The Chi-Squared Distribution is a special case of the Gamma Distribution and is widely used in statistical hypothesis testing, particularly in tests of independence and goodness of fit. It is characterized by its degrees of freedom (DF), which are determined by the number of categories or groups in the data being analyzed.

In essence, the Chi-Squared Distribution describes the distribution of the sum of the squares of k independent standard normal random variables. This distribution is always positive and is skewed to the right, especially for lower degrees of freedom. As the degrees of freedom increase, the distribution approaches a normal distribution.

The Chi-Squared Distribution is crucial for determining the p-value in hypothesis testing. For instance, when conducting a Chi-Squared test, if the calculated statistic exceeds a critical value from the Chi-Squared Distribution table, it indicates that the observed data significantly deviates from the expected data, leading to the rejection of the null hypothesis ¹²³.