Chi Test Statistic Calculator

Calculator

Test type

Alpha level

Estimated parameters

Observed counts

Expected source

Expected counts

Scale expected counts to observed total

Expected probabilities

Contingency table

Correction option

Use Yates correction for 2 by 2 tables

Table format

Enter one row per line. Separate counts with commas, spaces, or semicolons.

Example Data Table

Use case	Observed data	Expected data	Recommended mode
Club enrollment	32, 25, 21, 42	Equal categories	Goodness of fit
Survey by group	18, 12, 20 / 10, 24, 16	Computed from row and column totals	Independence table
Brand preference	40, 35, 25	0.50, 0.30, 0.20	Goodness of fit

Formula Used

Chi square statistic: χ² = Σ((O − E)² / E)

Goodness of fit degrees of freedom: df = k − 1 − estimated parameters

Table expected count: E = row total × column total / grand total

Table degrees of freedom: df = (rows − 1) × (columns − 1)

Cohen w: w = √(χ² / n)

Cramer V: V = √(χ² / (n × min(rows − 1, columns − 1)))

How to Use This Calculator

Choose goodness of fit for one categorical variable.
Choose table mode for independence or homogeneity tests.
Enter raw observed counts only.
Select equal expected counts, custom expected counts, or probabilities.
Set alpha and estimated parameters if needed.
Press calculate and review the result above the form.
Download the CSV or print the report as a PDF.

Overview

A chi test statistic measures how far observed counts move from expected counts. It is useful when data is grouped into categories. This calculator supports goodness of fit tests and contingency table tests. It also gives residuals, contributions, degrees of freedom, and p values. These details help you review more than one final number.

When to Use It

Use a goodness of fit test when one categorical variable has expected proportions. A common example compares survey answers with a planned distribution. Use a test of independence when two categorical variables form a table. Examples include product preference by age group or result type by treatment group. The calculator also works for homogeneity tests, because the table statistic is the same.

Understanding the Output

The chi square statistic adds category contributions. A large contribution shows a cell with a large gap between observed and expected counts. The p value estimates how unusual the statistic is when the null hypothesis is true. If the p value is below alpha, the result is usually called statistically significant. The effect size gives practical context. For goodness of fit, Cohen's w is shown. For tables, Cramer's V is shown.

Good Data Practices

Counts should be raw frequencies, not percentages. Expected counts should usually be at least five. Small expected counts can make the approximation weak. Combine rare categories when it is reasonable and planned. Do not remove categories only to force significance. Your categories should be independent, clear, and mutually exclusive. Always check assumptions before final reporting.

Practical Example

Suppose a school expects equal enrollment in four clubs. Actual counts are 32, 25, 21, and 42. The calculator can compare those counts with equal expected counts. It then shows which club causes the largest contribution. That makes the result easier to explain. The same workflow applies to survey choices, defect categories, genetics examples, and market research tables.

Reporting Tips

Report the test name, statistic, degrees of freedom, p value, alpha, and conclusion. Include effect size when possible. Mention important residuals if they explain the result. For a table, review which rows and columns drive the pattern. For a goodness of fit test, state the expected distribution. Clear reporting makes the conclusion easier to audit.

FAQs

What is a chi test statistic?

It is a sum of squared gaps between observed and expected counts. Each gap is divided by its expected count.

Can I use percentages?

Use raw counts when possible. Percentages can hide sample size and may produce misleading expected counts.

What does the p value mean?

It estimates how extreme the statistic is under the null hypothesis. Smaller values give stronger evidence against that null.

What is a good expected count?

A common rule is that expected counts should be at least five. Very small expected counts weaken the approximation.

When should I use goodness of fit?

Use it when one categorical variable is compared with a known, equal, or planned distribution.

When should I use table mode?

Use it when two categorical variables form rows and columns. It tests association or group homogeneity.

What does Cramer V show?

Cramer V is an effect size for tables. It helps judge practical strength after checking significance.

Why are residuals included?

Residuals show which categories or cells drive the statistic. Larger absolute residuals deserve closer review.