**2.1 Violations of frequentist assumptions**

Most frequentist statistical analyses follow a familiar pattern: assume the outcome follows a known statistical distribution, then test whether or not the observed data are unusual (unexpected) under the null hypothesis. However, beyond basic goodnessof-fit considerations, such analyses require other assumptions as well, many of which are clearly violated much of the time. Perhaps the most important of these assumptions is that the observations in a given sample are "iid"—independent and identically

distributed. When samples are strictly observational (i.e., not from a randomized trial) this assumption is often unwarranted. The implication of violating this assumption can be profound: differential probability of exposure and inequitable distributions of potential confounders can lead to what is known as *confounding by indication*, a subtle form of bias that can lead to misleading or even wholly wrong conclusions.
