levene_test() checks if different groups have similar amounts of variation.
This is an important assumption for many statistical tests - groups should spread
out in similar ways.
The test tells you:
Whether variance is consistent across groups
If you can trust standard ANOVA and t-test results
When to use alternative tests that don't assume equal variance
Usage
levene_test(x, ...)
# Default S3 method
levene_test(x, ...)
# S3 method for class 'data.frame'
levene_test(x, ..., group, weights = NULL, center = c("mean", "median"))
# S3 method for class 'oneway_anova'
levene_test(x, center = c("mean", "median"), ...)
# S3 method for class 't_test'
levene_test(x, center = c("mean", "median"), ...)
# S3 method for class 'mann_whitney'
levene_test(x, ...)
# S3 method for class 'grouped_df'
levene_test(x, variable, group = NULL, weights = NULL, center = "mean", ...)Arguments
- x
Either your data or test results from
t_test()oroneway_anova()- ...
Variables to test (when using data frame)
- group
The grouping variable for comparison
- weights
Optional survey weights for population-representative results
- center
How to measure center:
"mean"(default) or"median"(more robust)- variable
Variable to test (when using grouped data frame)
- data
Your survey data (when x is not a test result)
Value
Test results showing:
Whether groups have equal variances (p-value)
F-statistic measuring variance differences
Which variables meet the assumption
Details
Understanding the Results
P-value interpretation:
p > 0.05: Good! Groups have similar variance (assumption met)
p ≤ 0.05: Problem - groups vary differently (assumption violated)
Think of it like checking if all groups are equally "spread out":
Similar spread = can use standard tests
Different spread = need special methods
When to Use This
Check variance equality when:
Before running t-tests or ANOVA
Comparing groups with different sizes
Your statistical test assumes equal variances
You see very different standard deviations
What If Variances Are Unequal?
If Levene's test is significant (p ≤ 0.05):
For t-tests: Use Welch's t-test (var.equal = FALSE)
For ANOVA: Use Welch's ANOVA
Consider transforming your data
Use non-parametric alternatives
Report that equal variance assumption was violated
References
Levene, H. (1960). Robust tests for equality of variances. In I. Olkin (Ed.), Contributions to Probability and Statistics (pp. 278–292). Stanford University Press.
Brown, M. B., & Forsythe, A. B. (1974). Robust tests for the equality of variances. Journal of the American Statistical Association, 69(346), 364–367.
IBM Corp. (2023). IBM SPSS Statistics 29 Algorithms. IBM Corporation.
See also
oneway_anova for one-way ANOVA (which assumes equal variances).
t_test for group mean comparisons.
var.test for the base R F-test of variance equality.
Other posthoc:
dunn_test(),
pairwise_wilcoxon(),
scheffe_test(),
tukey_test()
Examples
# Load required packages and data
library(dplyr)
data(survey_data)
# Standalone Levene test (test homogeneity of variances)
survey_data %>% levene_test(life_satisfaction, group = region)
#>
#> Levene's Test for Homogeneity of Variance
#> ------------------------------------------
#>
#> - Grouping variable: region
#> - Center: mean
#>
#>
#> --- life_satisfaction ---
#>
#> Levene's Test Results:
#> ------------------------------------------------------------------
#> Variable F_statistic df1 df2 p_value sig Conclusion
#> life_satisfaction 3.164 1 2419 0.075 Variances equal
#> ------------------------------------------------------------------
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
#>
#> Interpretation:
#> - p > 0.05: Variances are homogeneous (equal variances assumed)
#> - p <= 0.05: Variances are heterogeneous (equal variances NOT assumed)
# Multiple variables
survey_data %>% levene_test(life_satisfaction, trust_government, group = region)
#>
#> Levene's Test for Homogeneity of Variance
#> ------------------------------------------
#>
#> - Grouping variable: region
#> - Center: mean
#>
#>
#> --- life_satisfaction ---
#>
#> Levene's Test Results:
