AP Statistics Chapter 11 Outline 11.1 Chi-Square Goodness-Of-Fit Tests Chi-Square Statistic The chi-square statistic is a measure of how far the observed counts are from the expected counts: Where the sum is over all possible values of the categorical variable The Chi-Square Distribution The chi-square distributions are a family of distributions that take only positive values and are skewed to the right. A particular chi-square distribution is specified by giving its degrees of freedom. The chi-square goodness-of-fit test uses the chi-square distribution with degrees of freedom = the number of categories - 1. The Chi-Square Goodness-of-Fit Test