χ² Chi-Square Test Calculator

Compute chi-square statistic, expected frequencies, degrees of freedom, and p-value for a 2×2 to 4×4 contingency table.

Table size: ×

Chi-Square Formula

χ² = Σ (O − E)² / E

where O = observed frequency, E = expected frequency

E_ij = (row_i total × col_j total) / grand total

df = (rows − 1) × (cols − 1)

How to Perform a Chi-Square Test

1

Set Table Size

Select the number of rows and columns that match your data categories.
2

Enter Observed Counts

Fill in each cell with the frequency count you observed in your data.
3

Review Expected Frequencies

The calculator shows what frequencies would be expected if the variables were independent.
4

Interpret the Result

If p < 0.05, reject H₀ — there is a statistically significant association between the variables.

Frequently Asked Questions

What is the chi-square test used for?

The chi-square test of independence determines whether two categorical variables are associated. For example, whether treatment type and recovery outcome are related, or whether gender and product preference are independent.

What is the null hypothesis?

H₀ states that the two categorical variables are independent — knowing one variable tells you nothing about the other. A significant result means the variables are associated.

What are expected frequencies?

Expected frequencies are what you would expect in each cell if H₀ were true (complete independence). They are calculated from the row totals, column totals, and grand total.

When is the chi-square test not appropriate?

The test requires that expected frequencies are ≥ 5 in at least 80% of cells, and no cell has an expected frequency < 1. If these assumptions are violated, consider Fisher's exact test instead.

What is Yates' correction?

Yates' continuity correction adjusts the chi-square formula for 2×2 tables to reduce overestimation of significance. It subtracts 0.5 from |O−E| before squaring, making the test more conservative.