mariposa (version 0.7.3)

levene_test: Test If Groups Vary Similarly

Description

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, ...)
# S3 method for default
levene_test(x, ...)
# S3 method for data.frame
levene_test(x, ..., group, weights = NULL, center = c("mean", "median"))
# S3 method for oneway_anova
levene_test(x, center = c("mean", "median"), ...)
# S3 method for t_test
levene_test(x, center = c("mean", "median"), ...)
# S3 method for mann_whitney
levene_test(x, ...)
# S3 method for grouped_df
levene_test(x, variable, group = NULL, weights = NULL, center = "mean", ...)

Value

Test results showing:

• Whether groups have equal variances (p-value)

• F-statistic measuring variance differences

• Which variables meet the assumption

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)

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.

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)

# Multiple variables
survey_data %>% levene_test(life_satisfaction, trust_government, group = region)

# Weighted analysis
survey_data %>% levene_test(income, group = education, weights = sampling_weight)

# Piped after ANOVA (common workflow)
result <- survey_data %>%
  oneway_anova(life_satisfaction, group = education)
result %>% levene_test()

# Piped after t-test
survey_data %>%
  t_test(age, group = gender) %>%
  levene_test()

# Using mean instead of median as center
survey_data %>% levene_test(income, group = region, center = "mean")