Chi Square Calculator Form
Example Data Table
| Category |
Observed Count |
Expected Count |
Use Case |
| Campaign A |
22 |
25 |
Marketing response check |
| Campaign B |
18 |
25 |
Marketing response check |
| Campaign C |
31 |
25 |
Marketing response check |
| Campaign D |
29 |
25 |
Marketing response check |
Formula Used
The calculator uses the standard chi square statistic:
χ² = Σ ((O - E)² / E)
Here, O means observed count, and E means expected count.
For goodness of fit, degrees of freedom are:
df = categories - 1 - estimated parameters
For a contingency table, degrees of freedom are:
df = (rows - 1) × (columns - 1)
The p value is found from the upper tail of the chi square distribution.
How to Use This Calculator
- Select the test type.
- Enter alpha, such as 0.05.
- For goodness of fit, enter observed counts and expected counts.
- Use probabilities when your expected pattern is based on shares.
- For independence testing, enter a row by column matrix.
- Press the calculate button.
- Review the chi square statistic, p value, and decision.
- Download the CSV or PDF report if needed.
Chi Square Testing For Clear Decisions
A chi square test helps you compare real counts with a stated pattern. It also helps you check whether two category variables appear related. The method is useful because it works with counts, not averages. You can test survey answers, product defects, student choices, traffic groups, or simple table data.
Why This Calculator Helps
This calculator supports goodness of fit and contingency table testing. Goodness of fit compares one list of observed counts against expected counts, expected probabilities, or equal shares. A contingency table checks whether row groups and column groups are independent. The tool also shows degrees of freedom, expected values, p value, critical value, and a decision at your chosen alpha level.
Reading The Result
The chi square statistic rises when observed counts move farther from expected counts. A larger statistic usually gives a smaller p value. When the p value is less than alpha, the result is statistically significant. That means the difference is unlikely under the null model. It does not prove a cause. It only shows that the count pattern is not well explained by the stated assumption.
Good Data Matters
Use raw category counts. Do not enter percentages as observed values unless they are actual counts. Expected counts should normally be positive. Many guides prefer expected cell counts of at least five for stable results. If several expected counts are very small, combine sensible categories or use a more exact method.
Practical Use Cases
A marketer can test whether orders are evenly spread across four campaigns. A teacher can compare grade bands with an expected distribution. A store manager can test whether defect types differ by supplier. A researcher can test whether preference varies by age group. These cases all need count data and a clear question.
Exporting Your Work
The CSV export is useful for spreadsheets and audit notes. The PDF export is helpful for quick reports. Always keep the original counts beside the test output. This makes the result easier to review, repeat, and explain later.
Use the result as evidence, not final truth. Check sample design, category meaning, and possible bias. A clean question makes every chi square result more useful for practical decisions today.
FAQs
What is a chi square test?
It is a statistical test for count data. It compares observed counts with expected counts or checks whether two category variables are related.
Can I enter percentages?
Use counts for observed data. Percentages are only suitable as expected probabilities when the goodness of fit probability option is selected.
What does the p value mean?
The p value shows how unusual the observed pattern is under the null hypothesis. Smaller values give stronger evidence against that assumption.
What alpha value should I use?
Many users choose 0.05. You can use 0.01 for stricter testing or 0.10 for more relaxed screening.
What is goodness of fit?
Goodness of fit tests one categorical variable. It checks whether observed counts match a known, equal, or expected distribution.
What is a test of independence?
It checks whether two categorical variables are associated. Data is entered as a contingency table with rows and columns.
When should I use Yates correction?
Yates correction is sometimes used for two by two tables. It reduces the statistic slightly and can make small table results more conservative.
What if expected counts are small?
Small expected counts can weaken the approximation. Combine sensible categories or consider an exact method when many expected cells are below five.