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Table 3 Three \(2 \times 2\) contingency tables for the data in Table 2

From: Simpson’s Paradox is suppression, but Lord’s Paradox is neither: clarification of and correction to Tu, Gunnell, and Gilthorpe (2008)

 Open surgeryPercutaneous nephrolithotomy 
Association between type of surgery and surgical outcome, disregarding kidney-stone size
 Failure7761 
 Success273289 
 Total350350 
 Percentage success78%83%Difference = 5%\(\phi = .06\)
 Large stoneSmall stone 
Association between kidney-stone size and surgical outcome, disregarding type of surgery
 Failure9642 
 Success247315 
 Total343357 
 Percentage success72%88%Difference = 16%\(\phi = .20\)
 Open surgeryPercutaneous nephrolithotomy 
Association between type of surgery and kidney-stone size, disregarding surgical outcome
 Large stone26380 
 Small stone87270 
 Total350350 
 Percentage small stone25%77%Difference = 52%\(\phi = .52\)
  1. Surgical outcome coded 0 = failure, 1 = success; type of surgery coded 0 = open surgery, 1 = percutaneous nepholithotomy; kidney-stone size coded 0 = large stone, 1 = small stone