[jvanderbot]

So, when one uses statistics to rule out deviations below 1E-17 radians (or whatever), you're all saying that's not accuracy, it's precision.

I'm also surprised, since IIRC precision is a measure of variance from a set of measurements, and accuracy is a measure of deviation of a value from true.

The statistical aggregation to get an estimate should (I think?) increase both the accuracy of that estimate (it will converge to the true value) and it's precision (the spread of subsequent estimates with more measurements converges to zero or some noise floor).

Here we're measuring something like eccentricity, which has a value and error bars. And the claim is we have eccentricity zero with precision high enough to rule out deviations below 1E-17 radians. So yeah, precision seems to be the better of the two, but accuracy matters.

Either way, this is insanely pedantic.

[zmgsabst]

Consider the case where there’s a configuration error — say, a cable not properly seated.

You can have results that are highly precise, but due to cable issue, not baselined correctly and therefore systemically inaccurate. Eg, faster than light neutrinos.

https://en.m.wikipedia.org/wiki/Faster-than-light_neutrino_a...

I think people get confused because they forget that systemic bias can impact precise measurements: if your system is wrong, you’ll precisely come to the wrong conclusion.

[jvanderbot]

You're talking about a specific measurement, not a derived measurement from statistical analysis, though, right? Is there an instrument? If not, we're not talking about precision or accuracy, we're talking about variance about the mean, and the mean is assumed to move towards true.

In that case, the assumption is zero mean error b/c systemic errors average out, so the accuracy is the mean minus true, and the precision is established by the Cramer rao lower bound, and estimated my the posterior variance about the mean. My point is that calling it anything but a statistical certainty (e.g. confidence interval) is just jargon.

[zmgsabst]

You can’t derive the correct value if all your measurements are (eg) +1ns due to inaccurate path length in your model.

Your collection of measurements will converge, just as if you had built the device you intended to — but they’ll converge to the wrong value, because you’re measuring the time incorrectly every measurement, and so averaging that out doesn’t do anything.

Your test is precise but inaccurate.

The whole context of this is about a specific instrument measuring electron properties — or in my example, timing neutrino flights. So… yes, we’re talking about precision and accuracy.

[jvanderbot]

You're explaining accuracy vs precision, which I get.

The answer actually was: Yes, there's only one instrument. So yes, you can't average out systemic biases. So yes, I guess you can say something about

"We measure eccentricity zero with 1 part in 1E+17, which is really precise, but you'll just have to trust us it's also accurate."

Anyway, we know what everyone meant.

[alexpetralia]

Yes, exactly: bias + imprecision = inaccuracy.