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In a practice exam I encountered a question about the standard error of a sample (calculating the mean order size of a random sample of 100 customers of a paper firm). A researcher (the subject of this question) advised against increasing the sample size because -although it would decrease the standard error- it also would increase the risk of sampling from more than one population. According to the provided answer the researcher was correct.

While I understand what problems may be caused by sampling from more than one population, I fail to see how this could be taken into account in this case. I mean, without knowing the total population of clients and its stratification (not given in the question), there's nothing to be said about this risk, and in fact any sample size (apart from N=1) could contain members from different populations (if there are any). In that case, N=100 could be seen as too big as well.

So, why would a sample of N=100 be free from that risk (or at least have a low risk) and a sample size of N>100 would all of the sudden be so much more risky in this respect that it might be advisable not to increase the sample size?

And, to turn this question around, what would be the standard operating procedure to protect oneself from this multi-population risk?

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There is nothing special about N = 100 that would make it the cutoff point from selecting from more than one population. It all depends on what you are studying. In order to protect yourself from this multi-population risk, you must examine the population you are sampling from and how your sampling algorithm may sample from other populations. Once you know that, build safeguards into your algorithm, such as rejecting if they are from another population, to avoid the problem.

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    $\begingroup$ So, I take it you agree with me that the unqualified advice not to increase the sample size based on the multiple-population argument is nonsense? $\endgroup$ Nov 14 '13 at 22:24
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    $\begingroup$ Yes, I agree with you. $\endgroup$ Nov 15 '13 at 14:08

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