1. Researchers conducted a study to if type of surgery: open surgery and percutaneous nephrolithotomy is associated with success or failure of treatment of renal calculi. But they also wonder sizes of the stones (<2 cm or 2 cm) may play role in the association. The information is given as followed:

Total 700 patients participated this study including 562 patients who had successful treatment and 138 patients with failed treatment, respectively. Out of 562 patients who had successful treatment, 273 of them had open surgery compared 77 out of 138 patients with failed treatment.

Of those who had open surgery, 81 successful patients and 6 failed patients had stone <2 cm; Of those who had percutaneous nephrolithotomy, 234 of successful patients and 36 failed patients who had stones <2 cm.

(Hint: decide the third variable size of the stones in this study is a confounding or interaction variable)

Decide if size of stones is a confounding or interaction variable and Report the association between type of surgery and success of treatment of renal calculi based on the information given above.