Goodness of Fit Error Calculator

Compare observed and expected counts with precise diagnostics. Track residual patterns, significance, and normalized errors. Create clean reports, charts, and exports for better decisions.

Calculator Input

Use multiple categories and optional model parameters for a stronger goodness-of-fit review.

Subtracts fitted parameters from degrees of freedom.
Common choices are 0.05 and 0.01.
Enter category names plus observed and expected values. Blank rows are ignored.

Example Data Table

This sample shows how category counts can be arranged before calculation.

Category Observed Expected Residual Chi Contribution
Category A 45 40 5 0.6250
Category B 38 40 -2 0.1000
Category C 52 40 12 3.6000
Category D 41 40 1 0.0250
Category E 24 40 -16 6.4000

Formula Used

Pearson Chi-Square:
χ² = Σ ((Oi − Ei)² / Ei)
Residual:
Residual = Oi − Ei
Standardized Residual:
Std Residual = (Oi − Ei) / √Ei
G-Statistic:
G = 2 × Σ [Oi × ln(Oi / Ei)] for Oi > 0
Error Metrics:
SSE = Σ (Oi − Ei)²
MSE = SSE / k
RMSE = √MSE
MAE = Σ |Oi − Ei| / k
MAPE = [Σ (|Oi − Ei| / Ei) × 100] / k
Degrees of Freedom and P-Value:
df = k − 1 − m, where k is the number of categories and m is the number of estimated parameters.
The p-value is the right-tail chi-square probability based on χ² and df.

How to Use This Calculator

1. Enter a label for each category you want to compare.
2. Fill in observed values from your dataset.
3. Enter expected values from your hypothesis, model, or reference distribution.
4. Add the number of estimated parameters if your expected distribution was fitted from data.
5. Choose a significance level such as 0.05.
6. Submit the form to view chi-square, p-value, error metrics, category residuals, and the comparison chart.
7. Export the report as CSV or PDF for documentation, review, or sharing.

FAQs

1. What does this calculator test?

It compares observed category values with expected values. It reports goodness-of-fit statistics, residuals, and practical error measures so you can judge whether a distribution matches a target pattern.

2. When should I use expected frequencies?

Use expected values when you have a theoretical distribution, historical benchmark, or planned allocation. The calculator then measures how far the observed counts depart from that reference.

3. What does the p-value mean here?

The p-value estimates how unusual your observed differences are if the expected distribution were true. A smaller p-value suggests the mismatch is less likely to be due to random variation alone.

4. Why are residuals important?

Residuals show which categories are above or below expectation. Large standardized residuals help identify the specific categories driving the overall chi-square result.

5. What happens if expected counts are small?

Very small expected counts can weaken the chi-square approximation. The calculator flags this condition so you can combine categories or consider an exact method when needed.

6. Why include RMSE, MAE, and MAPE?

These measures describe mismatch size in practical terms. They complement the hypothesis test by showing average error magnitude, squared-error sensitivity, and percent-based deviation.

7. What are estimated parameters?

Estimated parameters are values fitted from the same data, such as a sample-based distribution parameter. They reduce degrees of freedom because the model already used data information.

8. Can I export the analysis?

Yes. When results appear, use the CSV button for spreadsheet-friendly data and the PDF button for a formatted report snapshot.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.