This page discusses the χ2 test applied in three scenarios: 1) Goodness-of-Fit, assessing if a sample fits a known distribution; 2) Independence, evaluating the relationship between two qualitative va...This page discusses the χ2 test applied in three scenarios: 1) Goodness-of-Fit, assessing if a sample fits a known distribution; 2) Independence, evaluating the relationship between two qualitative variables; and 3) Homogeneity, determining if two populations share the same distribution. Each scenario has a null hypothesis positing a fit or independence, and an alternative hypothesis suggesting otherwise.
In this section, we will discuss independence, one of the fundamental concepts in probability theory. Independence is frequently invoked as a modeling assumption, and moreover, (classical) probability...In this section, we will discuss independence, one of the fundamental concepts in probability theory. Independence is frequently invoked as a modeling assumption, and moreover, (classical) probability itself is based on the idea of independent replications of the experiment. As usual, if you are a new student of probability, you may want to skip the technical details.
