Online Chi-Square Test Calculator

When to use this test

• •You have one categorical variable and want to check whether it follows a specified distribution (goodness-of-fit).
• •You have two categorical variables and want to know whether they are independent (test of independence).
• •Your observations fall naturally into counts or frequencies, not continuous measurements.
• •Each observation is classified into exactly one cell of your table — no overlap between categories.
• •You have at least ~5 expected observations per cell (otherwise use Fisher's exact test instead).

How to use it

1. 1

   Upload or paste raw or summarised data

   Two input formats work. Long format: one row per observation, with categorical columns for each variable. Summary format: a contingency table where rows and columns are categories and cells are counts. The analyzer accepts either.

2. 2

   Pick the chi-square variant

   In Hypothesis Tests choose Chi-square goodness-of-fit (one categorical variable against expected proportions) or Chi-square test of independence (two categorical variables in a contingency table).

3. 3

   Assign variables

   For goodness-of-fit, drag your single categorical column into the Category slot and enter expected proportions (equal, uniform or custom). For independence, drag one variable into Row and the other into Column.

4. 4

   Inspect the contingency table and result

   DeepStats builds the observed and expected frequency tables, highlights cells that deviate most, and returns chi-squared, degrees of freedom, p-value and Cramer's V. A mosaic plot shows the pattern visually.

5. 5

   Export or follow up

   Download the tables as CSV and the mosaic plot as PNG. If cells are sparse, the analyzer offers Fisher's exact test as a drop-in alternative.

Example with sample data

A simple test of independence between smoking status and lung condition, eight observations aggregated into a 2x2 table. Paste the raw rows below into the analyzer.

Smoker,Condition
Yes,Ill
Yes,Ill
Yes,Healthy
Yes,Ill
No,Healthy
No,Healthy
No,Ill
No,Healthy

With this tiny dataset the analyzer reports chi-squared ≈ 2.0, df = 1, p ≈ 0.157 and Cramer's V ≈ 0.5. You would fail to reject the null hypothesis at alpha = 0.05. Because cell counts are small, DeepStats also suggests Fisher's exact test as the safer alternative.

How to interpret the results

You will see: chi-squared statistic, degrees of freedom, p-value, Cramer's V (effect size), observed and expected frequency tables.

Chi-squared statistic

Computed as χ² = Σ (O − E)² / E, summed over every cell. O is the observed count and E is the expected count under the null hypothesis. Big differences in any cell push χ² up.

Degrees of freedom (df)

For goodness-of-fit, df = k − 1 where k is the number of categories. For a contingency table of r rows and c columns, df = (r − 1)(c − 1). The df determines which chi-squared distribution is used for the p-value.

p-value

The probability of observing a χ² at least as extreme as yours if the null were true. Below 0.05 indicates a significant deviation from the expected pattern. In a test of independence, a small p-value says the two variables are associated.

Cramer's V

Standardised effect size scaled from 0 (no association) to 1 (perfect). Rough benchmarks for a df of 1: 0.1 small, 0.3 medium, 0.5 large. Cramer's V is essential alongside the p-value because chi-squared grows with sample size and can flag trivially small associations in big datasets.

Observed vs expected table

The analyzer displays the expected frequencies under the null hypothesis. Cells where observed minus expected is large indicate which categories drive the result — a useful diagnostic for writing up your finding.

Assumptions

• Independent observations.Each count should come from a different subject or event. Repeated measurements on the same person violate the assumption. Use McNemar's test for paired 2x2 designs instead.
• Expected counts of at least 5 per cell.When more than 20% of cells have an expected count below 5, the chi-squared approximation breaks down. Switch to Fisher's exact test or collapse sparse categories before re-running.
• Fixed categories.Categories must be mutually exclusive and exhaustive. An observation cannot belong to two categories or to none.
• Random sampling.The data should be a random sample of the population you want to generalise to. Convenience samples may still be informative but limit external validity.

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