I feel like reporting the median is much simpler than these other proposals, and is probably what should be adopted.
I would note that by the Markov inequality, at least 25% of Americans must think that foreign aid is more than 25% of the budget in order to get the average response we see here. So I think it’s reasonable to use the reported mean to conclude that at least a sizable minority of Americans are very confused here.
I would note that by the Markov inequality, at least 25% of Americans must think that foreign aid is more than 25% of the budget in order to get the average response we see here.
Isn’t it more like at least ~1.3% of Americans must think that foreign aid is more than 25% of the budget? The extreme case here is where p% think it’s 100% and (1-p)% think it’s exactly 25%, which comes out to p=~1.3%. 25% only seems right if (1-p)% guess 0% and p% guess 100%.
No. The average estimate is 26%, which implies at least 26% of the polled population give an estimate of 26% or higher, i.e. a very large gravel of respondents are either very confused or intentionally giving inflated answers.
No? The entire post is about how the average estimate is computed using the arithmetic mean, so you can be skewed by a small % of respondents giving very high estimates. Maybe I’m missing something though.
I was trying to note that the answers are bounded above too, and in this particular case we can infer that at least a quarter of Americans have insane takes here. (Though the math I did was totally wrong.)
I feel like reporting the median is much simpler than these other proposals, and is probably what should be adopted.
I would note that by the Markov inequality,
at least 25% of Americans must think that foreign aid is more than 25% of the budget in order to get the average response we see here.So I think it’s reasonable to use the reported mean to conclude that at least a sizable minority of Americans are very confused here.Isn’t it more like at least ~1.3% of Americans must think that foreign aid is more than 25% of the budget? The extreme case here is where p% think it’s 100% and (1-p)% think it’s exactly 25%, which comes out to p=~1.3%. 25% only seems right if (1-p)% guess 0% and p% guess 100%.
Sorry, you’re totally right.
No. The average estimate is 26%, which implies at least 26% of the polled population give an estimate of 26% or higher, i.e. a very large gravel of respondents are either very confused or intentionally giving inflated answers.
No? The entire post is about how the average estimate is computed using the arithmetic mean, so you can be skewed by a small % of respondents giving very high estimates. Maybe I’m missing something though.
I was trying to note that the answers are bounded above too, and in this particular case we can infer that at least a quarter of Americans have insane takes here. (Though the math I did was totally wrong.)
That makes sense! (That comment is replying to what seems like a different claim that seems more obviously wrong than yours though.)