Chapter 13 Chi-Square Tests

Chi-Square TestsChapter 13Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/IrwinChi-Square Tests13.1 Chi-Square Goodness-of-Fit Tests13.2 A Chi-Square Test for Independence13-*13.1 Chi-Square Goodness-of-Fit TestsCollect count data to study how counts are distributed among cellsOften use categorical data for statistical inferenceMay use a multinomial experimentSimilar to a binomial experiment only more than two outcomes are possibleLO13-1: Test hypotheses about multinomial probabilities by using a chi-square goodness-of-fit test.13-*The Multinomial ExperimentCarry out n identical trials with k possible outcomes of each trialProbabilities are denoted p1, p2, , pk where p1 + p2 + + pk = 1The trials are independentThe results are observed frequencies of the number of trials that result in each of k possible outcomes, denoted f1, f2, , fkLO13-113-*Chi-Square Goodness of Fit TestsConsider the outcome of a multinomial experiment where each of n randomly selected items is classified into one of k groupsLet fi = number of items classified into group i (ith observed frequency)Ei = npi = expected number in ith group if pi is probability of being in group i (ith expected frequency)LO13-113-*A Goodness of Fit Test for Multinomial ProbabilitiesH0: multinomial probabilities are p1, p2, , pkHa: at least one of the probabilities differs from p1, p2, , pkTest statistic:Reject H0 if2 > 2 or p-value 2 or if p-value < 2 and the p-value are based on (r-1)(c-1) degrees of freedomLO13-313-*