4 ms·

Why does the population matter? Say you are an alien, and you want to know roughly the male-to-female ratio of people. Let's say the true ratio is 50%. Wouldn

Why does the population matter? Say you are an alien, and you want to know roughly the male-to-female ratio of people. Let's say the true ratio is 50%. Wouldn't this be done by an unbiased sample that's quite small, regardless of whether there's 100M or 8B people on the planet?

HPsquared 1y ago
How do you know the sample is unbiased?
- coderatlarge 1y ago
  you could for example be sampling in a country or geography that favors male over female offspring for cultural and social reasons. then you have to refine your research question to further clarify what you are really trying to estimate.
- lordnacho 1y ago
  My point was that assuming you could solve that bias issue, why would it matter how big the population was?
Etheryte 1y ago
The whole point of sample sizing is to try and make the sample unbiased. If you're an alien, you don't know anything about your sample. As an example, say the alien wants to know the ratio of female to male lions. They sample one hunting pack and conclude that all lions are female.
- CorrectHorseBat 1y ago
  No, that's a whole different problem which bigger samples don't solve (unless you're getting close to sampling the whole population)
CorrectHorseBat 1y ago
If you go to the extreme, say you sample 100M people of 100M and 100M of 8B then the first number is exact and the second has a very small error. So the error is a function of sample size and population. In not extreme cases when your population is much bigger than the sample size you're correct that it doesn't really make any difference.
derbOac 1y ago
I wondered about that too. When I was an undergrad first learning statistics I asked my stats instructor (a grad student) about this issue and they responded with something like "the population size doesn't matter because for the assumptions of the test to be met... such and such..." I kind of accepted that answer — we were talking about asymptotic inferences — but it never seemed quite right to me. The example I gave was actually motivated in part by a sort of real-world problem I was dealing with: let's say you only want to make inferences about a population of 20 individuals. Certainly if you have a sample of 19, the confidence about the population will be much stronger than if your population is 100 million. One thing he did say which is probably right, is that that 1/20 you didn't sample might throw things off, so it's more influential in a sense than a single member of a population of 100 million. At the time I hadn't learned about exact and Jaynesian-permutation statistics, but that's probably the right way to think about finite populations. That is, something like "what are all the outcomes you could observe, and what proportion of those does my observed result represent?" It's just that usually our population is so large that the exact test approach becomes infeasible to deal with without approximations, and you end up with the typical classical asymptotic statistics. It's all maybe a moot point but it's always a good idea to think about the population you're trying to make inferences about. I think that probably includes the population size, and I think population size is probably bigger than you might initially think sometimes. As for your last question, obtaining an unbiased sample is kind of harder as the number of attributes you're being unbiased with regard to increases. It's a permutation problem again, probably implicit usually with regard to sampling representativeness.

HPsquared 1y ago

How do you know the sample is unbiased?

coderatlarge 1y ago
you could for example be sampling in a country or geography that favors male over female offspring for cultural and social reasons. then you have to refine your research question to further clarify what you are really trying to estimate.
lordnacho 1y ago
My point was that assuming you could solve that bias issue, why would it matter how big the population was?

Etheryte 1y ago

The whole point of sample sizing is to try and make the sample unbiased. If you're an alien, you don't know anything about your sample. As an example, say the alien wants to know the ratio of female to male lions. They sample one hunting pack and conclude that all lions are female.

CorrectHorseBat 1y ago
No, that's a whole different problem which bigger samples don't solve (unless you're getting close to sampling the whole population)

CorrectHorseBat 1y ago

If you go to the extreme, say you sample 100M people of 100M and 100M of 8B then the first number is exact and the second has a very small error. So the error is a function of sample size and population. In not extreme cases when your population is much bigger than the sample size you're correct that it doesn't really make any difference.

derbOac 1y ago

I wondered about that too. When I was an undergrad first learning statistics I asked my stats instructor (a grad student) about this issue and they responded with something like "the population size doesn't matter because for the assumptions of the test to be met... such and such..." I kind of accepted that answer — we were talking about asymptotic inferences — but it never seemed quite right to me. The example I gave was actually motivated in part by a sort of real-world problem I was dealing with: let's say you only want to make inferences about a population of 20 individuals. Certainly if you have a sample of 19, the confidence about the population will be much stronger than if your population is 100 million. One thing he did say which is probably right, is that that 1/20 you didn't sample might throw things off, so it's more influential in a sense than a single member of a population of 100 million. At the time I hadn't learned about exact and Jaynesian-permutation statistics, but that's probably the right way to think about finite populations. That is, something like "what are all the outcomes you could observe, and what proportion of those does my observed result represent?" It's just that usually our population is so large that the exact test approach becomes infeasible to deal with without approximations, and you end up with the typical classical asymptotic statistics. It's all maybe a moot point but it's always a good idea to think about the population you're trying to make inferences about. I think that probably includes the population size, and I think population size is probably bigger than you might initially think sometimes. As for your last question, obtaining an unbiased sample is kind of harder as the number of attributes you're being unbiased with regard to increases. It's a permutation problem again, probably implicit usually with regard to sampling representativeness.