Suppose you have recently run a survey on a known population (N=1000). You surveyed a subset of that population randomly (n=250). Now, suppose that you have a number of variables that are known. Like geography, expenditures, number of sales.

Are there statstical tests that takes into account the known variables from the population to identify the accuracy, or precision of your sample. In other words, is there a way, beyond MoE, to denote the accuracy of your test based on these known parameters?

  • 2
    $\begingroup$ To clarify: are you asking if there are statistical tests that address whether or not two samples are from the same distribution? I.e. that $X$ (larger sample) and $x \subset X$ (subsample) are similar (or, that $x^C$ and $x$ are similar)? $\endgroup$ – Iterator Aug 10 '11 at 1:51
  • $\begingroup$ @Iterator: Essentially, I have a known population and I would like to assess the degree to which my sample matches the population based on those three variables. $\endgroup$ – Brandon Bertelsen Aug 10 '11 at 1:56
  • $\begingroup$ Also to clarify, do you know the distribution of the variables of interest in detail, or just their population totals or means? $\endgroup$ – DavidDLewis Aug 10 '11 at 2:04
  • $\begingroup$ @DavidDLewis I have the exact numbers for each member of the population for those three variables. $\endgroup$ – Brandon Bertelsen Aug 10 '11 at 3:36

For continuous variables, the uniformly most powerful test is Kolmogorov-Smirnov test. For discrete variables, you can use Pearson test for proportions.

If you really had a simple random sample from that population, all these tests would do is to produce type I error 5% of the time. Or 10% of the time. Or whatever your chosen significance level is.

In survey statistics, there are methods to utilize auxiliary population information with the random samples, such as post-stratification, calibration, and regression estimation. I am afraid that you need to have had at least an intro course on sampling at Lohr level to appreciate these though.

  • $\begingroup$ +1 This is mostly correct. I'm not sure that the second paragraph is necessary, at least as-is. $\endgroup$ – Iterator Aug 10 '11 at 2:17
  • $\begingroup$ +1 for both discreet and continuous tests. Way to think ahead! $\endgroup$ – Brandon Bertelsen Aug 10 '11 at 3:39

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