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Suppose I have survey responses that look like this:

N=60000, Population
n=1000, Total sample
n=800, Users of Company X
n=200, Randomly chosen from 800 and asked about their Future Use of Company X 
n=100, Planning to use Company X less in the future

The reason that only 200 of 800 users were asked about future use was due to them being asked about other companies as well. The survey would be far too long if they were asked about their future use of all companies that they use.

My goal is to understand the flow of future use. For example, of those individuals who are using Company X less in the future, which other companies are they planning on using more. However, with a sample of 100, there are not enough responses to other companies from the same users to other companies to get a usable proportion.

Can I, with some level of accuracy, infer the flow of business from a more robust sample of users of Company X?

Update: I think, what I may be referring to is called bootstrapping.

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    $\begingroup$ Please stop changing the title, you are obfuscating my purpose. Perhaps that suggests that this is a poorly defined problem. I'll update it again. $\endgroup$ – Brandon Bertelsen Apr 13 '11 at 4:52
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Your question is above my pay grade, as it were, but I can suggest a first look at the R survey package, which might implement some of the routines that you'd use to answer your questions.

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  • $\begingroup$ This package has methods built in for part of what I was looking for $\endgroup$ – Brandon Bertelsen Apr 19 '11 at 18:02
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  • Standard formulas for standard errors of a proportion would be suitable. With regards to your question about which companies the "n=100 sample" plan to use in the future, these standard errors would be based on n = 100. If this yields standard errors that are too large for your liking, then you need to increase your sample size.
  • In some cases you might be able to increase your effective sample size by engaging in more targeted sampling of the subset of the population that interests you (i.e., with company X, but planning to use company X less in the future).
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  • $\begingroup$ Thanks Jeremy, I'll keep that in mind. Although, I don't think this is exactly what I'm looking for (the question about error was more of an aside to my primary question) $\endgroup$ – Brandon Bertelsen Apr 13 '11 at 5:09
  • $\begingroup$ @Brandon. Okay. It seems that your sample size for given questions is being reduced because of (a) random sampling within a random sample and (b) a certain question is only applicable to a subset of your sample. However, I don't see how this would change the process of deriving standard errors. You have a final sample size for that question, and that's that. Perhaps, I'm not understanding what you mean by a "more robust sample of users". $\endgroup$ – Jeromy Anglim Apr 13 '11 at 7:39
  • $\begingroup$ Essentially, I'd like a statistical method for sampling the population of users of Company X, to be able to say which other companies they are planning on doing more business with in the future. aka, Who's eating who's lunch. $\endgroup$ – Brandon Bertelsen Apr 13 '11 at 8:33
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    $\begingroup$ @Brandon I still don't quite see how it is a special case. In survey research, we define a population, and attempt to sample from that population. In some cases the population is adults in a given country, in other cases it is people who use company X, in other cases it is people who use company Y, and in other cases it is people who use Company X, but are considering switching. In all these cases there are pragmatic challenges of actually getting a sample that is representative of the target population, and that is sufficiently large to draw relevant inferences. $\endgroup$ – Jeromy Anglim Apr 13 '11 at 10:20
  • $\begingroup$ I can't go back to the population at this point (we have a lockout time and our population is well known to us) so I must make the best use of the sample that I have. In my previous statement, I made an error. I'm looking for a statistical method for sampling my sample of users of company X to be able to converge upon which companies they are planning on doing more business with in the future. $\endgroup$ – Brandon Bertelsen Apr 17 '11 at 23:38

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