Test If Groups Vary Similarly

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() or oneway_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

Usage Flexibility

You can use this function two ways:

Standalone: Check any variables for equal variance
After tests: Pipe after t_test() or oneway_anova() to verify assumptions

Tips for Success

Always check this assumption for group comparisons
Visual inspection (boxplots) can supplement the test
Large samples make the test very sensitive
Use median-based test for skewed data (center = "median")
Don't panic if violated - alternatives exist!

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.

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: life_satisfaction by region
#>   F(1, 2419) = 3.164, p = 0.075 , variances equal
#> Use summary() for detailed output.

# Multiple variables
survey_data %>% levene_test(life_satisfaction, trust_government, group = region)
#> Levene's Test: life_satisfaction by region
#>   F(1, 2419) = 3.164, p = 0.075 , variances equal
#> Levene's Test: trust_government by region
#>   F(1, 2352) = 0.145, p = 0.703 , variances equal
#> Use summary() for detailed output.

# Weighted analysis
survey_data %>% levene_test(income, group = education, weights = sampling_weight)
#> Levene's Test: income by education [Weighted]
#>   F(3, 2196.9) = 102.048, p < 0.001 ***, variances unequal
#> Use summary() for detailed output.

# Piped after ANOVA (common workflow)
result <- survey_data %>%
  oneway_anova(life_satisfaction, group = education)
result %>% levene_test()
#> Levene's Test: life_satisfaction by education
#>   F(3, 2417) = 31.634, p < 0.001 ***, variances unequal
#> Use summary() for detailed output.

# Piped after t-test
survey_data %>%
  t_test(age, group = gender) %>%
  levene_test()
#> Levene's Test: age by gender
#>   F(1, 2498) = 0.534, p = 0.465 , variances equal
#> Use summary() for detailed output.

# Using mean instead of median as center
survey_data %>% levene_test(income, group = region, center = "mean")
#> Levene's Test: income by region
#>   F(1, 2184) = 1.631, p = 0.202 , variances equal
#> Use summary() for detailed output.