mariposa (version 0.7.3)

wilcoxon_test: Compare Two Related Measurements Without Assuming Normality

Description

wilcoxon_test() compares two paired measurements from the same subjects when your data isn't normally distributed. It's the non-parametric alternative to the paired t-test.

Think of it as:

• A way to test whether scores changed between two time points

• Comparing ratings of two items from the same respondents

• A robust paired comparison that works with any data shape

The test tells you:

• Whether scores are significantly different between the two measurements

• How many subjects increased, decreased, or stayed the same

• The strength of the effect (effect size r)

Usage

wilcoxon_test(data, x, y, weights = NULL, conf.level = 0.95)

Value

Test results showing whether the two measurements differ, including:

• Z statistic (standardized test statistic, normal approximation)

• P-value (is there a significant difference?)

• Effect size r (how strong is the difference?)

• Rank statistics (negative ranks, positive ranks, ties)

Arguments

data

Your survey data (a data frame or tibble) in wide format, with one row per subject and the two measurements in separate columns

x

The first measurement variable (e.g., pre-test, trust in government)

y

The second measurement variable (e.g., post-test, trust in media). The difference is computed as y - x

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, the two measurements are significantly different

• p < 0.001: Very strong evidence of a difference

• p < 0.01: Strong evidence of a difference

• p < 0.05: Moderate evidence of a difference

• p > 0.05: No significant difference found

Effect Size r (How strong is the difference?):

• < 0.1: Negligible effect

• 0.1 - 0.3: Small effect

• 0.3 - 0.5: Medium effect

• 0.5 or higher: Large effect

Rank Categories:

• Negative Ranks: subjects where y < x (decreased)

• Positive Ranks: subjects where y > x (increased)

• Ties: subjects where y = x (no change)

When to Use This

Use Wilcoxon signed-rank test when:

• Comparing two related measurements from the same subjects

• Your data is not normally distributed

• You have ordinal data (ratings, rankings)

• Sample size is small

• You want a robust alternative to the paired t-test

Relationship to Other Tests

• For normally distributed paired data: Use paired t-test instead

• For independent groups: Use mann_whitney() instead

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 3+ related measurements: Use friedman_test() instead

References

Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin, 1(6), 80-83.

Fritz, C. O., Morris, P. E., & Richler, J. J. (2012). Effect size estimates: current use, calculations, and interpretation. Journal of Experimental Psychology: General, 141(1), 2.

See Also

wilcox.test for the base R Wilcoxon test.

mann_whitney for comparing two independent groups.

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

Examples

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

# Compare trust in government vs trust in media
survey_data %>%
  wilcoxon_test(x = trust_government, y = trust_media)

# Weighted analysis
survey_data %>%
  wilcoxon_test(x = trust_government, y = trust_media,
                weights = sampling_weight)

# Grouped analysis (separate test per region)
survey_data %>%
  group_by(region) %>%
  wilcoxon_test(x = trust_government, y = trust_media)