Chi-Square Tests
Chi-Square Goodness of Fit Calculator
Chi-Square Goodness of Fit Calculator compare observed and expected frequencies.
Chi-Square Tests
Chi-Square Goodness of Fit Calculator
Compare observed and expected frequencies.
Formula
Chi-square goodness of fit compares one observed frequency vector with a named expected frequency vector using sum((O - E)^2 / E).
About the Chi-Square Goodness of Fit Calculator
Compare observed and expected frequencies. Chi-square and exact-table calculators analyze categorical counts, expected frequencies, or standardized contingency-table association.
How the Chi-Square Goodness of Fit Calculator Works
Chi-square goodness of fit compares one observed frequency vector with a named expected frequency vector using sum((O - E)^2 / E).
The calculation runs in your browser. Submitted values are validated for the required numeric range, data shape, units, and method-specific restrictions before a result is shown.
Required Inputs
- Observed frequencies (required)
- Expected frequencies (required)
- Alpha (required)
Results Reported
The result panel shows the final answer together with the intermediate quantities needed to audit the calculation. Depending on this method, reported values include:
methodcategoriesobserved_totalexpected_totalobserved_frequenciesexpected_frequenciescontributionschi_square_statisticdfp_valueexpected_frequency_warningtotal_mismatchdecision
Chi-Square Goodness of Fit Calculator Example
Use the example data button to load a known sample, then calculate and review the statistic, p-value or estimate, and interpretation.
| Input | Example value |
|---|---|
| Observed frequencies | 18,22,20 |
| Expected frequencies | 20,20,20 |
| Alpha | 0.05 |
How to Use the Calculator
- Confirm that the calculator title and method match the quantity, test, conversion, or planning question you need to solve.
- Enter values with compatible units and the requested sample, group, matrix, count, date, or option format.
- Select Example Data to inspect a valid input layout, or enter your own values and select Calculate.
- Review the result table, formula, worked substitutions, warnings, and interpretation rather than using only the headline number.
- Use Copy Result or Download CSV when you need a reusable record of the displayed calculation.
Understanding the Result
Enter counts rather than percentages and review expected-frequency warnings; sparse 2x2 tables may require Fisher exact inference.
Keep the entered values, units, selected options, and any warning shown beside the result. For a hypothesis test, report the statistic, degrees of freedom where applicable, p-value, alpha level, effect size, and decision. For an estimate or conversion, report the formula convention and final unit.
Accuracy and Limitations
The calculator keeps full browser precision during calculation and rounds only for display. Accuracy still depends on correct inputs and on whether the displayed model represents the real problem. Educational calculators cannot replace required professional review, current official rules, field measurements, laboratory methods, or specialist statistical software where those are necessary.
Frequently Asked Questions
What does the Chi-Square Goodness of Fit Calculator calculate?
Compare observed and expected frequencies.
Which formula does the Chi-Square Goodness of Fit Calculator use?
Chi-square goodness of fit compares one observed frequency vector with a named expected frequency vector using sum((O - E)^2 / E).
What input does this calculator need?
The calculator form shows the required values and validates them before calculating.
Are the formulas visible?
Yes. Each calculator displays its method, assumptions, and interpretation unless disabled by the site administrator.