How to interpret inferential statistics when your data aren’t a random sample

Someone named Adam writes: I’m having a bit of a ‘crisis’ of confidence regarding inferential statistics. I’ve been reading some of the work by Stephen Gorard (e.g. “Against Inferential Statistics”) and David Freedman and Richard Berk (e.g. “Statistical Assumptions as empirical commitments”). These authors appear to be saying this: (1) Inferential statistics assume random sampling …