Calculate the chi-square test statistic and p-value from observed and expected values. This statistical test helps determine if there is a significant difference between expected and observed frequencies.
Chi-Square Statistic (χ²):-
Degrees of Freedom:-
P-Value:-
How to Use
Enter your observed values separated by commas (e.g., 10, 20, 30, 40)
Enter your expected values separated by commas (must have the same number of values)
Click "Calculate Chi-Square" to see the results
Review the chi-square statistic, degrees of freedom, and p-value
Understanding the Results
Chi-Square Statistic (χ²): Measures how much the observed values differ from the expected values
Degrees of Freedom: Number of categories minus one (n - 1)
P-Value: Probability of obtaining test results at least as extreme as the observed results, assuming the null hypothesis is true
Interpretation: A p-value less than 0.05 typically indicates a statistically significant difference between observed and expected values
About Chi-Square Tests
The chi-square test is a statistical hypothesis test used to determine whether there is a significant association between categorical variables or whether observed frequency distributions differ from expected distributions. It's commonly used in goodness-of-fit tests and tests of independence.