Survey Chi Square Calculator

Example data table

Example: Satisfaction by Device Type (counts from a fictional survey).

Formula used

How to use this calculator

1. Select the number of row and column categories.
2. Optionally rename categories using the label fields.
3. Enter the observed survey counts into the table.
4. Choose Yates correction if you have a small 2×2 table.
5. Press Submit to view results above the form.
6. Use the export buttons in the Results card to download CSV or PDF.

Why cross-tab testing matters in surveys

Survey teams often compare two categorical questions, such as device type and satisfaction. A contingency table summarizes joint frequencies and reveals where responses concentrate. The chi-square test evaluates whether observed patterns differ from independence beyond random fluctuation, using the full table rather than isolated percentages.

Building reliable observed counts

Use mutually exclusive categories and ensure each respondent contributes to one cell only. Remove missing or “prefer not to say” responses or treat them as explicit categories. Larger total N increases power, but small subgroup counts can still destabilize expected values and inflate uncertainty.

If your survey uses weights, convert to weighted counts only when the test fits your design; otherwise, analyze unweighted counts or use survey methods. For 2×2 tables with small counts, Yates continuity correction can reduce overstatement of significance in small samples.

Expected frequencies and assumption checks

Expected counts are computed from row and column totals. A common practical rule is that most expected cells should be at least 5. When many expected values fall below 5, collapse sparse categories, revisit the question design, or consider exact or simulation-based alternatives for inference.

Interpreting p-values with effect size

A small p-value indicates an association, not its strength. Cramer's V scales the chi-square statistic by sample size and table dimensions, enabling comparisons across studies. As a rough guide, V around 0.1 may be small, 0.3 moderate, and 0.5 large for many survey contexts.

Reporting results for stakeholders

In reports, include the variables, table dimensions, N, χ², degrees of freedom, p-value, and Cramer's V. Highlight cells with large standardized residuals to explain drivers, for example “mobile users were more satisfied than expected.” Exporting CSV supports auditing, while PDF aids quick sharing. State the decision threshold and note any category merges made before testing.

FAQs

1) What does this chi-square test evaluate?

It tests whether two categorical survey variables are independent by comparing observed cell counts to expected counts under independence, producing χ², degrees of freedom, and a p-value.

2) When should I avoid using the test?

Avoid it when many expected counts are below 5, categories overlap, or your design requires complex-survey inference. In those cases, collapse sparse categories or use exact or design-based methods.

3) What is Yates correction and when does it apply?

Yates continuity correction adjusts χ² for 2×2 tables with small counts to reduce false positives. This calculator applies it only when you select it and the table is 2×2.

4) How do I interpret Cramer's V?

Cramer's V summarizes association strength on a 0–1 scale. Values near 0 suggest weak association; larger values suggest stronger relationships, while context and category structure determine practical importance.

5) What are standardized residuals used for?

They show which cells drive χ². Large positive residuals indicate more responses than expected; large negative residuals indicate fewer. They help you explain the specific categories behind a significant result.

6) Can I use percentages instead of counts?

Use counts, not percentages, because χ² relies on frequencies and the total sample size. If you only have percentages, convert them back to counts using the sample N for each group.