Calculator
Distribution Graph
Example Data Table
| Case | Chi-square | df | Alpha | Expected decision |
|---|---|---|---|---|
| Genetics test | 10.50 | 4 | 0.05 | Reject if p ≤ 0.05 |
| Survey fit | 5.30 | 3 | 0.05 | Compare p with alpha |
| Quality count | 14.20 | 6 | 0.01 | Strict significance check |
Formula Used
Right-tail p value: p = Q(k / 2, x / 2)
Left-tail probability: p = P(k / 2, x / 2)
Here, x is the chi-square statistic. The value k is degrees of freedom. P and Q are regularized incomplete gamma functions.
How to Use This Calculator
Enter the chi-square statistic from your test. Add the degrees of freedom. Choose the significance level. Select the tail type. Press the calculate button. The result appears above the form. Use the p value to decide whether your result is statistically significant.
Chi Square P Value Guide
What the Test Shows
A chi square p value helps measure evidence against a null hypothesis. It is common in goodness of fit tests. It is also used in independence tests. The method works with count data. It compares observed values with expected values. A large chi square statistic usually means stronger disagreement.
Why Degrees of Freedom Matter
Degrees of freedom shape the distribution. They depend on categories and restrictions. A test with more categories often has more degrees of freedom. The same statistic can produce different p values when degrees of freedom change. That is why both inputs are required.
Reading the P Value
The p value is the probability of seeing a result at least as extreme as the statistic, assuming the null hypothesis is true. A small value suggests the observed pattern is unlikely under that assumption. Many studies use 0.05 as alpha. Some technical studies use 0.01 for stricter control.
Right Tail and Left Tail
Most chi square tests use the right tail. This is because larger statistics show greater distance from expected counts. The calculator also provides left-tail probability. This helps when you need cumulative probability from zero to the statistic.
Practical Use
Use this tool for classroom work, research checks, quality control, survey analysis, and contingency table review. Always check assumptions before final reporting. Expected counts should usually be large enough. Categories should be independent. The calculator supports quick exporting, so results can be saved in reports.
FAQs
1. What is a chi square p value?
It is the probability linked with a chi square statistic and degrees of freedom. It helps judge whether observed count differences are statistically meaningful.
2. Which tail should I use?
Most chi square hypothesis tests use the right tail. Larger chi square values usually indicate stronger departure from expected counts.
3. What are degrees of freedom?
Degrees of freedom describe how many values can vary freely. They shape the chi square distribution used to calculate probability.
4. What does p ≤ 0.05 mean?
It means the result is statistically significant at the 5% level. You normally reject the null hypothesis.
5. Can this calculator test independence?
It calculates the p value after you already have the chi square statistic and degrees of freedom from an independence test.
6. Can I export my result?
Yes. Use the CSV button for spreadsheet data. Use the PDF button for a simple report.
7. Is a smaller p value always better?
No. A smaller p value shows stronger evidence against the null. It does not prove practical importance or study quality.
8. What input values are required?
You need a positive chi square statistic, degrees of freedom, alpha level, and tail type.