Its not the same, but it gives the same result. I am too tired to go into the specifics, so on some of this I ask you to take me at my word. Failing that you should be able to find some mathematical proofs that back me up with a bit of googling. Sorry for the laziness, but I am running dead tired lately.
What you are looking for with sample is to get, essentially, a small scale version of the larger population. For example, if the population is 10% musicisans then you would want 10 people to be musicians in a sample of 100. This does not always work out as probability does not work over the short term. You can flip a coin 10 times and easily have it land on the same side each time. This poses a large potential problem that kind of corrects itself.
As it turns out over a large number you start seeing the laws of probability kick in. Flip a coin a hundred times and it will be very close to 50%. On a small scale it is easy for a few improbably picks to skew the results dramatically. A sample size of hundred is thrown off 1% for every odd answer. Increase it to just 500 though and it is down to 0.2%. As a result you get a slower growth for sample size needed to iron out a possible random selection bias. You just are not that likely to get 1 of the 6,000 people with one eye in a population of 20 million with two eyes. You do want to increase the size to account for the increase in general population, but not even close to a perfect correlation.
Hopefully this isn't too confused. I am sleep deprived, in pain, and hopped up on codine so it takes a lot of effort to think clearly. I am certain Demotruk will clarify anything I leave vague.
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