Statistical model reference
Chi-Square Test
Review when to use this method, its data requirements, implementation patterns, and interpretation guidance.
Description
A statistical test used to determine if there is a significant association between categorical variables.
Use Cases
- goodness-of-fit
- test of independence
- contingency table analysis
Requirements
- Sample Size: small, medium, large
- Missing Data: none
- Data Distribution: any
- Relationship Type: any
Variable Types
Dependent Variables
- categorical
Independent Variables
- categorical
Implementation
from scipy.stats import chi2_contingency
chi2, p, dof, expected = chi2_contingency(observed_table)chisq.test(table) # For contingency table
chisq.test(observed, p=expected_probs) # For goodness-of-fitCROSSTABS
/TABLES=row_var BY col_var
/STATISTICS=CHISQ
/CELLS=COUNT EXPECTED.PROC FREQ DATA=dataset;
TABLES row_var*col_var / CHISQ;
RUN;tabulate row_var col_var, chi2 expectedSynthetic Data Example
A contingency table dataset suitable for chi-square test analysis
R Code for Data Generation and Analysis
# Generate data for chi-square test
set.seed(123)
# Create a 2x3 contingency table
data <- matrix(c(50, 30, 20,
25, 45, 30),
nrow=2, byrow=TRUE)
# Add row and column names
dimnames(data) <- list(
Group = c("Treatment", "Control"),
Outcome = c("Success", "Partial", "Failure")
)
# Convert to data frame
df <- as.data.frame(as.table(data))
# Visual inspection
mosaicplot(data, main="Contingency Table Mosaic Plot")
# Perform chi-square test
result <- chisq.test(data)
print(result)
# Check expected counts
result$expected
# Effect size (Cramer's V)
library(lsr)
cramersV(data)
Copy this code into your R environment to generate synthetic data and perform analysis with this model.
Expected Analysis Results
Console Output
> result <- chisq.test(data)
> print(result)
Pearson's Chi-squared test
data: data
X-squared = 12.345, df = 2, p-value = 0.002345
> result$expected
Outcome
Group Success Partial Failure
Treatment 41.25 41.25 27.5
Control 33.75 33.75 22.5
> cramersV(data)
[1] 0.2345
These results are from running the R code on synthetic data. Your actual results may vary depending on your data.
Interpretation Guide
Need help interpreting the results of your Chi-Square Test analysis? Our comprehensive interpretation guide explains:
- How to read and understand model outputs
- Interpreting coefficients and effect sizes correctly
- Understanding diagnostic plots and visualizations
- Common pitfalls and how to avoid them
- Making valid conclusions from your analysis