Chi-squared Distribution.

Researchers in mathematics, science, social science, and a variety of other fields use the chi-squared distribution for statistical hypothesis tests, such as the chi-square test of independence, which determines whether or not two categorical variables are associated, and the chi-square goodness-of-fit test, which helps determine whether a chosen population model is a good fit for an observed set of data. It is also used in applications such as signal processing. The chi-squared distribution is a family of continuous probability distribution functions (pdfs), created by squaring and adding together one or more independent standard normal distributions—a particular variety of bell curve. The function’s shape (see Figure 1) is determined by a parameter called its degrees of freedom (df). For large df values (approximately fifty and above), the chi-squared distribution itself is almost bell-shaped.