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    $\begingroup$ Theoretical justification for the bootstrap in frequentist analysis isn't exactly a piece of cake, and I remember I have seen asymptotical results that looked like it would need very similar assumptions to the Central Limit Theorem to work - which is the same situation in which a standard t-test will work as well (for large enough samples such as 2*500 appeal to the CLT is fine and there's not much worry about non-normality, unless there's worry for the bootstrap, too). $\endgroup$
    – Christian Hennig
    Commented May 1 at 10:45
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    $\begingroup$ Check stats.stackexchange.com/q/447532/7224 $\endgroup$
    – Xi'an
    Commented May 1 at 19:20
  • $\begingroup$ Thanks, both these comments were useful, especially the link - it seems this is a thing, just a bit niche. $\endgroup$
    – Amorphia
    Commented May 3 at 9:12