5. An article in the British Medical Journal provided the following discussion of success rates in kidney stone removals. Open surgery had a success rate of 78% (273 patients out of 350) and a newer method, percutaneous nephrolithotomy (PN), had a success rate of 83% (289 patients out of 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 patients out of 87) of cases of open surgery were successful, compared with only 87% (234 patients out of 270) of cases of PN. For larger stones, the success rates were 73% (192 patients out of 263) and 69% (55 patients out of 80) for open surgery and PN, respectively. Open surgery is better for both stone sizes, but less successful in total. This apparent contradiction was pointed out by the statistician E. H. Simpson in 1951, and is known as the Simpson's paradox. Explain how open surgery can be better for both stone sizes but inferior overall. (

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5. An article in the British Medical Journal provided the following discussion of success rates in kidney
stone removals. Open surgery had a success rate of 78% (273 patients out of 350) and a newer method,
percutaneous nephrolithotomy (PN), had a success rate of 83% (289 patients out of 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 patients out of 87) of cases of open surgery were successful,
compared with only 87% (234 patients out of 270) of cases of PN. For larger stones, the success
rates were 73% (192 patients out of 263) and 69% (55 patients out of 80) for open surgery and PN,
respectively.
Open surgery is better for both stone sizes, but less successful in total. This apparent contradiction
was pointed out by the statistician E. H. Simpson in 1951, and is known as the Simpson's paradox.
Explain how open surgery can be better for both stone sizes but inferior overall. (
Transcribed Image Text:5. An article in the British Medical Journal provided the following discussion of success rates in kidney stone removals. Open surgery had a success rate of 78% (273 patients out of 350) and a newer method, percutaneous nephrolithotomy (PN), had a success rate of 83% (289 patients out of 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 patients out of 87) of cases of open surgery were successful, compared with only 87% (234 patients out of 270) of cases of PN. For larger stones, the success rates were 73% (192 patients out of 263) and 69% (55 patients out of 80) for open surgery and PN, respectively. Open surgery is better for both stone sizes, but less successful in total. This apparent contradiction was pointed out by the statistician E. H. Simpson in 1951, and is known as the Simpson's paradox. Explain how open surgery can be better for both stone sizes but inferior overall. (
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