chi squared distribution

The chi-squared distribution is a fundamental concept in statistics, particularly in hypothesis testing and the analysis of categorical data. It arises when summing the squares of independent standard normal random variables, making it essential for evaluating the goodness of fit between observed and expected frequencies. This distribution is characterized by its degrees of freedom, which correspond to the number of independent variables involved. The chi-squared test is widely used to assess relationships between categorical variables, helping researchers determine if their data deviates significantly from a theoretical model. Its applications span various fields, including social sciences, biology, and machine learning.