K-Group Chi-Square (k×2)

Chi-square with 3+ groups and pairwise comparisons

Overview

When one (or both) categorical variables has three or more levels, a significant omnibus chi-square must be followed by pairwise 2×2 comparisons. chi_square_kgroup_answers() handles the full workflow: the omnibus test, all pairwise comparisons, and effect sizes.

1. Run the Analysis

library(psych350lab)
library(psych350data)
library(dplyr)

data(superman, package = "psych350data")

# Run k-group chi-square
kgroup_chi <- chi_square_kgroup_answers(
  data       = superman,
  var1       = "decade",
  var2       = "tomatometer",
  var1_labels = c("1950s", "1970-80s", "2000s", "2010s"),
  var2_labels = c("Rotten", "Fresh")
)

# Omnibus results
kgroup_chi$Chi_Square

# Observed frequencies
kgroup_chi$Observed

# Pairwise comparisons
kgroup_chi$Pairwise

What chi_square_kgroup_answers() returns

Element	Contents
$Chi_Square	chi_square, p_value, df, n
$Observed	Matrix of observed cell frequencies
$Expected	Matrix of expected cell frequencies
$Pairwise	List of all pairwise 2×2 comparisons
$var1_labels	Display labels for the k-group variable
$var2_labels	Display labels for the 2-level variable

Pairwise comparison elements

Each entry in $Pairwise contains:

• comparison — which two groups are being compared
• chi_sq, p_value, df — test statistics for the 2×2 sub-table
• effect_size — phi/r coefficient for the pair
• observed — 2×2 observed frequency table

2. Create Checker Widgets

Omnibus checker

create_chisq_omnibus_table() creates the omnibus statistics checker:

create_chisq_omnibus_table(
  rh_name          = "RH1",
  chi_results_list = kgroup_chi,
  var1_labels      = c("1950s", "1970-80s", "2000s", "2010s"),
  var2_labels      = c("Rotten", "Fresh")
)

Pairwise checker

create_chisq_pairwise_checker() creates fill-in-the-blank widgets for each pairwise comparison:

create_chisq_pairwise_checker(
  rh_name          = "RH1",
  chi_results_list = kgroup_chi
)

3. Create APA Tables

Combined results table

create_chi_combined_table() produces a single table with the omnibus result and all pairwise comparisons:

create_chi_combined_table(
  chi_results_list = kgroup_chi,
  var1_name        = "Decade",
  var2_name        = "Tomatometer",
  var1_labels      = c("1950s", "1970-80s", "2000s", "2010s"),
  var2_labels      = c("Rotten", "Fresh"),
  table_title      = "Chi-Square Results for Decade × Tomatometer"
)

Pairwise results table

create_chisq_pairwise_table(
  chi_results_list = kgroup_chi,
  var1_labels      = c("1950s", "1970-80s", "2000s", "2010s"),
  var2_labels      = c("Rotten", "Fresh")
)

4. Generate APA Write-Up

apa_kgroup_chi_writeup() produces a write-up covering the omnibus test and any significant pairwise follow-ups:

writeup <- apa_kgroup_chi_writeup(
  chi_results_list = kgroup_chi,
  var1_name        = "decade",
  var2_name        = "Tomatometer rating",
  var1_labels      = c("1950s", "1970-80s", "2000s", "2010s"),
  var2_labels      = c("Rotten", "Fresh"),
  hypothesis       = list(
    rh_text = "the distribution of Fresh vs Rotten ratings would differ across decades"
  ),
  include_posthoc  = TRUE
)

# cat(writeup)

5. Format Omnibus Results

format_chi_omnibus_results() creates markdown output for the omnibus portion of the worksheet:

format_chi_omnibus_results(
  rh_name          = "RH1",
  chi_results_list = kgroup_chi,
  KEY              = TRUE
)

Complete Lab Setup Example

library(psych350lab)
library(psych350data)
library(dplyr)

data(superman, package = "psych350data")

# ── Analysis ─────────────────────────────────────────────
RH1_kchi <- chi_square_kgroup_answers(
  data = superman,
  var1 = "decade",
  var2 = "tomatometer",
  var1_labels = c("1950s", "1970-80s", "2000s", "2010s"),
  var2_labels = c("Rotten", "Fresh")
)

# ── Checkers (for HTML) ──────────────────────────────────
# Omnibus checker
create_chisq_omnibus_table("RH1", RH1_kchi,
  var1_labels = c("1950s", "1970-80s", "2000s", "2010s"),
  var2_labels = c("Rotten", "Fresh")
)

# Pairwise checker
create_chisq_pairwise_checker("RH1", RH1_kchi)

# Pairwise answer key
chisq_pairwise_KEY(RH1_kchi)

# ── APA Tables ───────────────────────────────────────────
create_chi_combined_table(
  chi_results_list = RH1_kchi,
  var1_name = "Decade", var2_name = "Tomatometer",
  var1_labels = c("1950s", "1970-80s", "2000s", "2010s"),
  var2_labels = c("Rotten", "Fresh"),
  table_title = "Chi-Square Results for Decade × Tomatometer"
)

# ── Write-Up ─────────────────────────────────────────────
RH1_writeup <- apa_kgroup_chi_writeup(
  chi_results_list = RH1_kchi,
  var1_name = "decade",
  var2_name = "Tomatometer rating",
  var1_labels = c("1950s", "1970-80s", "2000s", "2010s"),
  var2_labels = c("Rotten", "Fresh"),
  hypothesis = list(
    rh_text = "the distribution of ratings would differ across decades"
  ),
  include_posthoc = TRUE
)

Key Functions Reference

Function	Purpose
chi_square_kgroup_answers()	K-group chi-square with pairwise comparisons
create_chisq_omnibus_table()	Omnibus statistics checker widget
create_chisq_pairwise_checker()	Pairwise comparison checker widget
create_chisq_pairwise_table()	Pairwise results table (flextable)
create_chi_combined_table()	Combined omnibus + pairwise table
chisq_pairwise_KEY()	Pairwise comparison answer key
format_chi_omnibus_results()	Markdown output for omnibus results
apa_kgroup_chi_writeup()	Full APA write-up with post-hoc