Compare Three or More Related Measurements Without Assuming Normality

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)

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)

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?)

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.

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)
#> Friedman Test: trust_government, trust_media, trust_science
#>   chi2(2) = 1009.035, p < 0.001 ***, W = 0.236, N = 2135
#> Use summary() for detailed output.

# Using tidyselect helpers
survey_data %>%
  friedman_test(starts_with("trust_"))
#> Friedman Test: trust_government, trust_media, trust_science
#>   chi2(2) = 1009.035, p < 0.001 ***, W = 0.236, N = 2135
#> Use summary() for detailed output.

# Weighted analysis
survey_data %>%
  friedman_test(trust_government, trust_media, trust_science,
                weights = sampling_weight)
#> Friedman Test: trust_government, trust_media, trust_science [Weighted]
#>   chi2(2) = 1012.084, p < 0.001 ***, W = 0.235, N = 2150
#> Use summary() for detailed output.

# Grouped analysis (separate test per region)
survey_data %>%
  group_by(region) %>%
  friedman_test(trust_government, trust_media, trust_science)
#> [region = 1]
#> Friedman Test: trust_government, trust_media, trust_science
#>   chi2(2) = 217.100, p < 0.001 ***, W = 0.257, N = 422
#> [region = 2]
#> Friedman Test: trust_government, trust_media, trust_science
#>   chi2(2) = 792.344, p < 0.001 ***, W = 0.231, N = 1713
#> Use summary() for detailed output.