Reproducible sampling and simulation

The idea

Randomized analysis needs both a statistical design and a reproducibility record. Set a seed before a repeatable run, and record the relevant R version and random-generator settings when exact cross-environment reproduction matters. A seed determines a sequence under those settings; it does not guarantee that a small sample is representative or that an estimator is unbiased.

Sampling with replacement allows the same observation to appear several times, while sampling without replacement does not. Write that choice into the experiment rather than accepting a default accidentally. Do not reset the same seed inside every replicate when independent simulated draws are intended. Test invariant properties, such as output size and permitted values, alongside a controlled reproducibility check.

set.seed(42)
a <- sample.int(10,4)
set.seed(42)
b <- sample.int(10,4)
cat(identical(a,b),"\n",sep="")

TRUE

Both runs start from the same random state with the same settings and operations, so their sampled sequences match.