Chi-Square (2×2)

Pearson’s chi-square test of independence for two categorical variables

Overview

This guide covers the 2×2 chi-square test of independence workflow in psych350lab: running the analysis, creating contingency tables, formatting worksheet output, generating APA write-ups, and building interactive homework checkers.

1. Run the Analysis

chi_square_answers() performs a Pearson’s chi-square test for two categorical variables and returns observed/expected frequencies along with the test statistic.

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

data(superman, package = "psych350data")

# Run chi-square test
chi_result <- chi_square_answers(
  data = superman,
  var1 = "clark_grp",
  var2 = "tomatometer"
)

# Inspect the results
str(chi_result)

What chi_square_answers() returns

Element	Contents
$ChiSquare	chi_sq, p_value, df, n, phi
$Observed	Matrix of observed cell frequencies
$Expected	Matrix of expected cell frequencies
$Effect_Size	phi and r effect size

2. Create Hypothesis Contingency Tables

Before running the analysis, students label a contingency table with <, >, or = to predict the expected pattern. create_rh_crosstabs() generates this table in both KEY and BLANK modes.

# Blank version for students to fill in
create_rh_crosstabs(
  var1_name      = "Actor Height",
  var2_name      = "Tomatometer",
  var1_levels    = c("Under 6ft", "6ft or taller"),
  var2_levels    = c("Rotten", "Fresh"),
  KEY            = FALSE,
  include_totals = TRUE
)

# Answer key version with hypothesis pattern
create_rh_crosstabs(
  var1_name          = "Actor Height",
  var2_name          = "Tomatometer",
  var1_levels        = c("Under 6ft", "6ft or taller"),
  var2_levels        = c("Rotten", "Fresh"),
  KEY                = TRUE,
  chi_results        = chi_result,
  hypothesis_pattern = c("<", "="),
  include_totals     = TRUE
)

Understanding the hypothesis pattern

The hypothesis_pattern is a character vector with one symbol per row of the contingency table (one per level of var1). Each symbol describes the expected relationship between the two columns of var2:

• "<" — the first column count is expected to be less than the second
• ">" — the first column count is expected to be greater than the second
• "=" — no expected difference between columns

3. Format Results for Worksheets

format_chi2_results() creates markdown output with the test statistic, observed frequencies, and effect size. Toggle KEY for answer key vs. blank student versions.

# Answer key
chi_KEY <- format_chi2_results(
  rh_name          = "RH2",
  vars             = c("clark_grp", "tomatometer"),
  chi_results_list = chi_result,
  var1_labels      = c("Under 6ft", "6ft or taller"),
  var2_labels      = c("Rotten", "Fresh"),
  KEY              = TRUE
)

# Student worksheet (blanks)
chi_BLANK <- format_chi2_results(
  rh_name          = "RH2",
  vars             = c("clark_grp", "tomatometer"),
  chi_results_list = chi_result,
  var1_labels      = c("Under 6ft", "6ft or taller"),
  var2_labels      = c("Rotten", "Fresh"),
  KEY              = FALSE
)

# In your Quarto document (results: asis):
# cat(chi_KEY)

4. Create APA Contingency Tables

create_apa_chi_crosstabs_table() produces a publication-ready crosstab as a flextable.

# Answer key table
create_apa_chi_crosstabs_table(
  chi_results_list = chi_result,
  var1_name        = "Actor Height",
  var2_name        = "Tomatometer",
  var1_labels      = c("Under 6ft", "6ft or taller"),
  var2_labels      = c("Rotten", "Fresh"),
  KEY              = TRUE,
  table_title      = "Crosstabulation of Actor Height and Critic Ratings",
  table_number     = 2
)

# Blank version (pass NULL for chi_results_list)
create_apa_chi_crosstabs_table(
  chi_results_list = NULL,
  var1_name        = "Actor Height",
  var2_name        = "Tomatometer",
  var1_labels      = c("Under 6ft", "6ft or taller"),
  var2_labels      = c("Rotten", "Fresh"),
  KEY              = FALSE
)

5. Generate APA Write-Ups

apa_chi_writeup() generates a complete statistical write-up with hypothesis evaluation and effect size interpretation.

writeup <- apa_chi_writeup(
  chi_results_list = chi_result,
  var1_name        = "actor height",
  var2_name        = "critic rating",
  var1_labels      = c("Under 6ft", "6ft or taller"),
  var2_labels      = c("Rotten", "Fresh"),
  hypothesis       = list(
    pattern              = c("=", "<"),
    rh_text              = "actors over 6ft tall would be more likely to appear in Fresh-rated media",
    comparison_var2_level = 2
  )
)

# cat(writeup)

Hypothesis pattern for write-ups

The hypothesis list contains:

• pattern — character vector of <, >, = for each row of the table
• rh_text — plain-English description of the hypothesis
• comparison_var2_level — which column of var2 is the “target” for the comparison (1 or 2)

6. Create Interactive Homework Checkers

create_chisq_checker() produces an HTML widget where students enter observed frequencies and chi-square statistics.

