Poll: U.S. sees Obama as liberal

[Igel]

51. It's a question of sampling.

If your assumptions are right, what's the likelihood that the group you have is an accurate, proportional subset of the total population.

If the population is 200 million, the best sample is 200 million. But it's likely that if you randomly pick 100 million your sample is going to be a really good reflection of the population.

If you pick 2, it's possible that you'll pick a good sample--1 male, 1 female, 1 white and one that's non-white, etc., etc. While it's more likely that you'll pick this kind of set than any other, it's still not horribly likely.

If you have 20 different groups of 30 people, you have to calculate the probability that a random sample with 30 people will accurately reflect the larger group, the entire population. Will you get the right mix of ages or sexes or ethnicities or education or jobs?

Now, if I merge all those groups of 30 into a single group of 600, it's more likely that my one large group will mirror the overall population. The any one group of 30 may not have enough Asians or Latinos or whites, but it's likely that any bias in any one small group will be mostly countered by opposite biases in other small groups.

So a standard way of disposing of error is to combine random samples. It's widely used in meta-studies, where 5 researchers will have random samples of perhaps 300 to 1000 people and be looking for something rare. Some groups find what they're after, but other groups don't. You merge the groups into one large group, statistically, and it's easier to see if what they were looking for *was* there. Sometimes it's not, random variation gave positive results. Sometimes it was, and random variation gave negative results. Sometimes the trait's there, but too small to be reliably measured using any one of the small groups.