Running pairwise chi-square tests with the `vivainsights` R library

2025-07-25

This script shows an example of how to perform pairwise chi-square tests for categorical variables in a dataset.

A pairwise chi-square test helps detect associations between distinct pairs of categorical variables. By running multiple chi-square tests on each pair, it allows you to pinpoint which specific pairs exhibit significant relationships.

Step 1: load libraries and sample data

In this example, we will use the sample pq_data dataset from the vivainsights package. We will also use dplyr and purrr for data manipulation and iteration respectively, and optionally you can just load the tidyverse package instead.

library(vivainsights)
library(dplyr)
library(purrr)

sample_data <- pq_data

Step 2: simulating a dataset with categorical variables

The next step is to simulate additional categorical variables for the sample data. In this example, we will create three fake categorical variables: Teams, Regions, and Functions. We will then merge these variables with the sample data.

# Set random seed for reproducibility
set.seed(123)

# Number of unique PersonId in data
n_personid <- length(unique(sample_data$PersonId))

# Create fake categorical variables for each PersonId
cat_data <- data.frame(
  PersonId = unique(sample_data$PersonId),
  Teams = sample(c('Team 1', 'Team 2', 'Team 3'), size = n_personid, replace = TRUE),
  Regions = sample(c('East', 'South', 'West', 'North'), size = n_personid, replace = TRUE),
  Functions = sample(c('HR', 'Finance', 'Operations', 'Sales'), size = n_personid, replace = TRUE)
)

# Merge the datasets
sample_data_merged <- merge(sample_data, cat_data, by = "PersonId")

# Assign categorical variables names to `cat_vars`, alongside existing variables
cat_vars <- c("Teams", "Regions", "Functions", "Organization", "LevelDesignation")

Step 3: Perform pairwise chi-square tests for all categorical variables

In the following, we first use combn() to generate all combinations of variable pairs. combn() comes from the utils package, and generates all combinations of a vector of elements of a given size. Here, we set m = 2 to yield pairs.

Next, we use map_dfr() from the purrr package to loop over each combination and perform a chi-square test. The operation is similar to a for loop, but the results are row-bound (similar to rbind() or bind_rows()) and returned as a data frame. In R, it is generally more efficient to use map() functions from the purrr package than to use for loops.

Towards the end of the code, we add a significance level to the results based on the p-value. The significance level is denoted by asterisks, where *** indicates p < 0.001, ** indicates p < 0.01, and * indicates p < 0.05.

# Generate all combinations of variable pairs
cat_var_combinations <- combn(x = cat_vars, m = 2, simplify = FALSE)

# Use `map_dfr()` to loop over each combination
results_df <-
  map_dfr(cat_var_combinations, ~{
  var1 <- .x[1]
  var2 <- .x[2]
  
  # Create a contingency table
  contingency_table <- table(sample_data_merged[[var1]], sample_data_merged[[var2]])
  
  # Perform chi-square test
  chi_test <- chisq.test(contingency_table)
  
  # Return data frame with results
  tibble(
    var1 = var1,
    var2 = var2,
    chi2 = chi_test$statistic,
    p = chi_test$p.value,
    n = sum(contingency_table)
  ) %>%
    # Add significance level
    mutate(
      significance = case_when(
        p < 0.001 ~ "***",
        p < 0.01 ~ "**",
        p < 0.05 ~ "*",
        TRUE ~ ""
    ))
})

print(results_df)

## # A tibble: 10 × 6
##    var1         var2              chi2         p     n significance
##    <chr>        <chr>            <dbl>     <dbl> <int> <chr>       
##  1 Teams        Regions          186.  1.98e- 37  6900 ***         
##  2 Teams        Functions         69.7 4.69e- 13  6900 ***         
##  3 Teams        Organization     325.  3.19e- 62  6900 ***         
##  4 Teams        LevelDesignation 127.  6.93e- 25  6900 ***         
##  5 Regions      Functions        243.  2.39e- 47  6900 ***         
##  6 Regions      Organization     306.  2.93e- 54  6900 ***         
##  7 Regions      LevelDesignation 145.  7.75e- 27  6900 ***         
##  8 Functions    Organization     277.  2.14e- 48  6900 ***         
##  9 Functions    LevelDesignation  92.8 4.43e- 16  6900 ***         
## 10 Organization LevelDesignation 835.  1.40e-165  6900 ***

Finally, you can export the results to csv or clipboard using the following code:

# Copy to clipboard
results_df %>% export(method = "clipboard")

# Export to csv
results_df %>% export(method = "csv", path = "chi-square-results", timestamp = FALSE)