Tests of Homogeneity and Independence

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1 Tests of Homogeneity and Independence Lecture 52 Sections 14.5 Robb T. Koether Hampden-Sydney College Mon, Apr 26, 2010 Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

2 Outline 1 Homework Review 2 Degrees of Freedom 3 The Traffic Fatality Example 4 Practice 5 Assignment Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

3 Outline 1 Homework Review 2 Degrees of Freedom 3 The Traffic Fatality Example 4 Practice 5 Assignment Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

4 Homework Review Exercise 14.20, page 949. A certain job in a car assembly plant involves a great deal of stress. A study was conducted to assess whether there is any difference in how men versus women adjust to the stress. A random sample of 25 men and 25 women employed in this job were surveyed. The results are given as follows: Well Adjusted Not Well Adjusted Men 18 7 Women At the 1% significance level, test whether the adjustment status is the same for men versus women. Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

5 Homework Review Solution (1) H 0 : The populations are homogeneous. H 1 : The populations are not homogeneous. Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

6 Homework Review Solution (1) H 0 : The populations are homogeneous. H 1 : The populations are not homogeneous. (2) α = Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

7 Homework Review Solution (1) H 0 : The populations are homogeneous. H 1 : The populations are not homogeneous. (2) α = (3) χ 2 = all cells (O E) 2. E Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

8 Homework Review Solution (4) Enter the matrix [ ] as matrix A in the TI-83. Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

9 Homework Review Solution (4) Enter the matrix [ Use STAT > TEST > χ 2 -Test. ] as matrix A in the TI-83. Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

10 Homework Review Solution (4) Enter the matrix [ Use STAT > TEST > χ 2 -Test. The calculator reports that χ 2 = ] as matrix A in the TI-83. Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

11 Homework Review Solution (4) Enter the matrix [ Use STAT > TEST > χ 2 -Test. The calculator reports that χ 2 = ] as matrix A in the TI-83. (5) The calculator also reports that p-value = Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

12 Homework Review Solution (4) Enter the matrix [ Use STAT > TEST > χ 2 -Test. The calculator reports that χ 2 = ] as matrix A in the TI-83. (5) The calculator also reports that p-value = (6) Accept H 0. Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

13 Homework Review Solution (4) Enter the matrix [ Use STAT > TEST > χ 2 -Test. The calculator reports that χ 2 = ] as matrix A in the TI-83. (5) The calculator also reports that p-value = (6) Accept H 0. (7) The adjustment statuses of men and women are the same. Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

14 Outline 1 Homework Review 2 Degrees of Freedom 3 The Traffic Fatality Example 4 Practice 5 Assignment Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

15 Degrees of Freedom Consider the mortality data Row Tot Heart disease Cancer Stroke Respiratory Col Total What if we had only the row and column totals? How many values could we fill in arbitrarily? Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

16 Degrees of Freedom Row Tot Heart disease 2080 Cancer 2312 Stroke 464 Respiratory 644 Col Total Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

17 Degrees of Freedom Row Tot Heart disease Cancer 2312 Stroke 464 Respiratory 644 Col Total Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

18 Degrees of Freedom Row Tot Heart disease Cancer 2312 Stroke 464 Respiratory 644 Col Total Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

19 Degrees of Freedom Row Tot Heart disease Cancer Stroke 464 Respiratory 644 Col Total Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

20 Degrees of Freedom Row Tot Heart disease Cancer Stroke 464 Respiratory 644 Col Total Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

21 Degrees of Freedom Row Tot Heart disease Cancer Stroke Respiratory 644 Col Total Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

22 Degrees of Freedom Row Tot Heart disease Cancer Stroke Respiratory 644 Col Total Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

23 Degrees of Freedom Row Tot Heart disease Cancer Stroke Respiratory Col Total Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

24 Degrees of Freedom Row Tot Heart disease Cancer Stroke Respiratory Col Total Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

25 Outline 1 Homework Review 2 Degrees of Freedom 3 The Traffic Fatality Example 4 Practice 5 Assignment Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

26 The Traffic Fatality Example Example (The Traffic Fatality Example) Are the variables time of day and alcohol-impaired status of the driver independent in fatal traffic accidents? Does the value of one variable appear to influence the proportions of the other variable? 12-3am pm Impaired Not Impaired Test the hypotheses at the 5% level. Show the expected counts. Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

27 Outline 1 Homework Review 2 Degrees of Freedom 3 The Traffic Fatality Example 4 Practice 5 Assignment Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

28 Practice What type of problem is it? p. 967: 37. Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

29 Practice What type of problem is it? p. 967: 37. p. 967: 38. Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

30 Practice What type of problem is it? p. 967: 37. p. 967: 38. p. 969: 42. Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

31 Practice What type of problem is it? p. 967: 37. p. 967: 38. p. 969: 42. p. 971: 45. Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

32 Outline 1 Homework Review 2 Degrees of Freedom 3 The Traffic Fatality Example 4 Practice 5 Assignment Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

33 Assignment Homework Read Section 14.5, pages Let s Do It! 14.6, (14.6 is an example of Simpson s paradox.) Exercises 23-27, 31, 34, page 959. (Ex. 31 and 34 are examples of Simpson s paradox.) Chapter Review 35-40, 42, 47, page 966. Robb T. Koether (Hampden-Sydney College) Tests of Homogeneity and Independence Mon, Apr 26, / 22

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