Test variable independence using observed and expected frequencies. Review chi-square, degrees, p value, and strength. Download clean reports quickly for classes, audits, and research.
This sample shows a simple 3 by 3 contingency table.
| Store Channel | Low | Medium | High |
|---|---|---|---|
| Online | 22 | 31 | 17 |
| Retail | 18 | 26 | 29 |
| Phone | 14 | 21 | 32 |
The calculator applies the chi-square test of independence for two categorical variables with multiple categories.
The chi square test of independence checks whether two categorical variables are related. This calculator works with multiple row categories and multiple column categories. It turns a contingency table into a clear statistical result. You can use it for surveys, audits, classroom projects, market research, and quality reviews.
Many datasets contain labels instead of continuous values. Examples include location, response type, grade band, device type, and purchase choice. A chi square independence test helps you see whether the pattern in one variable changes across another variable. That makes it useful for comparing grouped behavior and category based outcomes.
The calculator first reads the observed frequencies. It then creates expected frequencies from the row totals and column totals. If the observed counts differ strongly from the expected counts, the chi square statistic rises. A small p value suggests the variables are not independent. A larger p value suggests the difference may be due to chance.
Degrees of freedom depend on the table size. Expected counts help you check whether the test conditions look reasonable. Cell contributions show which cells drive the total statistic. Standardized residuals help you spot unusually high or low cells. Cramer's V adds effect size, so you can describe strength instead of only significance.
This method is designed for frequencies, not percentages or averages. Each observation should belong to only one cell. Very small expected counts can weaken interpretation. If several cells fall below common thresholds, consider combining sparse categories before final reporting. Clear labels and careful data entry also improve reliability.
When you report the result, include the chi square statistic, degrees of freedom, sample size, p value, and a short conclusion. If your audience needs more detail, add expected counts and effect size. That creates a stronger summary and makes the analysis easier to review later.
This calculator is useful when you need a quick, repeatable workflow. It keeps the input table, output tables, and export options in one place. That saves time during revision, validation, and final documentation.
It tests whether two categorical variables appear independent or associated. It compares observed frequencies with expected frequencies built from the marginal totals.
No. The table should contain raw frequency counts. Percentages, means, and rates can distort the test and should not be entered directly.
This file allows between 2 and 10 row categories and between 2 and 10 column categories. That range covers many practical contingency tables.
Small expected counts can weaken the standard approximation. If many cells are below 5, consider combining sparse categories before reporting the final result.
Cramer's V is an effect size. It helps describe the strength of association after significance is tested. Higher values usually indicate a stronger relationship.
Residuals show which cells differ most from expectation. Large positive or negative values highlight cells that contribute strongly to the overall chi-square statistic.
No. A significant result only suggests association in the table. It does not prove that one variable causes change in the other.
Report the chi-square value, degrees of freedom, sample size, p value, and conclusion. Adding effect size and key residual findings often improves clarity.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.