Spearman's Rank Correlation Analysis

Calculates Spearman's rank correlation coefficients (rho) between variables with support for weighted correlations, grouped data, and multiple variable pairs. Provides significance testing and SPSS-compatible output formatting.

Spearman's rho is a non-parametric measure of rank correlation that assesses monotonic relationships between variables. It is particularly suitable for ordinal data or when the assumptions of Pearson correlation are not met.

Usage

spearman_rho(
  data,
  ...,
  weights = NULL,
  alternative = c("two.sided", "less", "greater"),
  use = c("pairwise", "listwise"),
  na.rm = NULL
)

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. Note: SPSS may not apply weights to Spearman's rho; our implementation uses weighted ranks for mathematically correct survey analysis.

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 use instead.

Value

Correlation results showing rank-based relationships between variables, including the rho coefficient, p-value, t-statistic, 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

Spearman's rho measures the strength and direction of a monotonic relationship between two variables. Unlike Pearson correlation, it does not require a linear relationship – it just needs one variable to consistently increase (or decrease) as the other increases. Think of it as ranking your data first, then checking if the ranks tend to go together.

The rho value ranges from -1 to +1:

Strong positive (0.7 to 1.0): High ranks in one variable go with high ranks in the other
Moderate positive (0.3 to 0.7): Moderate tendency for ranks to increase together
Weak positive (0 to 0.3): Slight tendency for ranks to increase together
No correlation (near 0): No relationship between the variables
Negative values: As one variable's rank increases, the other's tends to decrease

The output also provides:

p-value: Probability of seeing this correlation by chance
n: Number of observation pairs used
significance stars: Visual indicator (*** very strong, ** strong, * moderate evidence)

When to Use This

Choose Spearman's rho when:

Your relationship is monotonic but not necessarily linear
Your data has outliers (they have less impact on ranks)
Your variables are ordinal (ordered categories)
You are not sure if your data meets Pearson correlation assumptions
You want to detect any monotonic trend, not just linear ones

Spearman vs. Kendall

Spearman's rho is usually larger in magnitude than Kendall's tau
Spearman's rho is better for detecting linear relationships in ranks
Kendall's tau is more robust and has better statistical properties
Spearman's rho is more commonly reported in research

References

Spearman, C. (1904). The proof and measurement of association between two things. American Journal of Psychology, 15(1), 72–101.

Lehmann, E. L. (1975). Nonparametrics: Statistical Methods Based on Ranks. Holden-Day.

Examples

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

# Basic correlation between two variables
survey_data %>%
  spearman_rho(life_satisfaction, political_orientation)
#> Spearman Correlation: life_satisfaction x political_orientation
#>   rho = -0.004, p = 0.833 , N = 2228

# Correlation matrix for multiple variables
survey_data %>%
  spearman_rho(life_satisfaction, political_orientation, trust_media)
#> Spearman Correlation: 3 variables
#>   life_satisfaction x political_orientation: rho = -0.004, p = 0.833  
#>   life_satisfaction x trust_media: rho = 0.028, p = 0.181  
#>   political_orientation x trust_media: rho = 0.003, p = 0.885  
#>   0/3 pairs significant (p < .05), N = 2228

# Weighted correlations (mathematically correct, though SPSS may not apply weights)
survey_data %>%
  spearman_rho(age, income, weights = sampling_weight)
#> Spearman Correlation: age x income [Weighted]
#>   rho = 0.003, p = 0.870 , N = 2186

# Grouped correlations
survey_data %>%
  group_by(region) %>%
  spearman_rho(age, income, life_satisfaction)
#> [region = 1]
#> Spearman Correlation: 3 variables
#>   age x income:                  rho = 0.058, p = 0.234  
#>   age x life_satisfaction:       rho = -0.040, p = 0.391  
#>   income x life_satisfaction:    rho = 0.440, p < 0.001 *** 
#>   1/3 pairs significant (p < .05), N = 429
#> [region = 2]
#> Spearman Correlation: 3 variables
#>   age x income:                  rho = -0.008, p = 0.725  
#>   age x life_satisfaction:       rho = -0.020, p = 0.382  
#>   income x life_satisfaction:    rho = 0.470, p < 0.001 *** 
#>   1/3 pairs significant (p < .05), N = 1757

