Question

For this exercise, you will be navigating the problems listed under Dentistry in Chapter 9 (page 365), problems 9.1 to 9.3 only.Here are a few helpful hints: For 9.1, use a sign test (equation 9.1 in the book) to find the rejection region, and determine whether or not the results stated in the problem are significant at the .05 level.For 9.3, complete the ranking procedure outlined in Equation 9.5 in the book (p.347), and then use Equation 9.6 (p.348) to complete the test and then determine the p-value. AssignmentProvide your response to each of the problems listed in the textbook for the Dentistry case, problems 9.1 through 9.3 only. DentistryIn a study, 28 adults with mild periodontal disease are assessed before and 6 months after implementation of a dental-education program intended to promote better oral hygiene. After 6 months, periodontal status improved in 15 patients, declined in 8, and remained the same in 5.*9.1 Assess the impact of the program statistically (use a two-sided test).Suppose patients are graded on the degree of change in periodontal status on a 7-point scale, with +3 indicating the greatest improvement, 0 indicating no change, and -3 indicating the greatest decline. The data are given in Table 9.9.9.2 What nonparametric test can be used to determine whether a significant change in periodontal status has occurred over time?9.3 Implement the procedure in Problem 9.2, and report a p-value EQUATION 9.5 Ranking Procedure for the Wilcoxon Signed-Rank Test (1) Arrange the differences d, in order of bsolute value as in Table 9.1. (2) Count the number of differences with the same absolute value. (3) Ignore the observations where d, = 0, and rank the remaining observations from 1 for the observation with the lowest absolute value, up to n for the observation with the highest absolute value. (4) If there is a group of several observations with the same absolute value, then find the lowest rank in the range = 1 + R and the highest rank in the range = G + R, where R = the highest rank used prior to considering this group and G = the number of differences in the range of rauks for the group. Assign the average rank = (lowest rank in the range + highest rank in the range)/2 as the rank for each difference in the group. EXAMPLE 9.12 Dermatology Compute the ranks for the skin-ointment data in Table 9.1. Solution: First collect the differences with the same absolute value. Fourteen people have absolute value 1; this group has a rank range from 1 to 14 and an average rank of (1 + 14)/2 = 7.5. The group of 10 people with absolute value 2 has a rank range from (1 + 14) to (10 + 14) = 15 to 24 and an average rank = (15 + 24)/2 = 19.5, . , and so on. 348 CHAPTER9 Nonparametric Methods The test is based on the sum of the ranks, or rank sum (R,), for the group of people with positive d,that is, the rank sum for people for whom ointment A is not as good as ointment B. A large rank sum indicates that differences in burn degree in favor of treatment B tend to be larger than those for treatment A, whereas a small rank sum indicates that differences in burn degree in favor of treatment A tend to be larger than those for treatment B. If the null hypothesis is true, then the expected value and variance of the rank sum (when there are no ties) are given by E(R=n+1/4,VarR=n+12n+1/24 where is the number of nonzero differences. If the number of nonzero d,s is 16, then a normal approximation can be used for the sampling distribution of R,- This test procedure, the Wilcoxon signed-rank test, is given as follows. EQUATION 9.6 Wilcoxon Signed-Rank Test (Normal Approximation Method for Two-Sided Level Test) (1) Rank the differences as shown in Equation 9.5. (2 Compute the rank sum R, of the positive differences n+1 3aIf R and there re no ties (no groups of differences with the same absolute value), then 2/++/[-|+]= ences with the same absolute value in the ith tied group and g is the number of tied groups, then T=[R-nn+11 n+1(2n+1/24t/48 4If T > Zi-/2 then reject H. Otherwise, accept Hg (5) The p-value for the test is given by p=2[1(T] (6) This test should be used only if the number of nonzero differences is 16 and if the difference scores have an underlying continuous symmetric distribution. The computation of the p-value is illustrated in Figure 9.5. The rationale for the different test statistic in the absence (3a) or presence (3b) of tied values is that the variance of R, is reduced in the presence of ties (sometimes substantially) [1]

Name: for this exercise you will be navigating the problems listed under dentistry in chapter 9 page 365 problems 91 to 93 onlyhere are a few helpful hints for 91 use a sign test equation 91 in th 31108
Uploaded: 2023-03-14T10:34:49-08:00
Duration: 1 min 34 s
Channel: Adi S
Description: for this exercise you will be navigating the problems listed under dentistry in chapter 9 page 365 problems 91 to 93 onlyhere are a few helpful hints for 91 use a sign test equation 91 in th 31108

