Chi-Square Goodness-of-Fit Test

Determine if your data distribution aligns with your expectations using our Chi-Square calculator.

Enter Your Data

Counts observed in each category.

Frequencies expected under the null hypothesis.

e.g., 0.05 or 0.01

Probability of rejecting a true null hypothesis (Type I error).

Test Results

Chi-Square Statistic (χ²):

P-value:

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