# When is a sample size too large? [duplicate]

• At what point exactly is a sample size considered "really large"?
• In hypothesis testing, do small differences become consistently significant when n is 100,000?
• Is there a definite limit between a large and a small sample size?

An example in R or a published article would also be helpful!

• You might be interested by this post: stats.stackexchange.com/questions/2516/… Nov 22 '21 at 15:37
• As a general proposition, questions in statistics that use vague and unquantitative terms such as "really large" are considered ... vague and unquantitative; and therefore tend not to have general answers.
– whuber
Nov 22 '21 at 15:40
• With any sample size you need to have a clear idea what difference is of practical importance. // If you have used that difference in a power and sample size computation (and made the right assumptions) then sample size should be just the right size to have a good chance of detecting that difference. // If you have data on essentially the entire population of interest, you should be describing the population, not testing hypotheses about it. Nov 22 '21 at 15:40
• If one considers it a problem when a hypothesis test has enough power to reject small differences, I tend to believe that one is misapplying frequentist statistics.
– Dave
Nov 22 '21 at 15:42
• @Nate I wouldn't say any sample is too large. What you should do is looking at more information, in the first place a confidence interval. If the confidence interval does not contain zero (therefore the test is significant), but contains effect sizes that are so small to be practically meaningless, you haven't found anything of practical significance. (The wording "real difference" is misleading, as even a very small difference may be real but not meaningful.) Nov 22 '21 at 16:41