#> ------------------------------------------------------------------
#> Variable F_statistic df1 df2 p_value sig Conclusion
#> life_satisfaction 3.164 1 2419 0.075 Variances equal
#> ------------------------------------------------------------------
#>
#>
#> --- trust_government ---
#>
#> Levene's Test Results:
#> -----------------------------------------------------------------
#> Variable F_statistic df1 df2 p_value sig Conclusion
#> trust_government 0.145 1 2352 0.703 Variances equal
#> -----------------------------------------------------------------
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
#>
#> Interpretation:
#> - p > 0.05: Variances are homogeneous (equal variances assumed)
#> - p <= 0.05: Variances are heterogeneous (equal variances NOT assumed)
# Weighted analysis
survey_data %>% levene_test(income, group = education, weights = sampling_weight)
#>
#> Weighted Levene's Test for Homogeneity of Variance
#> ---------------------------------------------------
#>
#> - Grouping variable: education
#> - Weights variable: sampling_weight
#> - Center: mean
#>
#>
#> --- income ---
#>
#> Weighted Levene's Test Results:
#> -----------------------------------------------------------
#> Variable F_statistic df1 df2 p_value sig Conclusion
#> income 102.05 3 2197 0 *** Variances unequal
#> -----------------------------------------------------------
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
#>
#> Interpretation:
#> - p > 0.05: Variances are homogeneous (equal variances assumed)
#> - p <= 0.05: Variances are heterogeneous (equal variances NOT assumed)
# Piped after ANOVA (common workflow)
result <- survey_data %>%
oneway_anova(life_satisfaction, group = education)
result %>% levene_test()
#>
#> Levene's Test for Homogeneity of Variance
#> ------------------------------------------
#>
#> - Grouping variable: education
#> - Center: mean
#>
#>
#> --- life_satisfaction ---
#>
#> Levene's Test Results:
#> --------------------------------------------------------------------
#> Variable F_statistic df1 df2 p_value sig Conclusion
#> life_satisfaction 31.634 3 2417 0 *** Variances unequal
#> --------------------------------------------------------------------
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
#>
#> Interpretation:
#> - p > 0.05: Variances are homogeneous (equal variances assumed)
#> - p <= 0.05: Variances are heterogeneous (equal variances NOT assumed)
#>
#> Recommendation based on Levene test:
#> - Use Welch's t-test (unequal variances)
# Piped after t-test
survey_data %>%
t_test(age, group = gender) %>%
levene_test()
#>
#> Levene's Test for Homogeneity of Variance
#> ------------------------------------------
#>
#> - Grouping variable: gender
#> - Center: mean
#>
#>
#> --- age ---
#>
#> Levene's Test Results:
#> ---------------------------------------------------------
#> Variable F_statistic df1 df2 p_value sig Conclusion
#> age 0.534 1 2498 0.465 Variances equal
#> ---------------------------------------------------------
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
#>
#> Interpretation:
#> - p > 0.05: Variances are homogeneous (equal variances assumed)
#> - p <= 0.05: Variances are heterogeneous (equal variances NOT assumed)
#>
#> Recommendation based on Levene test:
#> - Student's t-test or Welch's t-test both appropriate
# Using mean instead of median as center
survey_data %>% levene_test(income, group = region, center = "mean")
#>
#> Levene's Test for Homogeneity of Variance
#> ------------------------------------------
#>
#> - Grouping variable: region
#> - Center: mean
#>
#>
#> --- income ---
#>
#> Levene's Test Results:
#> ---------------------------------------------------------
#> Variable F_statistic df1 df2 p_value sig Conclusion
#> income 1.631 1 2184 0.202 Variances equal
#> ---------------------------------------------------------
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
#>
#> Interpretation:
#> - p > 0.05: Variances are homogeneous (equal variances assumed)
#> - p <= 0.05: Variances are heterogeneous (equal variances NOT assumed)