The problem is that this assumes a perfectly normal distribution. There’s a possibility that anime fandom likely doesn’t follow a Gaussian distribution (dare I say it’s almost certainly not Gaussian, because anecdotally, people seem to either be neck deep into it, or are disgusted by it, with nary anything in between). If this is true, the above calculator doesn’t exactly work.
It’s been a while since I took statistics, but yes, I guess that is a binomial distribution. It does not influence the results in the way you are implying it does, though. The calculator does actually account for it (the Population Proportion input), and the sample size actually decreases the lower/higher your proportion is. My point was that a question like, “Do you watch anime weekly,” is not like a question like, “How many hours of anime do you watch in a week,” where you certainly couldn’t assume a normal distribution for the number of hours watched.
You don’t need a massive sample size for surveys to give meaningful information. Play around with this sample size calculator if you want to see what the margins of error are: https://www.calculator.net/sample-size-calculator.html?type=2&cl2=95&ss2=4000&pc2=5&ps2=500000000&x=Calculate
The problem is that this assumes a perfectly normal distribution. There’s a possibility that anime fandom likely doesn’t follow a Gaussian distribution (dare I say it’s almost certainly not Gaussian, because anecdotally, people seem to either be neck deep into it, or are disgusted by it, with nary anything in between). If this is true, the above calculator doesn’t exactly work.
Normal distribution with regards to what? “Do you watch anime weekly” is a binary question. There really isn’t a distribution associated with that.
Wouldn’t that be a binomial distribution then?
It’s been a while since I took statistics, but yes, I guess that is a binomial distribution. It does not influence the results in the way you are implying it does, though. The calculator does actually account for it (the Population Proportion input), and the sample size actually decreases the lower/higher your proportion is. My point was that a question like, “Do you watch anime weekly,” is not like a question like, “How many hours of anime do you watch in a week,” where you certainly couldn’t assume a normal distribution for the number of hours watched.