Calculates Kendall's tau-b rank correlation coefficients between variables with support for weighted correlations, grouped data, and multiple variable pairs. Provides significance testing and SPSS-compatible output formatting.
The function computes tau-b, which is adjusted for ties and is particularly suitable for ordinal data or when the assumptions of Pearson correlation are not met. For weighted correlations, it uses survey-weighted rank calculations.
Arguments
- data
Your survey data (a data frame or tibble)
- ...
The variables you want to correlate. List two for a single correlation or more for a correlation matrix. You can use helpers like
starts_with("trust").- weights
Optional survey weights for population-representative results.
- alternative
Direction of the test:
"two.sided"(default): Two-tailed test"less": One-tailed test (negative correlation)"greater": One-tailed test (positive correlation)
- use
How to handle missing values:
"pairwise"(default): Pairwise deletion - each correlation uses all available cases"listwise": Listwise deletion - only complete cases across all variables
- na.rm
Deprecated. Use
useinstead.
Value
Correlation results showing rank-based relationships between variables,
including the tau-b coefficient, p-value, z-score, and sample size for each
pair. For multiple variables, correlation, significance, and sample size
matrices are also provided.
Use summary() for the full SPSS-style output with toggleable sections.
Details
Understanding the Results
Kendall's tau measures how often pairs of observations are in the same order (concordant) versus different order (discordant). It is particularly useful for ordinal data, data with outliers, small sample sizes, and non-linear but monotonic relationships.
The tau value ranges from -1 to +1:
Strong positive (0.5 to 1.0): High values of one variable tend to go with high values of the other
Moderate positive (0.3 to 0.5): Some tendency for values to increase together
Weak positive (0 to 0.3): Slight tendency for values to increase together
No correlation (near 0): No relationship between the variables
Negative values: As one variable increases, the other tends to decrease
The output also provides:
p-value: Probability of seeing this correlation by chance (smaller = stronger evidence)
n: Number of observations used
significance stars: Quick visual indicator of statistical significance
When to Use This
Choose Kendall's tau when:
Your data is ordinal (ranked categories)
You have a small sample size (< 30 observations)
Your data has outliers that might affect Pearson correlation
Weighted variants
The weighted tau-b is an exact frequency-weighted computation (it
reproduces the unweighted tau when all weights equal 1, enforced by an
internal invariance suite), but its z statistic and p-value use a no-ties
normal approximation. SPSS NONPAR CORR ignores WEIGHT BY,
so weighted results have no SPSS reference; see
vignette("spss-compatibility") for validation status.
You want a more conservative measure than Spearman's rho
References
Kendall, M. G. (1938). A new measure of rank correlation. Biometrika, 30(1/2), 81–93.
Kendall, M. G. (1945). The treatment of ties in ranking problems. Biometrika, 33(3), 239–251.
Agresti, A. (2010). Analysis of Ordinal Categorical Data (2nd ed.). John Wiley & Sons.
See also
cor with method = "kendall" for the base R
implementation.
spearman_rho for Spearman's rank correlation.
pearson_cor for Pearson correlation analysis.
summary.kendall_tau for detailed output with toggleable sections.
Other correlation:
partial_cor(),
pearson_cor(),
spearman_rho()
Examples
# Load required packages and data
library(dplyr)
data(survey_data)
