And with 542 survivals, assuming Poisson statistics, the one-sigma bounds are around +-4% of that.
I’ll believe Spock most significant figure, but not the other three. :-)
To summarize the important bits of the “Do steel-Vulcans provide excessive significant digits?” discussion:
Suppose that the one-sigma range tells us that where the quote has 3745, some reasonable error analysis says 3745 plus or minus 173. Then the steel-Vulcan would still say 3745 and not, e.g., 3700 or 4000, for the following reasons:
3745 is still the midpoint of the range of reasonable values, and thus the closest single value to “the truth”.
Taking meta-uncertainty into account, you still should assign some probability to how likely you are to survive, which is going to be some probably-not-round number like 1 in 3745.
This sort of accuracy is probably not very helpful to humans: I don’t have a cognitive algorithm that lets me distinguish between 1 in 3745 odds and 1 in 3812 odds, so saying “about 1 in 4000” provides all the information I’ll actually use. Presumably a species that can come up with this kind of answer in the first place feels differently about this; in fact, there’s probably some strong cultural taboo against rounding.
And with 542 survivals, assuming Poisson statistics, the one-sigma bounds are around +-4% of that. I’ll believe Spock most significant figure, but not the other three. :-)
To summarize the important bits of the “Do steel-Vulcans provide excessive significant digits?” discussion:
Suppose that the one-sigma range tells us that where the quote has 3745, some reasonable error analysis says 3745 plus or minus 173. Then the steel-Vulcan would still say 3745 and not, e.g., 3700 or 4000, for the following reasons:
3745 is still the midpoint of the range of reasonable values, and thus the closest single value to “the truth”.
Taking meta-uncertainty into account, you still should assign some probability to how likely you are to survive, which is going to be some probably-not-round number like 1 in 3745.
This sort of accuracy is probably not very helpful to humans: I don’t have a cognitive algorithm that lets me distinguish between 1 in 3745 odds and 1 in 3812 odds, so saying “about 1 in 4000” provides all the information I’ll actually use. Presumably a species that can come up with this kind of answer in the first place feels differently about this; in fact, there’s probably some strong cultural taboo against rounding.