241 margin of error

This Wikipedia article on margin of error addresses the question that was asked in class last week, What does the newspaper article that says "plus or minus 3%" mean? In short, it's a calculation related to both sample size and confidence intervals.

You will see in the text that the name is a misnomer: there is not actually a margin (as in boundary) involved, and there are many kinds of error possible. The commonplace expression is about sampling error: and that is what we saw in Chapter 7.5. Compare question 7.85, part b, where it is asked what sample size is needed to get a proportion within .02, i.e., plus or minus 2%, with 95% confidence?

The "margin," which will be a percentage in the case of a qualitative study (such as a presidential poll, yes/no for/against etc.), depends on sample size and confidence, but not on population! A good analogy: to test the taste of soup, do you need to try a whole bowl? No, because you stir it well first. If your sample is truly random, then the sample need not be terribly large. That's a big if, isn't it?

A good reference on political polling is Mystery Pollster. (He became famous in a hurry after the 2004 election, when there were a lot of people saying with pseudo-scientific justifications that the Ohio results couldn't be right based on what the exit polls were showing.) Here's his page on sampling error, and here is a guidebook on surveys from the American Statistical Association (Chapter 10 is on margin of error).