          For this exercise, you will be navigating the problems listed under Dentistry in Chapter 9 (page 365), problems 9.1 to 9.3 only.Here are a few helpful hints: For 9.1, use a sign test (equation 9.1 in the book) to find the rejection region, and determine whether or not the results stated in the problem are significant at the .05 level.For 9.3, complete the ranking procedure outlined in Equation 9.5 in the book (p.347), and then use Equation 9.6 (p.348) to complete the test and then determine the p-value. AssignmentProvide your response to each of the problems listed in the textbook for the Dentistry case, problems 9.1 through 9.3 only. 
DentistryIn a study, 28 adults with mild periodontal disease are assessed before and 6 months after implementation of a dental-education program intended to promote better oral hygiene. After 6 months, periodontal status improved in 15 patients, declined in 8, and remained the same in 5.*9.1 Assess the impact of the program statistically (use a two-sided test).Suppose patients are graded on the degree of change in periodontal status on a 7-point scale, with +3 indicating the greatest improvement, 0 indicating no change, and -3 indicating the greatest decline. The data are given in Table 9.9.9.2 What nonparametric test can be used to determine whether a significant change in periodontal status has occurred over time?9.3 Implement the procedure in Problem 9.2, and report a p-value
EQUATION 9.5
Ranking Procedure for the Wilcoxon Signed-Rank Test (1) Arrange the differences d, in order of bsolute value as in Table 9.1. (2) Count the number of differences with the same absolute value. (3) Ignore the observations where d, = 0, and rank the remaining observations from 1 for the observation with the lowest absolute value, up to n for the observation with the highest absolute value. (4) If there is a group of several observations with the same absolute value, then find the lowest rank in the range = 1 + R and the highest rank in the range = G + R, where R = the highest rank used prior to considering this group and G = the number of differences in the range of rauks for the group. Assign the average rank = (lowest rank in the range + highest rank in the range)/2 as the rank for each difference in the group.
EXAMPLE 9.12 Dermatology Compute the ranks for the skin-ointment data in Table 9.1.
Solution: First collect the differences with the same absolute value. Fourteen people have absolute value 1; this group has a rank range from 1 to 14 and an average rank of (1 + 14)/2 = 7.5. The group of 10 people with absolute value 2 has a rank range from (1 + 14) to (10 + 14) = 15 to 24 and an average rank = (15 + 24)/2 = 19.5,  .  , and so on.
348
CHAPTER9 Nonparametric Methods
The test is based on the sum of the ranks, or rank sum (R,), for the group of people with positive d,that is, the rank sum for people for whom ointment A is not as good as ointment B. A large rank sum indicates that differences in burn degree in favor of treatment B tend to be larger than those for treatment A, whereas a small rank sum indicates that differences in burn degree in favor of treatment A tend to be larger than those for treatment B. If the null hypothesis is true, then the expected value and variance of the rank sum (when there are no ties) are given by E(R=n+1/4,VarR=n+12n+1/24
where  is the number of nonzero differences.
If the number of nonzero d,s is  16, then a normal approximation can be used for the sampling distribution of R,- This test procedure, the Wilcoxon signed-rank test, is given as follows.
EQUATION 9.6
Wilcoxon Signed-Rank Test (Normal Approximation Method for Two-Sided Level Test)
(1) Rank the differences as shown in Equation 9.5. (2 Compute the rank sum R, of the positive differences n+1 3aIf R and there re no ties (no groups of differences with the
same absolute value), then 2/++/[-|+]=
ences with the same absolute value in the ith tied group and g is the number of tied groups, then
T=[R-nn+11 n+1(2n+1/24t/48
4If T > Zi-/2 then reject H. Otherwise, accept Hg (5) The p-value for the test is given by
p=2[1(T]
(6) This test should be used only if the number of nonzero differences is  16 and if the difference scores have an underlying continuous symmetric distribution. The computation of the p-value is illustrated in Figure 9.5.
The rationale for the different test statistic in the absence (3a) or presence (3b) of tied values is that the variance of R, is reduced in the presence of ties (sometimes substantially) [1]

for this exercise you will be navigating the problems listed under dentistry in chapter 9 page 365 problems 91 to 93 onlyhere are a few helpful hints for 91 use a sign test equation 91 in th 31108

Added by Arthur G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

03/14/2023

Step 1

1, we will use a sign test to assess the impact of the dental education program statistically. We will calculate the number of patients who showed improvement, decline, or no change in periodontal status after 6 months and determine if the results are significant Show more…

Show all steps

Thanks for your feedback!

