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Chi-Square Test Calculator
Determine if there is a statistically significant association between two categorical variables. Build your contingency table below, enter your frequencies, and instantly calculate your $\chi^2$ statistic and p-value.
How to use this calculator
- Size your table: Use the + Row and + Column buttons to match the number of categories in your dataset. (For example, if you are comparing “Gender” (Male/Female) against “Voting Preference” (Candidate A/Candidate B/Undecided), you would need a 2×3 grid).
- Enter your data: Input the raw counts (frequencies) into the grid. These must be whole numbers — Chi-Square tests do not work with percentages or decimals.
- Set your parameters: Choose your significance level ($\alpha$). If you aren’t sure, 0.05 is the standard default for most scientific research.
Chi-Square Calculator
Test for independence in a contingency table.
Chi-Square (χ²)
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Degrees of Freedom
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P-Value
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*Technical note: P-values are calculated using an exact integer-degree series expansion of the Chi-Square probability density function. Expected values below 5 may compromise the reliability of the standard Chi-Square approximation.
Understanding Your Results
A Chi-Square Test of Independence compares the frequencies you actually observed against the frequencies you would expect to see if the two variables were completely unrelated.
- Chi-Square Statistic ($\chi^2$): A measure of how far your observed data deviates from the expected data. A value of 0 means the variables are completely independent. A larger value indicates a stronger potential association.
- Degrees of Freedom ($df$): Calculated based on the size of your grid: $(\text{Rows} – 1) \times (\text{Columns} – 1)$. It determines the shape of the Chi-Square distribution used to find your p-value.
- P-Value: The probability of getting a $\chi^2$ statistic this large (or larger) if the two variables were truly independent (the null hypothesis).
- Conclusion: If the p-value is less than your chosen significance level, you reject the null hypothesis and conclude that there is a statistically significant association between your variables.