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Chapter 13 - Chi-square tests. After mastering the material in this chapter, you will be able to: Test hypotheses about multinomial probabilities by using a chi-square goodness-of-fit test, perform a goodness-of-fit test for normality, decide whether two qualitative variables are independent by using a chi-square test for independence. | Chi-Square Tests Chapter 13 Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Chi-Square Tests 13.1 Chi-Square Goodness-of-Fit Tests 13.2 A Chi-Square Test for Independence 13- 13.1 Chi-Square Goodness-of-Fit Tests Collect count data to study how counts are distributed among cells Often use categorical data for statistical inference May use a multinomial experiment Similar to a binomial experiment only more than two outcomes are possible LO13-1: Test hypotheses about multinomial probabilities by using a chi-square goodness-of-fit test. 13- The Multinomial Experiment Carry out n identical trials with k possible outcomes of each trial Probabilities are denoted p1, p2, , pk where p1 + p2 + + pk = 1 The trials are independent The results are observed frequencies of the number of trials that result in each of k possible outcomes, denoted f1, f2, , fk LO13-1 13- Chi-Square Goodness of Fit Tests Consider the outcome of | Chi-Square Tests Chapter 13 Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Chi-Square Tests 13.1 Chi-Square Goodness-of-Fit Tests 13.2 A Chi-Square Test for Independence 13- 13.1 Chi-Square Goodness-of-Fit Tests Collect count data to study how counts are distributed among cells Often use categorical data for statistical inference May use a multinomial experiment Similar to a binomial experiment only more than two outcomes are possible LO13-1: Test hypotheses about multinomial probabilities by using a chi-square goodness-of-fit test. 13- The Multinomial Experiment Carry out n identical trials with k possible outcomes of each trial Probabilities are denoted p1, p2, , pk where p1 + p2 + + pk = 1 The trials are independent The results are observed frequencies of the number of trials that result in each of k possible outcomes, denoted f1, f2, , fk LO13-1 13- Chi-Square Goodness of Fit Tests Consider the outcome of a multinomial experiment where each of n randomly selected items is classified into one of k groups Let 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) LO13-1 13- A Goodness of Fit Test for Multinomial Probabilities H0: multinomial probabilities are p1, p2, , pk Ha: at least one of the probabilities differs from p1, p2, , pk Test statistic: Reject H0 if 2 > 2 or p-value 13- Normal Distribution Have seen many statistical methods based on the assumption of a normal distribution Can check the validity of this assumption using frequency distributions, stem-and-leaf displays, histograms, and normal plots Another approach is to use a chi-square goodness of fit test LO13-2: Perform a goodness of fit test for normality. 13- A Goodness of Fit Test for a Normal .
