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Chapter 13: Q9CQQ (page 597)

Sign Test and Wilcoxon Signed-Ranks Test What is a major advantage of the Wilcoxon signed-ranks test over the sign test when analyzing data consisting of matched pairs?

Short Answer

Expert verified

The Wilcoxon signed-ranks test uses more information about the data and tends to generate results that better reflect the true nature of the data since the sign test just uses signs of differences. The Wilcoxon signed-ranks test, on the contrary, incorporates ranks of the differences.

This is one major advantage of the Wilcoxon-signed ranks test.

Step by step solution

01

Given information

The Wilcoxon signed-ranks test uses the ranks of the differences between paired values to test if the median of the differences is equal to 0.

02

Wilcoxon signed-ranks test and sign test

The sign test and the Wilcoxon signed-ranks test are non-parametric tests that are used to check whether the given two samples are from the same population or not based on the median of the samples.

The sign test uses the signs of the differences between the values.

The Wilcoxon signed-ranks test uses the ranks as well as the signs of the differences between the values.

03

Advantage of Wilcoxon signed-ranks test

The Wilcoxon signed-ranks test is used to test whether the median of the differences of the paired values is equal to 0.

The major advantage of the Wilcoxon signed-ranks test is that it uses the ranks of the differences instead of just their signs.

The results of the Wilcoxon signed-ranks test generate better results that are more comprehensible than the sign test.

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Most popular questions from this chapter

Using Nonparametric Tests. In Exercises 1–10, use a 0.05 significance level with the indicated test. If no particular test is specified, use the appropriate nonparametric test from this chapter.

Presidents, Popes, Monarchs Listed below are numbers of years that U.S. presidents, popes, and British monarchs lived after their inauguration, election, or coronation, respectively. Assume that the data are samples randomly selected from larger populations. Test the claim that the three samples are from populations with the same median.

Presidents

10

29

26

28

15

23

17

25

0

20

4

1

24

16

12


4

10

17

16

0

7

24

12

4

18

21

11

2

9

36


12

28

3

16

9

25

23

32








Popes

2

9

21

3

6

10

18

11

6

25

23

6

2

15

32


25

11

8

17

19

5

15

0

26







Monarchs

17

6

13

12

13

33

59

10

7

63

9

25

36

15

Sign Test for Freshman 15 The table below lists some of the weights (kg) from Data Set 6 “Freshman 15” in Appendix B. Those weights were measured from college students in September and later in April of their freshman year. Assume that we plan to use the sign test to test the claim of no difference between September weights and April weights. What requirements must be satisfied for this test? Is there any requirement that the populations must have a normal distribution or any other specific distribution? In what sense is this sign test a “distribution-free test”?

September weight (kg)

67

53

64

74

67

70

55

74

62

57

April weight (kg)

66

52

68

77

67

71

60

82

65

58

Randomness Refer to the following ages at inauguration of the elected presidents of the United States (from Data Set 15 “Presidents” in Appendix B). Test for randomness above and below the mean. Do the results suggest an upward trend or a downward trend?

57

61

57

57

58

57

61

54

68

49

64

48

65

52

46

54

49

47

55

54

42

51

56

55

51

54

51

60

62

43

55

56

52

69

64

46

54

47

Pizza and the Subway The “pizza connection” is the principle that the price of a slice of pizza in New York City is always about the same as the subway fare. Use the data listed below to determine whether there is a correlation between the cost of a slice of pizza and the subway fare.

Year

1960

1973

1986

1995

2002

2003

2009

2013

2015

Pizza Cost

0.15

0.35

1.00

1.25

1.75

2.00

2.25

2.3

2.75

Subway Fare

0.15

0.35

1.00

1.35

1.5

2.00

2.25

2.5

2.75

CPI

30.2

48.3

112.3

162.2

191.9

197.8

214.5

233

237.2

Matched Pairs.In Exercises 5–8, use the sign test for the data consisting of matched pairs.

Speed Dating: Attractiveness Listed below are “attractiveness” ratings (1 = not attractive; 10 = extremely attractive) made by couples participating in a speed dating session. The listed ratings are from Data Set 18 “Speed Dating”. Use a 0.05 significance level to test the claim that there is a difference between female attractiveness ratings and male attractiveness ratings.

Rating of Male by Female

4

8

7

7

6

8

6

4

2

5

9.5

7

Rating of Female by Male

6

8

7

9

5

7

5

4

6

8

6

5
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