Calculator
Enter values as comma, space, or line separated numbers. Use equal expected values when each category should have the same expected count.
Example Data Table
This sample checks whether five categories match equal expected counts.
| Category | Observed | Expected | Difference |
|---|---|---|---|
| Category 1 | 18 | 20 | -2 |
| Category 2 | 22 | 20 | 2 |
| Category 3 | 20 | 20 | 0 |
| Category 4 | 25 | 20 | 5 |
| Category 5 | 15 | 20 | -5 |
Formula Used
The calculator uses the standard chi square statistic. It adds each category contribution.
X² = Σ ((O - E)² / E)
O means observed value.
E means expected value.
The p-value comes from the upper tail of the chi square distribution.
Degrees of freedom are normally k - 1 - estimated parameters.
How to Use This Calculator
- Enter observed counts in the first box.
- Select custom or equal expected values.
- Enter expected counts when custom mode is selected.
- Add estimated parameters when your model used fitted values.
- Set the alpha level, such as 0.05.
- Choose the decimal display length.
- Press calculate and review the result above the form.
- Use CSV or PDF buttons to save the report.
Chi Square Calculator Guide
What this tool checks
A chi square calculator compares actual counts with expected counts. It helps test whether differences are small or meaningful. The result is useful for surveys, genetics, quality control, marketing, education, and many other grouped data tasks. Each group must contain counts, not percentages. The expected values should come from a clear rule.
Why decimal control matters
Many simple tools round results too early. That can hide small differences in p-values. This calculator lets you display many decimal places. Long decimal output is helpful when reports require careful detail. It is also useful when comparing results across software. The display can be set from short output to extended output.
Observed and expected values
Observed values are the counts you collected. Expected values are the counts predicted by your null hypothesis. For example, a fair process may expect equal counts in every category. A known population share may create unequal expected counts. The calculator supports both cases. You can type custom expected values. You can also let the tool spread the observed total equally.
Degrees of freedom
Degrees of freedom affect the p-value. For a basic goodness of fit test, use categories minus one. If parameters were estimated from the same data, subtract them too. The calculator includes an estimated parameter field. You may also override degrees of freedom directly. This is useful for special study designs.
Reading the p-value
The p-value shows the upper tail probability. A small p-value suggests the observed pattern is unlikely under the null model. If the p-value is less than or equal to alpha, reject the null hypothesis. If it is greater than alpha, do not reject it. This does not prove the null is true. It only means the sample did not provide enough evidence.
Using the contribution table
The contribution table shows how each category affects the statistic. A large component means that category caused more disagreement. This helps you find the biggest source of difference. The share column turns each component into a percent of the total statistic. That makes the result easier to explain.
Best practices
Use counts from independent observations. Avoid very tiny expected counts when possible. Review data entry carefully before interpreting results. Keep the null hypothesis clear. Export the CSV file for spreadsheets. Export the PDF file for a quick report. The tool gives statistical guidance. Final decisions should also use context and study design.
FAQs
1. What is a chi square calculator?
It compares observed counts with expected counts. It returns the chi square statistic, p-value, degrees of freedom, and decision guidance.
2. What values should I enter?
Enter category counts. Use observed counts from your data. Use expected counts from your null hypothesis or selected equal expected mode.
3. Can I use percentages?
No. Use counts instead of percentages. Chi square testing works with frequencies from real observations.
4. What does the p-value mean?
It shows the probability of getting a result this extreme, assuming the null hypothesis is correct.
5. What is alpha?
Alpha is your chosen significance level. Common values are 0.05, 0.01, and 0.10.
6. What means reject the null hypothesis?
It means your sample gives enough evidence that observed counts differ from expected counts at the chosen alpha level.
7. What means fail to reject?
It means the result is not strong enough to reject the null hypothesis. It does not prove the null hypothesis.
8. How are degrees of freedom calculated?
For a simple goodness of fit test, degrees of freedom equal categories minus one, minus estimated parameters.
9. When should I use equal expected mode?
Use it when every category should have the same expected count under your null hypothesis.
10. What is Yates correction?
Yates correction adjusts small two-category calculations. It reduces the difference before calculating each component.
11. What is the contribution table?
It shows each category contribution to the total chi square statistic. Larger values show stronger disagreement.
12. Can I download my result?
Yes. After calculation, use the CSV button for spreadsheet data or the PDF button for a report.
13. Are infinite decimals truly possible?
Computer output is limited by numeric precision. This tool offers extended decimal display for detailed reporting.
14. What if expected values are very small?
Very small expected counts can weaken the test. Consider combining categories or using another suitable method.