  This paper describes Simpson's paradox, and explains its serious implications
for randomised control trials. In particular, we show that for any number of
variables we can simulate the result of a controlled trial which uniformly
points to one conclusion (such as 'drug is effective') for every possible
combination of the variable states, but when a previously unobserved
confounding variable is included every possible combination of the variables
state points to the opposite conclusion ('drug is not effective'). In other
words no matter how many variables are considered, and no matter how
'conclusive' the result, one cannot conclude the result is truly 'valid' since
there is theoretically an unobserved confounding variable that could completely
reverse the result.
