Chi Square Test Statistic Calculator

Calculator

Report title

Test type

Significance level

Observed counts

Use one row for goodness of fit. Use rows for a table.

Expected values

Use counts, proportions, or percentages for goodness tests.

Expected value mode

Estimated parameters

Only used for goodness of fit degrees of freedom.

Decimal places

Category labels

Used for goodness of fit output.

Row labels

Used for independence table output.

Column labels

Used for independence table output.

Rescale expected counts to observed total

Apply Yates correction for 2 by 2 tables

Example Data Table

Use case	Observed input	Expected input	Mode
Goodness of fit	18, 22, 20, 40	25, 25, 25, 25	Expected counts
Goodness with proportions	50, 30, 20	0.50, 0.30, 0.20	Proportions
Independence table	30, 10 20, 40	Leave blank	Table test

Formula Used

For a goodness of fit test, the formula is:

X² = Σ (O - E)² / E

Here, O means observed count. E means expected count.

For a table test, the expected cell value is:

E = row total × column total / grand total

The degrees of freedom are k - 1 - m for goodness of fit. They are (r - 1)(c - 1) for table tests.

The p value is the right tail area from the chi square distribution.

How To Use This Calculator

Select the test type first. Enter observed counts in the main data box. Use commas for categories. Use new lines for table rows. Add expected values when using a goodness of fit test. Leave them blank for equal expected counts.

Choose the expected value mode. Set alpha, usually 0.05. Add labels if you want clearer output. Press calculate. Review the statistic, p value, degrees of freedom, critical value, and decision. Use CSV or PDF buttons to save the result.

Understanding The X2 Test Statistic

The X2 test statistic measures how far observed counts move from expected counts. It is also called the chi square statistic. The calculator helps with goodness of fit tests and table based independence tests. Both methods compare count data, not averages or percentages alone.

Why The Statistic Matters

A small X2 value means the observed pattern is close to the expected pattern. A large value means the differences are stronger. The p value then shows how unusual that statistic is under the null hypothesis. The degrees of freedom control the shape of the reference distribution.

Goodness Of Fit Use

Use goodness of fit when you have one list of categories. Enter observed counts for each category. Then enter expected counts, expected proportions, or expected percentages. Leave expected values blank when all categories should be equal. The calculator rescales expected values when needed. This keeps totals aligned with the observed sample size.

Independence Table Use

Use the table option when you have a contingency table. Rows may represent groups. Columns may represent outcomes. The calculator finds row totals, column totals, expected counts, and each cell contribution. For a two by two table, you may apply Yates correction. This option reduces the statistic slightly for small tables.

Reading The Result

The main result is X2. The output also gives the p value, critical value, degrees of freedom, sample total, and effect size. For goodness of fit, the effect size is Cohen's w. For a table, the effect size is Cramer's V. Larger effect sizes show stronger practical difference.

Practical Notes

Expected counts should usually be at least five in most cells. Very small expected values can make the approximation weak. Combine rare categories when the grouping is reasonable. Use raw counts rather than rounded percentages. Always state the null hypothesis before testing. The calculator supports reports, teaching work, quality checks, survey tables, genetics examples, and categorical research summaries.

Exporting The Work

CSV export is useful for spreadsheet review. PDF export is helpful for sharing a compact summary. Keep the example table near your inputs when learning. It shows valid formats and expected interpretations. Recheck assumptions before making decisions from any hypothesis test with real project data carefully.

FAQs

What is the X2 test statistic?

It is a chi square value. It measures the gap between observed and expected counts. Larger values usually mean the observed pattern differs more from the expected pattern.

When should I use goodness of fit?

Use it when you have one categorical variable. It checks whether observed category counts follow expected counts, proportions, percentages, or equal shares.

When should I use the independence option?

Use it for a contingency table. It tests whether row groups and column outcomes appear related. It also works for homogeneity tests with similar table data.

What are expected counts?

Expected counts are the values predicted by the null hypothesis. In table tests, they are found from row totals, column totals, and the grand total.

What does the p value show?

The p value shows the right tail probability for the test statistic. A small p value gives stronger evidence against the null hypothesis.

What does degrees of freedom mean?

Degrees of freedom describe how many values can vary after totals and restrictions are considered. They shape the chi square reference distribution.

Should I use Yates correction?

Yates correction is only for two by two tables. It can make the statistic smaller. It is often used when sample sizes are limited.

Can I export the calculation?

Yes. Use the CSV button for spreadsheet work. Use the PDF button for a simple report summary with the statistic and cell contributions.