Chi-Square Goodness-of-Fit Test Calculator
Easily perform a Chi-Square Goodness-of-Fit test online to check if your observed data matches a hypothesized distribution. Enter your data and get instant results.
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Counts observed in each category.
Frequencies expected under the null hypothesis.
Probability of rejecting a true null hypothesis (Type I error).
Test Results
Chi-Square Statistic (χ²):
P-value:
Statistically significant at α = . Reject the null hypothesis.
Not statistically significant at α = . Fail to reject the null hypothesis.
Chi-Square Distribution Visualization
The shaded area under the curve represents the p-value.
Understanding Chi-Square Goodness-of-Fit Test
The Chi-Square Goodness-of-Fit test is used to check if observed data matches what we expect from a certain distribution. It helps us determine if differences between observed and expected counts are just random chance or if they are statistically significant.
For example, if we expect a fair die to roll each number (1-6) equally, we can use this test to see if actual rolls of the die fit this expectation. We compare what we observed to what we expected under the idea of a 'good fit'.
A low p-value (usually below 0.05) suggests that the observed data does not fit the expected distribution well, leading us to reject the idea of a 'good fit'. Conversely, a higher p-value suggests the data is consistent with the expected distribution.
Further reading: Wikipedia | Khan Academy