In textbooks and online the explanation for Bessel's correction is that the sample points are closer to the sample mean than the population mean.This is true for sampling with replacement as well. So, how come we don't use Bessel's correction when sampling with replacement?
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Welcome to CV. Your question is predicated on the false assumption that Bessel's correction is not used when sampling with replacement. The duplicate will explain things. Perhaps you meant to ask about sampling *without* replacement? – whuber Jan 23 '20 at 12:45
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I don't understand the difference between Bessel's correction and the modified population variance (which is described here: http://www.ph.ucla.edu/epi/rapidsurveys/RScourse/RSbook_ch3.pdf). – Tyra Jan 23 '20 at 16:25
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They are identical because the formulas are identical. The book merely uses an unusual phrase to describe the same formula. – whuber Jan 23 '20 at 17:01