mariposa (version 0.7.3)

friedman_test: Compare Three or More Related Measurements Without Assuming Normality

Description

friedman_test() compares three or more related measurements from the same subjects when your data isn't normally distributed. It's the non-parametric alternative to repeated-measures ANOVA.

Think of it as:

• Comparing ratings of multiple items by the same respondents

• Testing whether scores change across three or more time points

• A robust repeated-measures comparison that works with any data shape

The test tells you:

• Whether at least one measurement is significantly different from the others

• Which measurements tend to be rated higher or lower (via mean ranks)

• The strength of the overall effect (Kendall's W)

Usage

friedman_test(data, ..., weights = NULL, conf.level = 0.95)

Value

Test results showing whether the measurements differ, including:

• Chi-Square statistic (chi_squared, the Friedman test statistic)

• Degrees of freedom (number of measurements minus 1)

• P-value (are measurements different?)

• Kendall's W (effect size: how strong is the overall pattern?)

• Mean rank for each measurement (which measurements are higher/lower?)

Arguments

data

Your survey data (a data frame or tibble) in wide format, with one row per subject and each measurement in a separate column

...

The measurement variables to compare (at least 3). You can list them individually or use helpers like starts_with("trust_")

weights

Optional survey weights for population-representative results

conf.level

Confidence level for intervals (Default: 0.95 = 95 percent)

Details

Understanding the Results

P-value: If p < 0.05, at least one measurement is significantly different

• p < 0.001: Very strong evidence of differences

• p < 0.01: Strong evidence of differences

• p < 0.05: Moderate evidence of differences

• p > 0.05: No significant differences found

Kendall's W (Effect size: How consistent is the pattern?):

• < 0.1: Negligible agreement/effect

• 0.1 - 0.3: Weak agreement

• 0.3 - 0.5: Moderate agreement

• 0.5 or higher: Strong agreement

Mean Ranks:

• Higher mean rank = measurement tends to have higher values

• Lower mean rank = measurement tends to have lower values

• Compare mean ranks to see which measurements stand out

When to Use This

Use the Friedman test when:

• You have 3 or more related measurements from the same subjects

• Your data is not normally distributed

• You have ordinal data (ratings, rankings)

• You want a robust alternative to repeated-measures ANOVA

• You're comparing multiple ratings by the same respondents

Relationship to Other Tests

• For 2 related measurements: Use wilcoxon_test() instead

• For normally distributed repeated measures: Use repeated-measures ANOVA

Weighted variants

SPSS NPAR TESTS ignores WEIGHT BY, so weighted results have no SPSS reference. The weighted variant is an R-only frequency-weight extension that reduces exactly to the unweighted test when all weights equal 1 (enforced by an internal invariance suite); see vignette("spss-compatibility") for validation status.

• For independent groups: Use kruskal_wallis() instead

References

Friedman, M. (1937). The use of ranks to avoid the assumption of normality implicit in the analysis of variance. Journal of the American Statistical Association, 32(200), 675-701.

Kendall, M. G., & Babington Smith, B. (1939). The problem of m rankings. The Annals of Mathematical Statistics, 10(3), 275-287.

See Also

friedman.test for the base R Friedman test.

wilcoxon_test for comparing two related measurements.

kruskal_wallis for comparing independent groups.

Other hypothesis_tests: ancova(), binomial_test(), chi_square(), chisq_gof(), factorial_anova(), fisher_test(), kruskal_wallis(), mann_whitney(), mcnemar_test(), oneway_anova(), t_test(), wilcoxon_test()

Examples

# Load required packages and data
library(dplyr)
data(survey_data)

# Compare three trust items (rated by same respondents)
survey_data %>%
  friedman_test(trust_government, trust_media, trust_science)

# Using tidyselect helpers
survey_data %>%
  friedman_test(starts_with("trust_"))

# Weighted analysis
survey_data %>%
  friedman_test(trust_government, trust_media, trust_science,
                weights = sampling_weight)

# Grouped analysis (separate test per region)
survey_data %>%
  group_by(region) %>%
  friedman_test(trust_government, trust_media, trust_science)