At what point can very large samples, as a proportion of the population, be treated as a census? For example, if your sample contains 90% of the population units, can one dispense with inferential statistical inferences? What about 80%? And so on . . ..

  • $\begingroup$ Consider looking at this previous question and answer: stats.stackexchange.com/questions/14323/…. This concept should generalize to any near census tests. $\endgroup$ – russellpierce Mar 14 '14 at 17:44
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    $\begingroup$ I think it depends on how you define "population". By "population", if you mean a collection of observations that can never be sampled again (representing the universe of obs in its entirity), then yes you could use a finite population correction factor to shrink the stnd error on sample estimates as n approaches N. However if your "population" can be considered a random sample from a much larger theoretical population of observations, then inferential statistics still apply without an fpc. $\endgroup$ – RobertF Mar 14 '14 at 17:47
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    $\begingroup$ It depends. In the US there is a decennial political debate about whether the Bureau of the Census can be allowed to use statistical sampling procedures to make estimates, rather than attempting to perform a complete census. The argument against attempting a census is that the bias introduced by nonresponse and other missing information, even with a 99+% census, is too large to be ignored. In general some questions cannot be answered without a 100% census, such as "what is the largest value in the population?" $\endgroup$ – whuber Mar 14 '14 at 18:11
  • $\begingroup$ @whuber, maybe we shouldn't be asking questions that cant be answered by sampling. $\endgroup$ – Aksakal Nov 19 '18 at 20:01
  • $\begingroup$ Possible duplicate of When the population has a known fixed size, are tables for the t statistic wrong? $\endgroup$ – mkt Sep 11 at 11:55

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