What test is commonly used to assess how well theoretical distributions align with empirical distributions?

The chi-squared test is commonly utilized to assess the goodness of fit between theoretical distributions and empirical data. This statistical test evaluates whether the observed frequencies of occurrences in categories differ significantly from the expected frequencies based on a specific theoretical distribution.

When conducting a chi-squared test, one compares the occurrences of different categories in the collected data to what would be expected if the theoretical distribution were accurate. The test produces a chi-squared statistic that can be compared to a critical value from the chi-squared distribution, allowing researchers to determine if any differences are statistically significant.

This approach is essential for validating models and theories by determining how closely the empirical data aligns with what is theoretically expected, making it a staple in statistical analysis.