Week 15 Lecture 20 May 3rd, 2017 Chi Square Goodness of Fit GoodnessofFit Test A goodnessoft test is a procedure used in inferential statistics to test claims regarding entire probability distributions. Goodnessoft 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 classied 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). Compare observed frequencies and expected frequencies. If they differ signicantly, then we have evidence against the claimed probabilities. Goodnessoft tests use the X^2 (chisquare) 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 tdistribution). As the number of degrees of freedom increases, the shapes of the X^2 distributions become more and more symmetric.