Statistical sampling works
because of the law of large numbers.
Think of this as the statistician's answer to cost over-runs. The law of large numbers says that as the size of the sample increases, so does the chance it accurately reflects the whole.

If you don't think a random sample can represent a much larger group, look at the situation backwards. If you selected 1,600 people at random in the U.S. population, how likely is it that they would not represent the whole?

If the law is so great, why would you ever want to increase the sample size beyond 1,000 or so? (I'm thinking of polls and studies with thousands, or even hundreds of thousands, of respondents...). Because:

Then again, sometimes the opposite of the law is true.

Reader Beware
A legitimate political poll should come with some information to help you assess it: the number of people contacted, when the poll was conducted, and the margin of error. The margin is typically phrased as "accurate to plus or minus 3 percentage points," for a true range of uncertainty of 6 percent.

That's All There Is To It?
Sorry. We need to discuss some limitations. First of all, one time in 20, the results can be outside the margin of error. So if you read a lot of polls, some of them will be wrong. It's part of the statistical game of chance.

More important, remember that the margin of error is only valid if the poll was perfectly designed and perfectly executed. That means no errors in writing the questionnaire. And it means making sure everybody was treated equally.

Want to read about statistical issues in medical epidemiology?

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