A Monte Carlo scheme randomly samples M separate I J tables having observed margins to approximate P o P(X 2 X 2 o ) for an exact test Let P be the sample proportion of the M tables with X 2 X 2 o Show that P( P P o B) 1 requires that M z 2 2 P o (1P o ) B 2 ...

P P P o B PP P o P o 1P o M BP ...

A Monte Carlo scheme randomly samples M separate I J tables having observed margins to approximate

Question:

A Monte Carlo scheme randomly samples M separate I × J tables having observed margins to approximate P_o = P(X² ≥ X²_o) for an exact test. Let P̂ be the sample proportion of the M tables with X² ≥ X²_o. Show that P(|P̂ – P_o| ≤ B) = 1 – α requires that M ≈ z²_α/2 P_o(1–P_o)/B².