254 Kidney Stone Treatment A study94 collected data comparing treatments for kidney stones. Two of the treatments studied were open surgery and...

1. 2.254 Kidney Stone Treatment A study94 collected data comparing treatments for kidney stones. Two of the treatments studied were open surgery and percutaneous nephrolithotomy. Treatment was deemed "successful" if, after three months, the kidney stones were either eliminated or less than 2 mm. The latter treatment (nephrolithotomy) is cheaper and less invasive, but is it as successful? Results are shown in Figure 2.97, first overall and then broken down by stone size. (If the answers are not obvious visually, in each case you can calculate the proportion of successes using the numbers shown on the graph.)

In order to answer the questions below make sure you show work with proportions and the notation

P(A), P(B), and P(A | B) (see Blackboard).

When all stone sizes are considered, which treatment is more successful?

When only small kidney stones are considered, which treatment is more successful?

When only large kidney stones are considered, which treatment is more successful?

Which stone size results in higher success rates, regardless of treatment type?

Which treatment is more commonly used for small stones?

Which treatment is more commonly used for large stones?

This is an example of Simpson's Paradox. Use your answers to parts (d) to (f) to explain how one treatment can be better for both small AND large stones, yet the other treatment appears to be better overall.

Do you think this was a randomized experiment, with treatment randomly assigned? Why or why not?