  Simulation-based inference plays a major role in modern statistics, and often
employs either reallocating (as in a randomization test) or resampling (as in
bootstrapping). Reallocating mimics random allocation to treatment groups,
while resampling mimics random sampling from a larger population; does it
matter whether the simulation method matches the data collection method?
Moreover, do the results differ for testing versus estimation? Here we answer
these questions in a simple setting by exploring the distribution of a sample
difference in means under a basic two group design and four different
scenarios: true random allocation, true random sampling, reallocating, and
resampling. For testing a sharp null hypothesis, reallocating is superior in
small samples, but reallocating and resampling are asymptotically equivalent.
For estimation, resampling is generally superior, unless the effect is truly
additive. Moreover, these results hold regardless of whether the data were
collected by random sampling or random allocation.
