# Comparing sample to a known population

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?

• 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)? – Iterator Aug 10 '11 at 1:51
• @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. – Brandon Bertelsen Aug 10 '11 at 1:56
• Also to clarify, do you know the distribution of the variables of interest in detail, or just their population totals or means? – DavidDLewis Aug 10 '11 at 2:04
• @DavidDLewis I have the exact numbers for each member of the population for those three variables. – Brandon Bertelsen Aug 10 '11 at 3:36