Chi Square Goodness Of Fit Calculator

Work out chi square goodness of fit instantly with clear inputs, formula shown and shareable results.

About Chi Square Goodness Of Fit Calculator

The goodness-of-fit test sums (observed − expected)²/expected across categories. Large values indicate the data does not match the hypothesised distribution, judged against chi-square on k − 1 degrees of freedom.

Formula

Chi-square statistic

χ² = Σ (O − E)² / E, df = categories − 1

Worked example

With the default values below, Chi Square Goodness Of Fit Calculator returns Chi-square statistic of 37.81801802. Change any input above and every figure here is recalculated in your browser.

Inputs used

Observed frequencies: 30, 14, 34, 45, 57, 20
Expected frequencies: 33.3, 33.3, 33.3, 33.3, 33.3, 33.3

Results

Chi-square statistic: 37.81801802
p value: 0.00000041
Degrees of freedom: 5
Critical value at 5%: 11.070498

Step by step

1Values used
2Chi-square statistic
3Chi-square statistic= 37.81801802
4p value= 0.00000041
5Degrees of freedom= 5
6Critical value at 5%= 11.070498

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax or fees or charges into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For the sample dice counts?

χ² ≈ 30.4 on 5 df, far beyond the 5% critical value of 11.07, so the die is almost certainly not fair.

What if an expected count is small?

The approximation degrades. A common rule requires every expected count to be at least 5.