Compute Chi-Square tests, generate expected frequencies, and interpret results with confidence
You can paste CSV or Excel-like data directly. Separate values with commas, tabs, or spaces.
Null Hypothesis (H₀): No association exists between variables
Alternative Hypothesis (H₁): Significant association exists between variables
Create a contingency table with observed frequencies for each variable combination
Ensure data meets all test assumptions before proceeding
Use the formula: E = (Row Total × Column Total) / Grand Total
Calculate expected values for every cell in the contingency table
Apply the formula: χ² = Σ[(O - E)² / E] for each cell
Sum all individual contributions to get the total Chi-Square value
Calculate: df = (number of rows - 1) × (number of columns - 1)
This determines the appropriate critical value for comparison
Compare calculated χ² with critical value from Chi-Square distribution table
Reject H₀ if calculated value exceeds critical value at chosen significance level
Scenario: Testing if recovery rates differ between two treatment groups
Variables: Treatment Type (Drug A vs Drug B) × Outcome (Recovered/Not Recovered)
Finding: Significant association found (χ² = 8.45, p < 0.05), suggesting Drug A is more effective
Scenario: Analyzing if product preference varies by age group
Variables: Age Group (18-25, 26-40, 41+) × Product Preference (A/B/C)
Finding: No significant association (χ² = 4.32, p > 0.05), preferences consistent across ages
Scenario: Comparing exam pass rates across different teaching approaches
Variables: Teaching Method (Traditional/Online/Hybrid) × Exam Result (Pass/Fail)
Finding: Strong association (χ² = 12.78, p < 0.01), hybrid method shows highest success
Scenario: Investigating if defect rates vary by production shift
Variables: Production Shift (Morning/Evening/Night) × Product Quality (Acceptable/Defective)
Finding: Significant difference (χ² = 9.67, p < 0.05), night shift shows higher defect rates
Highly Significant: Very strong evidence against null hypothesis
Very Significant: Strong evidence against null hypothesis
Significant: Evidence against null hypothesis
Not Significant: Insufficient evidence to reject null hypothesis
Range: 0 to 1
Interpretation:
0.1 = Small effect
0.3 = Medium effect
0.5 = Large effect
Formula: φ = √(χ² / n)
Range: 0 to 1
Interpretation:
0.1 = Small effect
0.3 = Medium effect
0.5 = Large effect
Formula: V = √(χ² / [n × (min(rows, cols) - 1)])
Range: 0 to < √[(k-1)/k]
Interpretation: Higher values indicate stronger association
Formula: C = √(χ² / (χ² + n))
Menu-driven interface, excellent for social sciences
CommercialPowerful open-source platform with extensive statistical capabilities
FreeProgramming approach with scipy.stats.chi2_contingency()
FreeEnterprise-level statistical analysis software
CommercialUser-friendly interface with detailed output and visualization
FreeSimple calculator with basic Chi-Square functionality
FreeComprehensive statistical calculators for researchers
FreeCHISQ.TEST() function for basic Chi-Square analysis
CommercialCHISQ.TEST function with cloud collaboration
FreeOpen-source alternative with statistical functions
FreeA measure of how expected counts compare to observed counts
The number of values free to vary in a statistical calculation
The probability of obtaining results at least as extreme as observed
The threshold for determining statistical significance
Data that can be divided into groups or categories
Categorical data without inherent order (e.g., colors, brands)
Categorical data with natural order (e.g., ratings, levels)
A table displaying frequency distribution of variables
The default assumption of no effect or no difference
The hypothesis researchers want to prove
False positive - rejecting true null hypothesis
False negative - failing to reject false null hypothesis
The Chi-Square test is a statistical method used to determine if there's a significant association between categorical variables. It compares observed frequencies with expected frequencies to assess whether any observed differences are statistically significant or due to chance.
The Chi-Square statistic is calculated using the formula:
Where:
O = Observed frequency
E = Expected frequency
Σ = Summation across all categories
For a contingency table: df = (rows - 1) × (columns - 1)
Analyze customer preferences across different demographics to identify significant patterns in product choices or brand loyalty.
Examine relationships between treatment types and patient outcomes in clinical trials and medical research.
Study associations between demographic factors and social behaviors, attitudes, or preferences.
Test whether defect rates differ significantly across production lines or time periods.
Variables must be categorical (nominal or ordinal)
Observations must be independent of each other
Expected frequency should be at least 5 in most cells
Categories must be mutually exclusive
When expected frequencies are too small (<5), consider Fisher's Exact Test instead
Chi-Square shows association, not necessarily causation or strength of relationship
Always check that data meets test assumptions before interpreting results
Chi-Square tests relationships between categorical variables, while t-tests compare means of continuous variables between groups.
Standard Chi-Square tests two variables. For multiple variables, consider log-linear analysis or other multivariate methods.
Consider combining categories, using Fisher's Exact Test, or applying Yates' correction for continuity.
Report: χ²(degrees of freedom, N = sample size) = value, p = significance level, and effect size measure.
Applied to 2x2 tables with small sample sizes to improve accuracy
Alternative test based on maximum likelihood estimation
Used for paired nominal data in 2x2 tables
Decision tree technique based on Chi-Square tests