An empirical p value is a \(p\) value that is calculated from simulated samples supposed to be drawn from a null distribution (generally based on the observed data). This approach is sometimes advisable because, among other things, (1) unlike say a \(t\) statistic, some test statistics don’t have a standard distribution and (2) the distribution may not be appropriate for too small sample sizes (North et al. Am J Hum Genet 2002). Let’s see how that works out for the following example:

A randomised controlled trial is carried through, involving 200 people: 100 who receive a placebo (control group) and 100 who receive a new drug (treatment group). At the end of the trial, five people in the treatment group have died.

Is the new drug to be blamed for this? Clearly articulate your hypotheses and carry out simulations to compute an empirical \(p\) value to answer that question.

Answer: \(p = 0.03\).