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If I have a population of 5000, statistics suggests that I need to sample about 350+ to get a confidence interval of 95% with margin of error 5%.

So why do I see that sometimes we can get away with as low as 30?! That seems so much lower than what all these tables and calculators suggest.

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    $\begingroup$ Depends on your effect size, standard error, etc. Read about sample size calculation, power analysis, and study design. $\endgroup$
    – Ellis Valentiner
    Jan 30, 2014 at 17:57
  • $\begingroup$ Under what circumstances does it make sense to use a sample size of 30? For a population of 5000 at the 95% confidence level, the error is like 18! $\endgroup$
    – Remy F
    Jan 30, 2014 at 18:01
  • $\begingroup$ If the effect size is very large, it is quite easy for a model to discriminate. In such a scenario a small sample size might be appropriate $\endgroup$
    – bdeonovic
    Jan 30, 2014 at 18:05
  • $\begingroup$ What does that mean? $\endgroup$
    – Remy F
    Jan 30, 2014 at 18:06
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    $\begingroup$ It means that you cannot make a sample size prediction only based on "the size of your population" (not exactly sure what this is or how you are using this to calculate CI). You need to know other factors such as the effect size, power, type I error, etc. If you are confused you need to do more reading on power analysis as someone suggested $\endgroup$
    – bdeonovic
    Jan 30, 2014 at 18:14

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The sample size of 30 is typically a rule of thumb for how large of a sample size you need for the sample average to be approximatelly normally distributed. This is necessary if you are doing some kind of inference on a population parameter.

As another user pointed out, you might need a larger sample size if you want your hypotheses test to have a particular power.

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  • $\begingroup$ The statement in the first sentence is accurate (that it's a typical rule of thumb), but the 'rule of thumb' itself is deeply flawed, almost to the point of being dangerous. As such, I disagree with the second sentence. Can you justify n=30 on the basis that you need it for doing inference on a population parameter? $\endgroup$
    – Glen_b
    Jan 31, 2014 at 0:51
  • $\begingroup$ I meant that it was necessary to know the distribution of your test statistic if you want to do inference on a population parameter. The CLT provides this. $\endgroup$
    – bdeonovic
    Jan 31, 2014 at 2:51
  • $\begingroup$ But the CLT only tells you about behavior as $n\rightarrow\infty$. 30 is very often not sufficiently close to infinity. By way of example, see the discussion here. $\endgroup$
    – Glen_b
    Jan 31, 2014 at 3:10

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