For this exercise, you will be navigating the problems listed under Dentistry in Chapter 9 (page 365), problems 9.1 to 9.3 only.Here are a few helpful hints: For 9.1, use a sign test (equation 9.1 in the book) to find the rejection region, and determine whether or not the results stated in the problem are significant at the .05 level.For 9.3, complete the ranking procedure outlined in Equation 9.5 in the book (p.347), and then use Equation 9.6 (p.348) to complete the test and then determine the p-value. AssignmentProvide your response to each of the problems listed in the textbook for the Dentistry case, problems 9.1 through 9.3 only. DentistryIn a study, 28 adults with mild periodontal disease are assessed before and 6 months after implementation of a dental-education program intended to promote better oral hygiene. After 6 months, periodontal status improved in 15 patients, declined in 8, and remained the same in 5.*9.1 Assess the impact of the program statistically (use a two-sided test).Suppose patients are graded on the degree of change in periodontal status on a 7-point scale, with +3 indicating the greatest improvement, 0 indicating no change, and -3 indicating the greatest decline. The data are given in Table 9.9.9.2 What nonparametric test can be used to determine whether a significant change in periodontal status has occurred over time?9.3 Implement the procedure in Problem 9.2, and report a p-value EQUATION 9.5 Ranking Procedure for the Wilcoxon Signed-Rank Test (1) Arrange the differences d, in order of bsolute value as in Table 9.1. (2) Count the number of differences with the same absolute value. (3) Ignore the observations where d, = 0, and rank the remaining observations from 1 for the observation with the lowest absolute value, up to n for the observation with the highest absolute value. (4) If there is a group of several observations with the same absolute value, then find the lowest rank in the range = 1 + R and the highest rank in the range = G + R, where R = the highest rank used prior to considering this group and G = the number of differences in the range of rauks for the group. Assign the average rank = (lowest rank in the range + highest rank in the range)/2 as the rank for each difference in the group. EXAMPLE 9.12 Dermatology Compute the ranks for the skin-ointment data in Table 9.1. Solution: First collect the differences with the same absolute value. Fourteen people have absolute value 1; this group has a rank range from 1 to 14 and an average rank of (1 + 14)/2 = 7.5. The group of 10 people with absolute value 2 has a rank range from (1 + 14) to (10 + 14) = 15 to 24 and an average rank = (15 + 24)/2 = 19.5, . , and so on. 348 CHAPTER9 Nonparametric Methods The test is based on the sum of the ranks, or rank sum (R,), for the group of people with positive d,that is, the rank sum for people for whom ointment A is not as good as ointment B. A large rank sum indicates that differences in burn degree in favor of treatment B tend to be larger than those for treatment A, whereas a small rank sum indicates that differences in burn degree in favor of treatment A tend to be larger than those for treatment B. If the null hypothesis is true, then the expected value and variance of the rank sum (when there are no ties) are given by E(R=n+1/4,VarR=n+12n+1/24 where is the number of nonzero differences. If the number of nonzero d,s is 16, then a normal approximation can be used for the sampling distribution of R,- This test procedure, the Wilcoxon signed-rank test, is given as follows. EQUATION 9.6 Wilcoxon Signed-Rank Test (Normal Approximation Method for Two-Sided Level Test) (1) Rank the differences as shown in Equation 9.5. (2 Compute the rank sum R, of the positive differences n+1 3aIf R and there re no ties (no groups of differences with the same absolute value), then 2/++/[-|+]= ences with the same absolute value in the ith tied group and g is the number of tied groups, then T=[R-nn+11 n+1(2n+1/24t/48 4If T > Zi-/2 then reject H. Otherwise, accept Hg (5) The p-value for the test is given by p=2[1(T] (6) This test should be used only if the number of nonzero differences is 16 and if the difference scores have an underlying continuous symmetric distribution. The computation of the p-value is illustrated in Figure 9.5. The rationale for the different test statistic in the absence (3a) or presence (3b) of tied values is that the variance of R, is reduced in the presence of ties (sometimes substantially) [1]