# Kendall's tau is O(n^2); the examples run on a subset for speed.
# On your own data, simply drop the subsetting.
mini_survey <- survey_data[1:300, ]
# Basic correlation between two variables
mini_survey %>%
kendall_tau(life_satisfaction, political_orientation)
#> Kendall's Tau: life_satisfaction x political_orientation
#> tau = -0.028, p = 0.582 , N = 260
# Correlation matrix for multiple variables
mini_survey %>%
kendall_tau(life_satisfaction, political_orientation, trust_media)
#> Kendall's Tau: 3 variables
#> life_satisfaction x political_orientation: tau = -0.028, p = 0.582
#> life_satisfaction x trust_media: tau = 0.026, p = 0.608
#> political_orientation x trust_media: tau = -0.037, p = 0.471
#> 0/3 pairs significant (p < .05), N = 260
# Weighted correlations
mini_survey %>%
kendall_tau(age, income, weights = sampling_weight)
#> Kendall's Tau: age x income [Weighted]
#> tau = -0.036, p = 0.374 , N = 271
# Listwise deletion for missing data
mini_survey %>%
kendall_tau(age, income, use = "listwise")
#> Kendall's Tau: age x income
#> tau = -0.038, p = 0.370 , N = 267
# One-tailed test
mini_survey %>%
kendall_tau(age, income, alternative = "greater")
#> Kendall's Tau: age x income
#> tau = -0.038, p = 0.815 , N = 267
# \donttest{
# Grouped correlations
mini_survey %>%
group_by(region) %>%
kendall_tau(age, income, life_satisfaction)
#> [region = 1]
#> Kendall's Tau: 3 variables
#> age x income: tau = 0.102, p = 0.265
#> age x life_satisfaction: tau = 0.061, p = 0.532
#> income x life_satisfaction: tau = 0.315, p = 0.002 **
#> 1/3 pairs significant (p < .05), N = 58
#> [region = 2]
#> Kendall's Tau: 3 variables
#> age x income: tau = -0.068, p = 0.149
#> age x life_satisfaction: tau = -0.034, p = 0.491
#> income x life_satisfaction: tau = 0.361, p < 0.001 ***
#> 1/3 pairs significant (p < .05), N = 209
# Using tidyselect helpers for ordinal variables
mini_survey %>%
kendall_tau(starts_with("trust"), weights = sampling_weight)
#> Kendall's Tau: 3 variables [Weighted]
#> trust_government x trust_media: tau = 0.084, p = 0.037 *
#> trust_government x trust_science: tau = -0.028, p = 0.493
#> trust_media x trust_science: tau = 0.007, p = 0.870
#> 1/3 pairs significant (p < .05), N = 274
# --- Three-layer output ---
result <- mini_survey %>%
kendall_tau(life_satisfaction, political_orientation, trust_media,
weights = sampling_weight)
result # compact one-line overview
#> Kendall's Tau: 3 variables [Weighted]
#> life_satisfaction x political_orientation: tau = -0.026, p = 0.535
#> life_satisfaction x trust_media: tau = 0.025, p = 0.534
#> political_orientation x trust_media: tau = -0.039, p = 0.350
#> 0/3 pairs significant (p < .05), N = 262
summary(result) # full correlation, p-value, and N matrices
#>
#> Weighted Kendall's Tau-b Correlation
#> -------------------------------------
#>
#> - Weights variable: sampling_weight
#> - Missing data handling: pairwise deletion
#> - Alternative hypothesis: two.sided
#>
#>
#> Kendall's Tau-b Matrix:
#> -----------------------
#> life_satisfaction political_orientation trust_media
#> life_satisfaction 1.000 -0.026 0.025
#> political_orientation -0.026 1.000 -0.039
#> trust_media 0.025 -0.039 1.000
#> -----------------------
#>
#> Significance Matrix (p-values, 2-tailed):
#> -----------------------------------------
#> life_satisfaction political_orientation trust_media
#> life_satisfaction 0.0000 0.5346 0.5345
#> political_orientation 0.5346 0.0000 0.3497
#> trust_media 0.5345 0.3497 0.0000
#> -----------------------------------------
#>
#> Sample Size Matrix:
#> -------------------
#> life_satisfaction political_orientation trust_media
#> life_satisfaction 290 262 277
#> political_orientation 262 272 259
#> trust_media 277 259 289
#> -------------------
#>
#> Pairwise Results:
#> ----------------
#> Pair tau_b z p n sig
#> life_satisfaction × political_orientation -0.026 -0.621 0.5346 262
#> life_satisfaction × trust_media 0.025 0.621 0.5345 277
#> political_orientation × trust_media -0.039 -0.935 0.3497 259
#> ----------------
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
summary(result, pvalue_matrix = FALSE) # hide p-values
#>
#> Weighted Kendall's Tau-b Correlation
#> -------------------------------------
#>
#> - Weights variable: sampling_weight
#> - Missing data handling: pairwise deletion
#> - Alternative hypothesis: two.sided
#>
#>
#> Kendall's Tau-b Matrix:
#> -----------------------
#> life_satisfaction political_orientation trust_media
#> life_satisfaction 1.000 -0.026 0.025
#> political_orientation -0.026 1.000 -0.039
#> trust_media 0.025 -0.039 1.000
#> -----------------------
#>
#> Sample Size Matrix:
#> -------------------
#> life_satisfaction political_orientation trust_media
#> life_satisfaction 290 262 277
#> political_orientation 262 272 259
#> trust_media 277 259 289
#> -------------------
#>
#> Pairwise Results:
#> ----------------
#> Pair tau_b z p n sig
#> life_satisfaction × political_orientation -0.026 -0.621 0.5346 262
#> life_satisfaction × trust_media 0.025 0.621 0.5345 277
#> political_orientation × trust_media -0.039 -0.935 0.3497 259
#> ----------------
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
# }