Download presentation

Presentation is loading. Please wait.

Published byZaire Beale Modified over 2 years ago

1
McGraw-Hill/Irwin Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved. Chi-Square Tests Chapter 12

2
12-2 Chapter Outline 12.1Chi-Square Goodness of Fit Tests 12.2A Chi-Square Test for Independence

3
12-3 12.1 Chi-Square Goodness of Fit Tests 1.Carry out n identical trials with k possible outcomes of each trial 2.Probabilities are denoted p 1, p 2, …, p k where p 1 + p 2 + … + p k = 1 3.The trials are independent 4.The results are observed frequencies, f 1, f 2, …, f k

4
12-4 Chi-Square Goodness of Fit Tests Continued Consider the outcome of a multinomial experiment where each of n randomly selected items is classified into one of k groups Let f i = number of items classified into group i (i th observed frequency) E i = np i = expected number in i th group if p i is probability of being in group i (i th expected frequency)

5
12-5 A Goodness of Fit Test for Multinomial Probabilities H 0 : multinomial probabilities are p 1, p 2, …, p k H a : at least one of the probabilities differs from p 1, p 2, …, p k Test statistic: Reject H 0 if 2 > 2 or p-value < 2 and the p-value are based on p-1 degrees of freedom

6
12-6 Example 12.1: The Microwave Oven Preference Case Tables 12.1 and 12.2

7
12-7 Example 12.1: The Microwave Oven Preference Case Continued

8
12-8 Example 12.1: The Microwave Oven Preference Case #3 Figure 12.1

9
12-9 A Goodness of Fit Test for Multinomial Probabilities f i =the number of items classified into group i E i =np i H 0 :The values of the multinomial probabilities are p 1, p 2,…p k H 1 :At least one of the multinomial probabilities is not equal to the value stated in H 0

10
12-10 A Goodness of Fit Test for a 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

11
12-11 A Goodness of Fit Test for a Normal Distribution Continued 1.H 0 : the population has a normal distribution 2.Select random sample 3.Define k intervals for the test 4.Record observed frequencies 5.Calculate the expected frequencies 6.Calculate the chi-square statistics 7.Make a decision

12
12-12 12.2 A Chi-Square Test for Independence Each of n randomly selected items is classified on two dimensions into a contingency table with r rows an c columns and let f ij = observed cell frequency for i th row and j th column r i = i th row total c j = j th column total Expected cell frequency for i th row and j th column under independence

13
12-13 A Chi-Square Test for Independence Continued H 0 : the two classifications are statistically independent H a : the two classifications are statistically dependent Test statistic Reject H 0 if 2 > 2 or if p-value < 2 and the p-value are based on (r-1)(c-1) degrees of freedom

14
12-14 Example 12.3 The Client Satisfaction Case Table 12.4

15
12-15 Example 12.3 The Client Satisfaction Case #2 Figure 12.2 (a)

16
12-16 Example 12.3 The Client Satisfaction Case #3 H 0 : fund time and level of client satisfaction are independent H 1 : fund time and level of client satisfaction are dependent Calculate frequencies under independence assumption Calculate test statistic of 46.44 Reject H 0

Similar presentations

OK

Chapter 16 – Categorical Data Analysis Math 22 Introductory Statistics.

Chapter 16 – Categorical Data Analysis Math 22 Introductory Statistics.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on polynomials in maths draw Ppt on operating system free download Download ppt on power steering Ppt on conservation agriculture in india Ppt on bluetooth technology Ppt on natural and artificial satellites and their uses Ppt on condition monitoring of induction motor File type ppt on cybercrime articles Ppt on two point perspective buildings Ppt on automatic car parking system