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An article in the British Medical Journal [“Comparison of

Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger ISBN: 9781118539712 55

Solution for problem 131E Chapter 2.5

Applied Statistics and Probability for Engineers | 6th Edition

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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger

Applied Statistics and Probability for Engineers | 6th Edition

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Problem 131E

Problem 131E

An article in the British Medical Journal [“Comparison of treatment of renal calculi by operative surgery, percutaneous nephrolithotomy, and extracorporeal shock wave lithotripsy” (1986, Vol. 82, pp. 879–892)] provided the following discussion of success rates in kidney stone removals. Open surgery had a success rate of 78% (273/350) and a newer method, percutaneous nephrolithotomy (PN), had a success rate of 83% (289/350). This newer method looked better, but the results changed when stone diameter was considered. For stones with diameters less than 2 centimeters, 93% (81/87) of cases of open surgery were successful compared with only 83% (234/270) of cases of PN. For stones greater than or equal to 2 centimeters, the success rates were 73% (192/263) and 69% (55/80) for open surgery and PN, respectively. Open surgery is better for both stone sizes, but less successful in total. In 1951, E. H. Simpson pointed out this apparent contradiction (known as Simpson’s paradox), and the hazard still persists today. Explain how open surgery can be better for both stone sizes but worse in total.

Step-by-Step Solution:

Solution :

Step 1 of 1:

From the given information the success rate in kidney stone removals table is given below.

The the total open surgery had success rate is

Type

Percent

Fraction

Open surgery

78%

PN

83%

Then stone diameter is less than 2 centimeters.

The table is given below.

Type

Percent

Fraction

Open surgery

93%

PN

83%

Our goal is:

We need to explain how open surgery can be better for both stone sizes but worse in total.

Now the stone diameter is greater or equals to 2 centimeters.

Then the table is given below.

Type

Percent

Fraction

Open surgery

73%

PN

69%

Now we have to explain how open surgery can be better for both stone sizes but worse in total.

The open surgery table is given below.

Success

Failure

Sample size

Sample percentage

Conditional success rate

Large stone

192

71

263

75%

73%

Small stone

81

6

87

25%

93%

Total

273

77

350

100%

78%

The PN surgery table is given below.

Success

Failure

Sample size

Sample percentage

Conditional success rate

Large stone

55

25

80

23%

69%

Small stone

234

36

270

77%

83%

Total

289

61

350

100%

83%

From the above table there are a lot more open surgeries the stone have diameter is less than 2 centimeters, so when the stones have a diameter of less than 2 centimeters then there are a lot of PN’s.

Here the total success rate is depends on the success rate for each stone size, but same as the probability group.

So this the weighted average of the group success rate weighted by the group size is

P(overall success) = P.

So open surgery, the large stone has a smaller success rate while for PN, the small stone has a larger rate.


Step 2 of 1

Chapter 2.5, Problem 131E is Solved
Textbook: Applied Statistics and Probability for Engineers
Edition: 6
Author: Douglas C. Montgomery, George C. Runger
ISBN: 9781118539712

The full step-by-step solution to problem: 131E from chapter: 2.5 was answered by , our top Statistics solution expert on 07/28/17, 07:57AM. The answer to “An article in the British Medical Journal [“Comparison of treatment of renal calculi by operative surgery, percutaneous nephrolithotomy, and extracorporeal shock wave lithotripsy” (1986, Vol. 82, pp. 879–892)] provided the following discussion of success rates in kidney stone removals. Open surgery had a success rate of 78% (273/350) and a newer method, percutaneous nephrolithotomy (PN), had a success rate of 83% (289/350). This newer method looked better, but the results changed when stone diameter was considered. For stones with diameters less than 2 centimeters, 93% (81/87) of cases of open surgery were successful compared with only 83% (234/270) of cases of PN. For stones greater than or equal to 2 centimeters, the success rates were 73% (192/263) and 69% (55/80) for open surgery and PN, respectively. Open surgery is better for both stone sizes, but less successful in total. In 1951, E. H. Simpson pointed out this apparent contradiction (known as Simpson’s paradox), and the hazard still persists today. Explain how open surgery can be better for both stone sizes but worse in total.” is broken down into a number of easy to follow steps, and 174 words. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9781118539712. This full solution covers the following key subjects: surgery, open, nephrolithotomy, success, stone. This expansive textbook survival guide covers 97 chapters, and 2005 solutions. Since the solution to 131E from 2.5 chapter was answered, more than 540 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 6.

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