chi squared distribution

The chi-squared distribution is a fundamental concept in statistics, particularly in hypothesis testing and data analysis. It arises when summing the squares of independent standard normal random variables, making it essential for evaluating relationships between categorical variables. This distribution is widely used in the chi-squared test, which assesses how well observed data fit expected outcomes. The chi-squared statistic, derived from this distribution, helps determine the likelihood of observing a particular result under a null hypothesis. Its applications extend to goodness-of-fit tests and tests of independence, making it a crucial tool in various fields, including data science and machine learning.