Chi-Square Test Calculator

Analyze categorical data with Chi-Square tests for goodness of fit or independence. Enter your observed frequencies into our calculator to get the chi-square statistic and determine statistical significance.

Chi-Square Test Calculator

Perform chi-square test of independence for contingency tables

Observed Frequencies

Enter each row on a new line, separate values with spaces or commas.

Significance Level (α)

About Chi-Square Test

The chi-square test of independence determines whether there is a significant association between two categorical variables. It compares observed frequencies to expected frequencies under the assumption of independence.

Null Hypothesis (H₀): The variables are independent (no association).
Alternative Hypothesis (H₁): The variables are associated.

How the Chi-Square Test Calculator Works

Choose between goodness of fit test or independence test (contingency table). For goodness of fit, enter your observed frequencies and expected frequencies or proportions. For independence, enter data in a table format with rows and columns representing different categories.

The calculator computes the chi-square statistic by summing the squared differences between observed and expected values, divided by expected values. It then determines degrees of freedom and calculates the p-value from the chi-square distribution.

Results include the chi-square value, degrees of freedom, p-value, and interpretation of statistical significance. A small p-value (typically less than 0.05) indicates the observed data differs significantly from what was expected.

When You'd Actually Use This

Testing survey response distributions

You surveyed 200 people about their favorite color. Compare observed preferences to an equal distribution to see if some colors are genuinely more popular.

Analyzing A/B test conversion rates

Test if conversion rates differ across multiple page variants. Enter conversions and non-conversions for each variant in a contingency table.

Quality control defect analysis

Compare defect counts across different production shifts or machines. Determine if certain shifts produce significantly more defects.

Genetics inheritance patterns

Test if offspring phenotypes match expected Mendelian ratios. Enter observed counts and compare to predicted 3:1 or 9:3:3:1 ratios.

Market research segmentation

Check if product preference is independent of demographic factors like age group or gender. Use a contingency table to test for associations.

Medical treatment outcomes

Compare recovery rates across multiple treatment groups. Determine if treatment type is associated with patient outcomes.

What to Know Before Using

Expected frequencies should be adequate.Each expected cell count should ideally be 5 or more. Smaller expected values can make the test unreliable. Consider combining categories if needed.

Data must be independent observations.Each observation should belong to only one category. Repeated measures or paired data require different statistical tests.

Goodness of fit tests one variable.Use goodness of fit to compare one categorical variable to a theoretical distribution. Use independence test for relationships between two variables.

Degrees of freedom depend on categories.For goodness of fit: df = number of categories minus 1. For independence: df = (rows - 1) × (columns - 1).

Pro tip: A significant chi-square tells you there's a difference, but not where it is. For contingency tables with more than 2×2, follow up with post-hoc tests or examine standardized residuals to identify which cells contribute most to the difference.

Common Questions

What does a significant p-value mean?

A p-value less than 0.05 suggests the observed frequencies differ significantly from expected. For independence tests, it means the two variables are associated.

Can I use percentages instead of counts?

No. Chi-square requires raw frequency counts, not percentages or proportions. The test uses actual sample size in its calculations.

What if my expected values are small?

If more than 20% of cells have expected counts below 5, consider combining categories or using Fisher's exact test for 2×2 tables.

Is chi-square one-tailed or two-tailed?

Chi-square is always right-tailed. Large chi-square values indicate greater deviation from expected, leading to smaller p-values.

How do I interpret effect size?

For 2×2 tables, use phi coefficient. For larger tables, use Cramer's V. Values around 0.1 are small, 0.3 medium, 0.5 large effects.

Can chi-square tell me direction of relationship?

No. Chi-square only tells you if variables are associated, not the direction. Examine the observed vs expected counts to see which categories differ.

What's the minimum sample size?

There's no strict minimum, but you need enough observations for expected cell counts of at least 5. Very small samples limit the test's reliability.

Other Free Tools

Search tools

Chi-Square Test Calculator