Yeah how do they manage to get that kind of accuracy. Mind boggling.
Yes it is precise ... to 17 decimal places or whatever. But it is also I believe accurate? I mean are they wrong and the electron is as bumpy as my chin on a weekend?
The point is, with the information given, we haven't been told anything about the accuracy of the test. Maybe it is. Maybe it isn't. That's just blank information. We've only been told the precision.
If my measurement device always measures 42 it may by hyper-precise - but it won't helping me to detect a bump on the North Pole the height of a single sugar molecule nor anything else.
I can say Pi = 3.0000004 and be precise but not accurate.
But that's not where the confusion comes from. It comes from measuring equipment.
Example, if I have a scale that is sensitive enough to give several decimals of precision, it is very difficult to calibrate it so it is accurate.
Anyone who owns a gram scale knows you basically have to recalibrate it after every measurement. It will gladly give you many decimals of precision that is just wrong.
Veritasium - How To Measure The Tiniest Forces In The Universe https://youtu.be/pXoZQsZP2PY (it gets into measuring piconewtons and femtonetwons)
[0]: https://wp.stolaf.edu/it/files/2017/06/precsionvsaccuracy_cr...
If something is extremely accurate, it will also be extremely precise by necessity, it seems like? The difference between low precision but high & low accuracies is that points are closer to center. If you keep getting closer to center, more accurate, don't you necessarily get more precise too?
Precise has always felt like a shitty alternate of accuracy. It's accuracy but with drift, accuracy to not the right place. But if you're accurate, you're both.
Am I missing something? And, here specifically, if this is a case of very high precision but lower accuracy, can someone explain what the drift from center is about? Isn't a radius a radius? Where is the drift off center in these measures?
Accurate but imprecise means we can throw more and more shells down range and eventually hit the target. Inaccurate and imprecise means we may never hit the target. Inaccurate but precise also means we may never hit the target, but if we could introduce a second, different measurement that was accurate, we could compensate.
https://alexpetralia.com/2023/01/31/what-does-it-mean-for-da...
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.
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.
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.
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.
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.
Accuracy is about how well those measurements reflect reality.
If you are just trying to see how smooth a ball is by measuring the diameter many times at different points, then a high precision can tell you that, even if the actual diameter is different to your measurement.
You don't care about the actual diameter, you care about the variation in it.
And again, I was only commenting on what was being commented on here. I don't know if the experiment was also highly accurate. But people here were commenting on the precision and calling it accuracy.
Say we had a perfect ruler to measure the length of something. It's absolutely precise and accurate. All measurements from it return the exact, same value, and preternaturally we know it's the "correct" value.
Now say some bandit comes in while we're not looking and adds a small chunck of diamond to the end of the ruler without telling us. Our ruler is still precise, but no longer accurate. If we take many measurements with it, they always come back with the same value. Averaging those values does not improve the accuracy at all.
Alternatively, say the bandit starts randomly changing the temperature of the room we are in. Thermal expansion is constantly changing the length of the ruler. The average length of the ruler is still the same, so it's still accurate, but it's no longer precise. We could average the measurements we take with it and get a more precise measurement.
What the central limit theorem says is that the averages of our measurements will be normally distributed, even if the change in temperature is not.