Chi-Square Tests
Chi-Square Test of Independence Calculator
Chi-Square Test of Independence Calculator test whether two categorical variables are independent using a contingency table.
Chi-Square Tests
Chi-Square Test of Independence Calculator
Test whether two categorical variables are independent using a contingency table.
Formula
chi-square = sum((observed - expected)^2 / expected); expected = row total * column total / grand total
About the Chi-Square Test of Independence Calculator
Test whether two categorical variables are independent using a contingency table. Chi-square and exact-table calculators analyze categorical counts, expected frequencies, or standardized contingency-table association.
How the Chi-Square Test of Independence Calculator Works
chi-square = sum((observed - expected)^2 / expected); expected = row total * column total / grand total
The calculation runs in your browser. Submitted values are validated for the required numeric range, data shape, units, and method-specific restrictions before a result is shown.
Required Inputs
- Observed contingency table (required)
- Alpha (required)
Results Reported
The result panel shows the final answer together with the intermediate quantities needed to audit the calculation. Depending on this method, reported values include:
chi_square_statisticdfp_valuecramers_vdecisionexpected_table
Chi-Square Test of Independence Calculator Example
Paste the sample data, click Calculate, and compare the detailed table with the expected output.
| Input | Example value |
|---|---|
| Observed contingency table | 20,30
30,20 |
| Alpha | 0.05 |
How to Use the Calculator
- Confirm that the calculator title and method match the quantity, test, conversion, or planning question you need to solve.
- Enter values with compatible units and the requested sample, group, matrix, count, date, or option format.
- Select Example Data to inspect a valid input layout, or enter your own values and select Calculate.
- Review the result table, formula, worked substitutions, warnings, and interpretation rather than using only the headline number.
- Use Copy Result or Download CSV when you need a reusable record of the displayed calculation.
Understanding the Result
Enter counts rather than percentages and review expected-frequency warnings; sparse 2x2 tables may require Fisher exact inference.
Keep the entered values, units, selected options, and any warning shown beside the result. For a hypothesis test, report the statistic, degrees of freedom where applicable, p-value, alpha level, effect size, and decision. For an estimate or conversion, report the formula convention and final unit.
Accuracy and Limitations
The calculator keeps full browser precision during calculation and rounds only for display. Accuracy still depends on correct inputs and on whether the displayed model represents the real problem. Educational calculators cannot replace required professional review, current official rules, field measurements, laboratory methods, or specialist statistical software where those are necessary.
Frequently Asked Questions
What does the Chi-Square Test of Independence Calculator calculate?
Test whether two categorical variables are independent using a contingency table.
Which formula does the Chi-Square Test of Independence Calculator use?
chi-square = sum((observed - expected)^2 / expected); expected = row total * column total / grand total
Is this calculator free to use?
Yes. Visitors can use it publicly through the shortcode page.
Does the calculator store visitor data?
No. Calculations run in the browser and do not store visitor data.