Let's say that I have a population of 10000, and I have a sample of 300 that have responded to an online survey. Of 10000 invitations, 300 hundred have replied. Would I be able to use the finite population correction for margin of error?

Population: 10000
Sample: 300
Response: 3%

  • $\begingroup$ if you have a representative sample why do you need corrections? $\endgroup$ – Dmitrij Celov Jun 22 '11 at 11:09
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    $\begingroup$ It sounds like you have an intended sample size of 10000 and a 97% non-response rate. Your "population" is probably much, much greater than 10000. $\endgroup$ – whuber Jun 22 '11 at 14:40
  • $\begingroup$ Perhaps my understanding of "population" is misconstrued. Essentially, I'm trying to estimate the margin of error associated with a survey I recently ran on the clients of a company. What I'd like to be able to say is something like. "X% Clients of company Y agree that Z, with a margin of error of A." $\endgroup$ – Brandon Bertelsen Jun 23 '11 at 7:20

With a 3% response rate, it is highly likely that self-selection has made this a biased sample. whuber has also pointed out that 10000 may not be the whole population.

If the population was 10000 and if you had a random sample of 300 then you could make a finite population correction. Wikipedia suggests a multiplicative factor for the standard error of $$\sqrt{\dfrac{N-n}{N-1}}$$ which with $N=10000$ and $n=300$ is about $0.985$, not something that is going to make a lot of difference.

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    $\begingroup$ Yes, perhaps my terminology is incorrect and certainly self-selection is a problem in all online research. However, 10k is truely the universe for this population. So how do I calculate MoE? Or can I? $\endgroup$ – Brandon Bertelsen Jun 23 '11 at 7:22
  • $\begingroup$ The Wikipedia article also says that the FPC is intended for use when the sample size is greater than 5% of the population. For example, if your sample is 25%, the FPC is .8703, which could make more of a difference $\endgroup$ – user7483 Nov 20 '11 at 4:13
  • $\begingroup$ Which formula for M of E is less important than whether to report one. There is a short discussion at stats.stackexchange.com/questions/7134/… that is relevant to this. Lots and lots of people report, for self-selected samples, inferential statistics derived from methods intended only for random samples. But as a reflective, informed person, you'll know that to do so is unsound and that margins of error will not have their nominal limits. At the post linked above I described a sort of workaround to this, which was met with mixed reviews. $\endgroup$ – rolando2 Nov 20 '11 at 4:32

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