# Using tidyselect helpers
survey_data %>%
  spearman_rho(starts_with("trust"), weights = sampling_weight)
#> Spearman Correlation: 3 variables [Weighted]
#>   trust_government x trust_media: rho = 0.008, p = 0.723  
#>   trust_government x trust_science: rho = 0.027, p = 0.207  
#>   trust_media x trust_science:   rho = 0.016, p = 0.453  
#>   0/3 pairs significant (p < .05), N = 2227

# Listwise deletion for missing data
survey_data %>%
  spearman_rho(age, income, use = "listwise")
#> Spearman Correlation: age x income
#>   rho = 0.003, p = 0.870 , N = 2186

# One-tailed test
survey_data %>%
  spearman_rho(age, income, alternative = "greater")
#> Spearman Correlation: age x income
#>   rho = 0.003, p = 0.435 , N = 2186

# --- Three-layer output ---
result <- spearman_rho(survey_data, age, income, life_satisfaction)
result              # compact one-line overview
#> Spearman Correlation: 3 variables
#>   age x income:                  rho = 0.003, p = 0.870  
#>   age x life_satisfaction:       rho = -0.024, p = 0.238  
#>   income x life_satisfaction:    rho = 0.464, p < 0.001 *** 
#>   1/3 pairs significant (p < .05), N = 2186
summary(result)     # full correlation, p-value, and N matrices
#> 
#> Spearman's Rank Correlation Analysis 
#> -------------------------------------
#> 
#> - Method: Spearman's rho (rank correlation)
#> - Variables: age, income, life_satisfaction
#> - Missing data handling: pairwise deletion
#> - Alternative hypothesis: two.sided
#> 
#> 
#> Spearman's Rho Matrix:
#> ---------------------- 
#>                       age  income life_satisfaction
#> age                 1.000   0.003            -0.024
#> income              0.003   1.000             0.464
#> life_satisfaction  -0.024   0.464             1.000
#> ---------------------- 
#> 
#> Significance Matrix (p-values, 2-tailed):
#> ----------------------------------------- 
#>                       age  income life_satisfaction
#> age                0.0000  0.8703            0.2383
#> income             0.8703  0.0000            0.0000
#> life_satisfaction  0.2383  0.0000            0.0000
#> ----------------------------------------- 
#> 
#> Sample Size Matrix:
#> ------------------- 
#>                     age income life_satisfaction
#> age                2500   2186              2421
#> income             2186   2186              2115
#> life_satisfaction  2421   2115              2421
#> ------------------- 
#> 
#> Pairwise Results:
#> --------------------------------------------------------------------- 
#>                        Pair    rho      t      p    n sig
#>                age × income  0.003  0.163 0.8703 2186    
#>     age × life_satisfaction -0.024 -1.180 0.2383 2421    
#>  income × life_satisfaction  0.464 24.073 0.0000 2115 ***
#> --------------------------------------------------------------------- 
#> 
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
summary(result, pvalue_matrix = FALSE)  # hide p-values
#> 
#> Spearman's Rank Correlation Analysis 
#> -------------------------------------
#> 
#> - Method: Spearman's rho (rank correlation)
#> - Variables: age, income, life_satisfaction
#> - Missing data handling: pairwise deletion
#> - Alternative hypothesis: two.sided
#> 
#> 
#> Spearman's Rho Matrix:
#> ---------------------- 
#>                       age  income life_satisfaction
#> age                 1.000   0.003            -0.024
#> income              0.003   1.000             0.464
#> life_satisfaction  -0.024   0.464             1.000
#> ---------------------- 
#> 
#> Sample Size Matrix:
#> ------------------- 
#>                     age income life_satisfaction
#> age                2500   2186              2421
#> income             2186   2186              2115
#> life_satisfaction  2421   2115              2421
#> ------------------- 
#> 
#> Pairwise Results:
#> --------------------------------------------------------------------- 
#>                        Pair    rho      t      p    n sig
#>                age × income  0.003  0.163 0.8703 2186    
#>     age × life_satisfaction -0.024 -1.180 0.2383 2421    
#>  income × life_satisfaction  0.464 24.073 0.0000 2115 ***
#> --------------------------------------------------------------------- 
#> 
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05