Contingency Table Chi Square Calculator

Calculator Input

Observed count table

Use commas, spaces, tabs, or semicolons.

Row labels

Separate labels with commas or new lines.

Column labels

Separate labels with commas or new lines.

Alpha level

Decimal places

Two by two option

Apply Yates continuity correction

Example Data Table

This sample compares customer satisfaction across three stores.

Store	Positive	Neutral	Negative
Group A	28	16	10
Group B	12	24	18
Group C	20	10	22

Formula Used

The calculator uses the Pearson chi square test for a contingency table.

Expected count: E_ij = row total_i × column total_j ÷ grand total.
Chi square statistic: χ² = Σ((O_ij − E_ij)² ÷ E_ij).
Degrees of freedom: df = (number of rows − 1) × (number of columns − 1).
P value: upper tail probability from the chi square distribution.
Cramer's V: V = √(χ² ÷ (n × min(r − 1, c − 1))).
Pearson residual: (O_ij − E_ij) ÷ √E_ij.

How To Use This Calculator

Enter observed counts in the table box. Put one row per line.
Use commas, spaces, tabs, or semicolons between columns.
Add row and column labels for clearer output.
Choose an alpha level, such as 0.05.
Select Yates correction only for a two by two table.
Press the submit button to view results above the form.
Review expected counts, residuals, warnings, and effect sizes.
Use CSV or PDF buttons to save the report.

About This Calculator

A contingency table is useful when two categorical variables must be compared. It organizes observed counts into rows and columns. This calculator turns that table into a full chi square analysis. It estimates expected counts, measures differences, and reports practical effect size.

Why The Test Matters

The chi square test of independence checks whether row groups and column groups appear related. It does not prove cause. It only measures whether the observed pattern is unlikely under independence. That makes it helpful for surveys, experiments, marketing segments, product tests, classroom data, and health research.

What The Results Show

The main statistic is the chi square value. Larger values mean observed counts are farther from expected counts. Degrees of freedom come from table size. The p value compares the statistic with the chi square distribution. When the p value is below alpha, the evidence suggests an association.

Expected Counts And Residuals

Expected counts show the counts predicted when variables are independent. Pearson residuals show which cells drive the result. A large positive residual means a cell is higher than expected. A large negative residual means it is lower than expected. Adjusted residuals also account for row and column proportions.

Effect Size

Statistical significance can grow with large samples. Effect size gives more context. Cramer's V summarizes association strength for any table size. Phi is most useful for a two by two table. The contingency coefficient gives another compact association measure.

Good Practice

Check expected counts before trusting the test. Many small expected counts can weaken the approximation. Combine rare categories when that choice is meaningful. Avoid using percentages as input. Enter raw counts only. Labels make reports easier to read, especially when tables have many groups.

Reporting The Test

A clear report states the table purpose, sample size, chi square value, degrees of freedom, p value, alpha level, decision, and effect size. Mention cells with large residuals. Exporting CSV or PDF helps preserve the calculation. This is useful for assignments, internal reports, audits, and repeatable research notes.

Use Care

The method assumes independent observations. Each subject should appear in one cell only. Related or repeated measurements need different methods. Always match analysis with the study design before publishing findings.

FAQs

What is a contingency table?

A contingency table displays counts for two categorical variables. Rows represent one variable. Columns represent another variable. Each cell contains an observed count for one combined category.

What does the chi square test check?

It checks whether two categorical variables appear independent. A small p value suggests the observed pattern is unlikely if the variables are truly independent.

Can I enter percentages?

No. Enter raw observed counts. Percentages can distort the test because the chi square statistic depends on actual frequencies and sample size.

What is an expected count?

An expected count is the cell count predicted under independence. It is calculated from the row total, column total, and grand total.

When should I use Yates correction?

Use Yates correction only for a two by two table. It reduces the chi square value slightly and can be conservative for small samples.

What does Cramer's V mean?

Cramer's V is an effect size measure. It ranges from zero upward toward one. Higher values suggest a stronger association between categories.

Why are residuals useful?

Residuals identify cells that contribute most to the result. Large positive values mean observed counts exceed expectations. Large negative values mean they fall below expectations.

What if expected counts are small?

Small expected counts can weaken the chi square approximation. Consider combining meaningful rare categories or using an exact method for small two by two tables.