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While an overwhelming sample size isn't necessary to extrapolate results, this is poll only represents 0.00001% of voters. One voice in a hundred thousand isn't enough to make any claim.
500 is plenty as long as its random enough.
It is, though, when the selection is functionally binary.
Better / Worse / No Opinion isn't going to get you a ton of extra information with more responses.
You might be inclined to integrate individual responses and ask how things have improved / worsened / remained unchanged. And, at that point, a surveying a guy who became a Bitcoin millionaire against a guy who simply enjoys watching his browner neighbors get The Purge treatment matters more. But from the perspective of the "Are things better?" question, the answer is the same.
I'm going to go on a limb and say old conservatives are more likely to respond to a phone survey than Gen Z leftists.
Sure, but you can control for that in your sampling.
I'm not concerned about getting more information, I'm interested in getting more accurate information.
I recognize there isn't room for diverse answers when the question is 'choose 1, 2, or 3'. My thought is that turning up in Boulder, Colorado and asking the first person you see if they like chocolate, vanilla, or strawberry ice cream then claiming everyone in the city likes vanilla is misrepresentative.
You don't ask the first person you see. You ask fifty or sixty people, get their demographic data, and then feed that into a big pot. Then you pull some of them back out again based on the statistical norms across the whole country.
The principle being that you're not trying to get the "average" person in Colorado. You're trying to get the "average" person nationally, with a random sample of Colorado residents feeding that model.
I understand that. However I didn't choose Boulder, Colorado to ask a national question - I specifically posed a question irrelevant to location because the question being asked is not important to what I was attempting to illustrate.
I chose Boulder for its population size, which is proportionally the same as what the NYT has done. If the survey were completed by 50/100,000 of voters, the sample size would be 0.0005%, which in my opinion is much better than 0.00001%.
It's in the nation. I don't see why you wouldn't.
Pulling a sample is going to get you results consistent with the national average when the people you select are representative of the average
You don't see why I wouldn't ask the person in Boulder a question about the nation? I've been going on about it this entire thread. My point is the sample size, not the content of the survey nor its implications. National, international, local, intergalactic - it's not relevant to my thought because the question isn't relevant.
I was trying to show a similarity between the NYT survey and my hypothetical scenario using a population size that could serve as a common denominator, that's why I used Boulder. Bit tricky to get the average ice cream preference in Boulder when you ask only 1 in 100,000.
On one hand, I mostly agree. On the other, if the sample is correctly created (aka: both “really random” and “really representative”) then it should be enough. The additional problem is that polls are known to be poorly representative, because a lot of people just troll their way through them, giving bullshit answers that are undetectable and pollute the end results. Finally, truly random and truly representative and really hard to achieve, so that’s an additional source of errors.
Cool ignorance of statistics, brah. Larger populations don't necessarily require larger samples. They can determine the margin of error from the survey design.
Cool ignorance of my comment, brah.
Your second sentence and the first from my initial comment are saying the same thing.
Perhaps I should have written 'doesn't feel like enough' instead of 'isn't enough' to convey that it's just a thought in my head and not an empirically researched fact. Yourself and a few others evidently skipped over the bit where I wrote 'an overwhelming sample size is not required to extrapolate results'.
All I was intending to convey is that 1,625 is pretty small compared to 150,000,000 voters and I would've liked to see a sample size of even one decimal place further to the left. Apologies if I did not adequately frame my thought as strictly opinionated.
Your comment was understood & is still ignorant of statistics exactly as stated. Calling it opinion means about as much as calling "true is false" an opinion.
Yes, you have identified the definition of ignorance - I am not a statistician nor did I look up and reference any studies on the subject of sample size (just as no one in this thread has) before I made a comment on the internet.
Consider my opinion reinvented. In fact, I now agree with @WalrusDragonOnABike@reddthat.com. If five hundred is good enough for the electoral college, it's good enough for statistics.