# Difference between a census and a sample

I know when you do a census, you cover the entire population but when you take a sample, you select a group from the population. There can be only one census but there can be many different samples from the same population. Hence, the latter results in sampling error (because it is just one aspect of the population).

This may be a bit simplistic but I think it captures the essential differences between a census and a sample.

A consultant that my company has engaged is blurring this distinction between a census and a sample. He has essentially collected a sample, weighted it and then interpreted the findings as if they relate to the entire population. He is mostly using descriptive statistics. He has even calculated the sampling error.

My question is: Is it ever valid to treat a sample as a census? If so, what are the preconditions?

• Surely it depends on your question? For instance, if I was interested in the answer to the question because I was allocating my marketing budget: "is about 50% of the population of the USA female", a census and a sample would give indistinguishable results. But if you're a lottery company and you want to know if anyone holds the winning ticket to your lottery, I'd rather a census of the ticket holders than a sample of the ticket holders. – Patrick Caldon Jul 10 '12 at 6:33

It is standard practice, particularly in official statistics, to use "weighting to population" of a sample and then report estimates for the whole population, including sample error. This should not be confused with a census, but it is quite legitimate to refer to these estimates of population parameters (eg population total savings, total expenditure, etc).

Surveys are often designed specifically to facilitate this analytical approach; indeed, if they are not so designed, it can be difficult or impossible to do the appropriate weighting.

• Yes, this is "weighting to population" case. However, it still does not seem right that the report is called a "census"? – Amarald Jul 11 '12 at 4:18
• No, if it's following my example it shouldn't be called a "census", just a sample that has been analysed to provide estimates of population parameters. But your original post didn't mention he was calling it a census. – Peter Ellis Jul 11 '12 at 8:44
• The consultant states that the report describes the methodology so it does not matter if it is called a census (which I find quite misleading). – Amarald Jul 17 '12 at 6:04

I agree with Peter here. You probably have a miscommunication issue with your consultant. What a survey is supposed to give you are the estimates of the population parameters. If your consultant just talked about the sample as if they were a population, that would be bad. But if they computed sampling error, then he probably understands the distinction between the two. You, on the other hand, might want to read more on sampling statistics, although you do demonstrate the basic understanding, judging from your first paragraph. What Is a Survey by Fritz Scheuren, past president of the American Statistical Association, is one starting point; a good book such as Lohr (2009) is another.

What might have thrown you off is that the consultant computed the weights that sum up to the population total, and that is the appropriate practice (unlike the practice of providing the weights that sum up to the sample size). So now all counts look like they relate to the population -- and that's a good thing, especially if your "number of females who smoke in the country" is accompanied with a margin of sampling error.

I would also comment that it is probably a good practice to double check on the work of your consultant, especially if you feel that you don't quite understand what they have done. Make sure to not piss them off though by questioning their qualifications. I understand it when my clients check my work in the peer-review way; but I doubt I would return to do business with a client who would ask somebody else to redo my work, especially behind my back without telling me.