STAT 100 Lecture 20: Chi Square Goodness of Fit
11 May 2017
School
Department
Course
Professor
Document Summary
A goodness-of- t test is a procedure used in inferential statistics to test claims regarding entire probability distributions. Goodness-of- t tests apply to experiments that consist of a series of n independent trials (e. g. , simple random samples of size n). The (qualitative) outcome of each trial can be classi ed into one of k 3 categories. We let p1, p2, , pk be the claimed probabilities for the k categories (one pi for each of the possible outcomes). If they differ signi cantly, then we have evidence against the claimed probabilities. Goodness-of- t tests use the x^2 (chi-square) distribution, which has the following properties: Its values are greater than or equal to zero. It is not symmetric; it is skewed right. Its shape depends on the degrees of freedom (just like a t-distribution). As the number of degrees of freedom increases, the shapes of the x^2 distributions become more and more symmetric.
