Chi-square Goodness-of-fit Calculator
Compare observed category counts with entered expected weights and calculate chi-square contributions, residual degrees of freedom and an approximate upper-tail p-value.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Scale expected weights to the observed total, sum squared residuals over expected counts and use a chi-square upper tail with entered fitted-parameter adjustment.
χ²=Σ(O−E)²/E; df=categories−1−fitted parameters
Worked example
Observed 20, 30 and 50 against equal expected weights give expected counts of 100/3 and chi-square statistic 14. With no fitted parameters, df is 2 and upper-tail p is exp(−7).
Assumptions and input details
2–50 mutually exclusive categories with whole observed counts and strictly positive expected weights. Weights are normalized, so they can be ratios, probabilities or expected relative counts. You must correctly count parameters estimated from these data. Expected cells below five are flagged; dependence, sparse bins and post-selected categories may invalidate the chi-square approximation.
References: NIST: chi-square goodness-of-fit assumptions and degrees of freedom
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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