlett's Test, Levene's Test does not strictly require normally distributed data. This robustness is one of its primary advantages. With very small samples (< 5 per group), any variance test loses power regardless; sample size matters more than distributional shape in that range. For a deeper look at statistical assumptions, visit the assumptions guide.

Symbol and Concept Glossary

The table below defines every symbol used in Levene's Test. Each also notes the most common misinterpretation found in applied research.

Symbol Name Definition Common Error
W or F Levene statistic The test statistic; follows an F distribution under H₀ Confusing it with the ANOVA F — they differ in numerator
k Number of groups Count of distinct groups in the study Using N (total n) instead of k for df1
N Total sample size Sum of observations across all groups Using per-group n rather than total N
df1 Numerator degrees of freedom k − 1; equals the number of groups minus one Swapping df1 and df2 when looking up the table
df2 Denominator degrees of freedom N − k; total observations minus number of groups Computing N − k − 1 by analogy to regression
σᵢ² Population variance of group i The theoretical variance H₀ assumes is equal across all groups Confusing sample variance sᵢ² with population variance σᵢ²
α Significance level Probability of Type I error; typically 0.05 Using a different α than was declared a priori
Zij Absolute deviation |Yij − Ȳi.|; core transformation in Levene's statistic Using squared deviations (that gives Bartlett logic, not Levene)
The null hypothesis of Levene's Test states that all population variances are equal across the groups (H₀: σ₁² = σ₂² = … = σk²). The alternative hypothesis is that at least one group has a different variance. A non-significant result (p > α) indicates there is insufficient evidence to conclude that the variances differ, but it does not prove they are exactly equal.
Levene's Test is the preferred choice in most real-world analyses because it is robust to departures from normality. Bartlett's Test is more powerful when the data are perfectly normally distributed, but it is highly sensitive to non-normal data and may incorrectly detect unequal variances. Unless normality is well established, Levene's Test is generally the safer option.
No. A significant Levene's Test indicates that the equal variance assumption has been violated, making the standard pooled-variance ANOVA less appropriate. In this situation, Welch's ANOVA is usually recommended because it does not require equal variances. Standard ANOVA can still perform well when group sizes are equal and variance differences are only moderate.
The Brown-Forsythe test is a variation of Levene's Test that calculates deviations from the group median instead of the group mean. Because the median is less affected by outliers and skewed data, the Brown-Forsythe test is more robust for non-normal distributions while using the same F distribution and interpretation as Levene's Test.
If your exact denominator degrees of freedom (df₂) are missing from the F table, use the next smaller available value to obtain a slightly larger critical value, making the test more conservative. For large df₂ values, the critical values change very little, so the largest tabled value is usually a good approximation.
Yes. Levene's Test works with two groups as well as multiple groups. With two groups, it is commonly used before an independent-samples t-test to evaluate the assumption of equal variances. Many statistical software packages perform this test automatically and recommend either the equal-variance or unequal-variance version of the t-test based on the result.
A significance level of α = 0.05 is the most widely used choice for Levene's Test. Some researchers prefer α = 0.10 when checking assumptions because failing to detect unequal variances can lead to choosing an inappropriate statistical method. The most appropriate significance level depends on your research field and the consequences of assumption violations.
Levene's Test is based on a one-way ANOVA applied to the absolute deviations from each group's center. While standard ANOVA compares group means, Levene's Test compares group variances. Both methods use the same F distribution and degrees of freedom, but they answer different research questions.

Sources & Further Reading

The F critical values in this table are derived from the standard F distribution. They are validated against the following primary statistical references and software implementations:

Levene, H. (1960). "Robust tests for equality of variances." In I. Olkin (Ed.), Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling (pp. 278–292). Stanford University Press. The original paper defining the test statistic, assumptions, and the F distribution approximation.

Brown, M. B., & Forsythe, A. B. (1974). "Robust tests for the equality of variances." Journal of the American Statistical Association, 69(346), 364–367. doi:10.1080/01621459.1974.10482955 — Introduces the median-based variant that improves robustness for skewed data.

NIST/SEMATECH e-Handbook of Statistical Methods. Section 7.4.3.3: Levene Test for Equality of Variances. National Institute of Standards and Technology. itl.nist.gov — Government statistical reference with worked examples and formula documentation.

Penn State STAT 415: Introduction to Mathematical Statistics. Testing for Equal Variances. Pennsylvania State University. online.stat.psu.edu — Open-access course notes covering Levene, Bartlett, and F-test for variances with derivations.

Field, A. (2024). Discovering Statistics Using IBM SPSS Statistics (6th ed.). SAGE Publications. Chapter 6 covers homogeneity of variance testing with Levene's Test, practical interpretation guidance, and follow-up procedures when the assumption is violated.

Related Statistical Tables & Resources

Understanding What the Levene's Test Table Tells You

Why Fcrit Decreases as N Increases

Larger samples give more precise estimates of each group's variance. With more data, smaller differences between group variances become detectable. A small study with N = 20 requires a much larger Levene F to reach significance than a study with N = 200. This is why variance equality is harder to demonstrate as a problem in small studies — not because the problem is absent, but because the test lacks power.

Levene's Test and Unbalanced Designs

ANOVA is more sensitive to variance inequality when group sizes differ. With equal group sizes (balanced design), ANOVA is relatively robust to moderate variance heterogeneity. With unequal group sizes (unbalanced design), even moderate variance differences can distort ANOVA's Type I error rate. This is when Levene's Test matters most — and when a significant result most strongly suggests switching to Welch's ANOVA.

Should You Always Run Levene's Test Before ANOVA?

Some statisticians argue that Welch's ANOVA should always be used instead of standard ANOVA, removing the need to pre-test with Levene's. The argument is that two-stage procedures (test then choose) inflate actual Type I error. Others contend that standard ANOVA remains preferable when variances are equal because it uses more statistical power efficiently. Both positions have merit. Many researchers run Levene's Test and use its result to document their analytic decision, particularly when preparing work for peer review. See the statistical assumptions guide for a broader perspective.