Calculator
Example Data Table
This example compares product choices across three stores.
| Group | Basic | Standard | Premium |
|---|---|---|---|
| Store A | 42 | 18 | 30 |
| Store B | 55 | 25 | 20 |
| Store C | 38 | 32 | 30 |
Formula Used
Expected count: E = (row total × column total) / grand total
Chi squared statistic: χ² = Σ((O - E)² / E)
Degrees of freedom: df = (rows - 1)(columns - 1)
P value: upper tail probability from the chi squared distribution.
Cramer's V: V = √(χ² / (n × min(rows - 1, columns - 1)))
Standardized residual: r = (O - E) / √E
How to Use This Calculator
- Enter group names in the first field.
- Enter category names in the second field.
- Type observed counts in the large table box.
- Use one line for each group.
- Choose alpha and decimal places.
- Select Yates correction only for a 2 by 2 table.
- Press Calculate to view results above the form.
- Use CSV or PDF buttons to save the output.
Chi Squared Homogeneity Test Guide
A chi squared homogeneity test compares category patterns across two or more independent groups. It asks one practical question. Do the groups share the same population distribution, or do their observed counts show meaningful differences? The method works with counts, not percentages. Each subject or item should belong to one group and one category only.
When This Test Helps
Use this test for surveys, experiments, audits, marketing studies, education data, health tables, and quality checks. For example, a researcher may compare product choices across three stores. A school may compare grade bands across different classes. A business may compare complaint types across service teams. The table must contain raw frequencies. Very small expected counts can weaken the approximation, so the calculator flags the minimum expected value.
What The Results Mean
The calculator first totals every row and column. It then builds expected counts from the row total, column total, and grand total. A large difference between observed and expected counts increases the chi squared statistic. The p value shows how unusual the statistic is when all groups truly share the same distribution. If the p value is less than alpha, reject the homogeneity claim. If it is not less, the evidence is not strong enough.
Reading Residuals
Residuals show where the largest differences appear. A positive residual means the observed count is higher than expected. A negative residual means it is lower. Standardized residuals near plus or minus two may deserve attention. Contributions show how much each cell adds to the final statistic. This helps explain the test, not just report a p value.
Best Practices
Plan the groups before collecting data. Avoid moving rows or categories after seeing results. Keep categories clear and mutually exclusive. Combine rare categories only when it makes subject sense. Report the chi squared value, degrees of freedom, p value, alpha, decision, and effect size. Cramer's V helps describe practical strength. A significant result can still be small in effect. A nonsignificant result does not prove the groups are identical. It only means the sample did not show enough evidence. Always store the original table with your report. It supports review, replication, and later checking. Document any category changes too.
FAQs
What is a chi squared homogeneity test?
It checks whether two or more independent groups have the same distribution across categories. It uses observed counts and expected counts to measure differences.
What data should I enter?
Enter raw frequency counts. Do not enter percentages, averages, rates, or totals only. Each row should represent one group.
How many groups can I compare?
You can compare two or more groups. Each group must use the same category columns and the same category order.
What does the p value mean?
The p value shows how unusual the table is if all groups truly share the same distribution. Smaller values give stronger evidence against homogeneity.
What are expected counts?
Expected counts are the counts predicted by row totals and column totals when the null hypothesis is true. They are used in the chi squared formula.
When should I use Yates correction?
Use it only for a 2 by 2 table when you want a conservative continuity correction. It is not applied to larger tables.
What is Cramer's V?
Cramer's V is an effect size. It describes the strength of association between group membership and category outcome.
Can this test prove groups are identical?
No. A nonsignificant result only means the sample did not show strong evidence of different category distributions.