Simpson's paradox.

Consider a medical trial in which patient treatment and outcome are recovered. Two trials were conducted, one with 300 females and one with 300 males. The data are summarised in the table below. Does the drug cause increased recovery? According to the table for males, the answer is no, since more males recovered when they were not given the drug than when they were. Similarly, more females recovered when not given the drug than recovered when given the drug. The conclusion appears that the drug cannot be beneficial since it aids neither subpopulation. However, ignoring the gender information, and collating both the male and female data into one combined table, we find that more people recovered when given the drug than when not. Should we recommend the drug? a Bayes net for this problem needs to be constructed. How is it possible to avoid the 'paradox' by sampling?

Females Recovered Not recovered Recovery rate Given drug 120 80 60% Placebo 75 25 75% Males Recovered Not recovered Recovery rate Given drug 15 85 15% Placebo 42 158 21% Combined Recovered Not recovered Recovery rate Given drug Placebo 135 11? 165 183 45% 39%