Calculator
Category: Maths
Example Data Table
| Case | Observed | Expected | Use |
|---|---|---|---|
| Red | 18 | 20 | Goodness of fit |
| Blue | 22 | 20 | Goodness of fit |
| Green | 20 | 20 | Goodness of fit |
| Yellow | 25 | 20 | Goodness of fit |
| Purple | 15 | 20 | Goodness of fit |
Formula Used
Goodness of fit: χ² = Σ((O - E)² / E)
Expected count for independence: E = (row total × column total) / grand total
Degrees of freedom for goodness: df = categories - 1 - estimated parameters
Degrees of freedom for independence: df = (rows - 1) × (columns - 1)
Variance test: χ² = (n - 1)s² / σ²
How To Use This Calculator
- Select the chi square test type.
- Enter the significance level, usually 0.05.
- Enter observed values, expected values, or a table.
- Add labels to make the output easier to read.
- Press Calculate to view the result above the form.
- Download the CSV or PDF report when needed.
Understanding Chi Square Testing
A chi square test helps compare counted data. It works with categories. The method checks whether observed counts are far from expected counts. It does not measure averages. It studies frequencies. That makes it useful for surveys, genetics, market research, quality checks, and classroom problems.
Why This Calculator Helps
Manual chi square work can become slow. Each cell needs an expected value. Each difference is squared. Then every squared difference is divided by the expected value. This calculator completes those repeated steps. It also gives degrees of freedom, a p value, a critical value, and a decision.
Goodness Of Fit Uses
A goodness of fit test checks one list of categories. You may test whether dice rolls are fair. You may compare customer choices with a planned share. You can enter custom expected values. You can also use equal expected values when every category should have the same chance.
Independence Test Uses
An independence test works with a table. Rows often show groups. Columns often show outcomes. The test asks whether the row category is related to the column category. The calculator builds expected counts from row totals, column totals, and the grand total. Cramer’s V adds a helpful effect size.
Reading The Result
The chi square statistic gets larger when observed counts move away from expected counts. A small p value gives stronger evidence against the null idea. Compare the p value with your selected significance level. If the p value is lower, the result is marked significant. Still, practical meaning matters too.
Good Data Habits
Use counts, not percentages. Keep categories clear. Avoid negative values. Expected counts should usually be large enough for a reliable approximation. Many courses use five as a simple guide. When data are sparse, combine sensible categories or use another method. Always describe the source of your data.
Exporting Results
Exports help save your work. The CSV file is useful for spreadsheets. The PDF summary is useful for sharing. Both include the main test results and cell contributions. Review your inputs before exporting, especially when a report will be used for study, business, or publication.
Clear notes make later checking easier for teams. They also reduce mistakes during repeated analysis.
FAQs
What is a chi square test?
It is a statistical test for counted category data. It compares observed counts with expected counts and shows whether the difference is likely due to random variation.
Can I use percentages?
Use counts instead of percentages. If you only have percentages, convert them back to counts using the original sample size before calculating.
What is a p value?
The p value shows how unusual the test statistic is under the null hypothesis. A smaller p value gives stronger evidence against that null idea.
What does degrees of freedom mean?
Degrees of freedom describe how many values can vary after totals and restrictions are set. The formula depends on the selected chi square test.
When should I use goodness of fit?
Use it when you have one categorical variable. It checks whether observed category counts match equal or custom expected counts.
When should I use independence testing?
Use it when you have a contingency table. It checks whether two categorical variables appear related or independent.
What is Cramer’s V?
Cramer’s V is an effect size for contingency tables. It helps judge the strength of association after the chi square test is calculated.
Why are expected counts important?
Expected counts form the comparison baseline. Very small expected counts can make the chi square approximation less reliable and may require another method.