# In a Quarto HTML document:
create_chisq_checker(
  rh_name          = "RH2",
  chi_results_list = chi_result,
  var1_labels      = c("Under 6ft", "6ft or taller"),
  var2_labels      = c("Rotten", "Fresh")
)

7. Inline APA Statistics

# Returns something like: χ²(1) = 4.52, *p* = .034
apa_inline_chi2(chi_result)

8. Effect Size Conversion

pr_chi_to_r() converts 2×2 cell frequencies to an r effect size, useful for interpreting the practical significance of the association.

# a, b, c, d are the four cells of the 2x2 table
pr_chi_to_r(a = 15, b = 10, c = 8, d = 17)

Complete Lab Setup Example

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

data(superman, package = "psych350data")

# ── Analysis ─────────────────────────────────────────────
RH2_chi <- chi_square_answers(
  data = superman,
  var1 = "clark_grp",
  var2 = "tomatometer"
)

# ── Hypothesis Crosstabs ─────────────────────────────────
RH2_contingency_BLANK <- create_rh_crosstabs(
  var1_name = "Actor Height", var2_name = "Tomatometer",
  var1_levels = c("Under 6ft", "6ft or taller"),
  var2_levels = c("Rotten", "Fresh"),
  KEY = FALSE, include_totals = TRUE
)

RH2_contingency_KEY <- create_rh_crosstabs(
  var1_name = "Actor Height", var2_name = "Tomatometer",
  var1_levels = c("Under 6ft", "6ft or taller"),
  var2_levels = c("Rotten", "Fresh"),
  KEY = TRUE, chi_results = RH2_chi,
  hypothesis_pattern = c("<", "="),
  include_totals = TRUE
)

# ── Worksheet Output ─────────────────────────────────────
RH2_chi_BLANK <- format_chi2_results(
  rh_name = "RH2",
  vars = c("clark_grp", "tomatometer"),
  chi_results_list = RH2_chi,
  var1_labels = c("Under 6ft", "6ft or taller"),
  var2_labels = c("Rotten", "Fresh"),
  KEY = FALSE
)

RH2_chi_KEY <- format_chi2_results(
  rh_name = "RH2",
  vars = c("clark_grp", "tomatometer"),
  chi_results_list = RH2_chi,
  var1_labels = c("Under 6ft", "6ft or taller"),
  var2_labels = c("Rotten", "Fresh"),
  KEY = TRUE
)

# ── APA Tables ───────────────────────────────────────────
RH2_table_BLANK <- create_apa_chi_crosstabs_table(
  chi_results_list = NULL,
  var1_name = "Actor Height", var2_name = "Tomatometer",
  var1_labels = c("Under 6ft", "6ft or taller"),
  var2_labels = c("Rotten", "Fresh"),
  KEY = FALSE
)

RH2_table_KEY <- create_apa_chi_crosstabs_table(
  chi_results_list = RH2_chi,
  var1_name = "Actor Height", var2_name = "Tomatometer",
  var1_labels = c("Under 6ft", "6ft or taller"),
  var2_labels = c("Rotten", "Fresh"),
  KEY = TRUE,
  table_title = "Crosstabulation of Actor Height and Critic Ratings",
  table_number = 2
)

# ── Write-Up ─────────────────────────────────────────────
RH2_writeup <- apa_chi_writeup(
  chi_results_list = RH2_chi,
  var1_name = "actor height",
  var2_name = "critic rating",
  var1_labels = c("Under 6ft", "6ft or taller"),
  var2_labels = c("Rotten", "Fresh"),
  hypothesis = list(
    pattern = c("=", "<"),
    rh_text = "actors over 6ft would be more likely to appear in Fresh-rated media",
    comparison_var2_level = 2
  )
)

Key Functions Reference

Function	Purpose
chi_square_answers()	Run chi-square test, get χ², p, observed/expected
create_rh_crosstabs()	Hypothesis contingency table (KEY/BLANK)
format_chi2_results()	Markdown output for worksheets (KEY/BLANK)
create_apa_chi_crosstabs_table()	APA-style contingency table (flextable)
apa_chi_writeup()	Full APA write-up with hypothesis evaluation
create_chisq_checker()	Interactive HTML homework checker
apa_inline_chi2()	Inline APA-formatted χ² statistic
pr_chi_to_r()	Convert 2×2 cell frequencies to r effect size