Timeline for If a measurement has 5% error, can we say it has 95% accuracy?
Current License: CC BY-SA 4.0
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| Feb 19, 2022 at 17:16 | comment | added | rob♦ | At the level of the question being asked, my goal with this answer was to inform that the language the asker proposes is already occupied by another concept. I was being intentionally non-rigorous, but I crossed the line into "wrong," and I appreciate the comments pointing this out. Rather than loading the answer with enough caveats to make each statement correct, I've added (v3) a warning to read more. I'm still okay with the wording of Point 2, even though the "probably" there is 52% (as edited in); the probability that "your" and "my" error bars overlap is about 84%. | |
| Feb 19, 2022 at 16:54 | history | edited | rob♦ | CC BY-SA 4.0 |
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| Feb 19, 2022 at 12:36 | comment | added | Andrew | @StephanKolassa Point 2 is also not really right in analyzing physics data -- actually it is a warning sign in experimental data if all the error bars cover the expected value and if they are too consistent with each other. Basically it means your error bars are too large. | |
| Feb 19, 2022 at 11:58 | comment | added | Stephan Kolassa | Statistician here. I just joined specifically to upvote @Andrew's comment, which is spot-on. Also, I have to admit I have serious doubts about your point 2., which does not relate to any statistical concept of uncertainty I am familiar with. Then again, this may be a completely correct statement in the context of physics. | |
| Feb 18, 2022 at 23:46 | comment | added | eps | to see how absurd such an interpretation could be, imagine you are interested in the US average height and randomly sample 100 people and form a 99% CI. In the (extremely unlikely but still technically possible) event all of your sample contains NBA players, the chance another sample is contained in that CI would be functionally 0%. | |
| Feb 18, 2022 at 23:32 | comment | added | eps | i'm going to have to second @Andrew 's comment -- this is a very incorrect interpretation of a CI, even given the caveat of 'roughly' | |
| Feb 18, 2022 at 22:11 | comment | added | Joshua | I have instruments that can sometimes tell you when they're not working. I ended up parsing OP's question as 10% of the measurements are faulted measurements. | |
| Feb 18, 2022 at 16:23 | history | edited | rob♦ | CC BY-SA 4.0 |
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| Feb 18, 2022 at 13:37 | comment | added | Vladimir F Героям слава | Ad 1: In some languages, the words "mistake", "error", and in this context also "uncertainty", are expressed by the same word. That is why we also meet Stack Overflow users sometimes using the word "mistake" for an error message from the program or compiler. | |
| Feb 18, 2022 at 11:44 | comment | added | Andrew | Nice answer! Just wanted to say, strictly speaking, a 1-sigma confidence interval doesn't mean there is a 68% chance that future measurements will be in the range $95<x<105$ if you measured $x=100$ on the first trial. It means that if you run the experiment lots of times, on average 68% of the confidence intervals will contain the "true" value. There's no guarantee that any one confidence interval (such as the first one) will be close to the right value. | |
| Feb 18, 2022 at 8:42 | comment | added | Paul | I would just like to add to this excellent answer that accuracy has a specific meaning in metrology (the science of measurement). Accuracy says something about the deviation from the "true" value, whereas precision is a measure of experimental reproducibility and control. | |
| Feb 18, 2022 at 5:24 | history | answered | rob♦ | CC BY-SA 4.0 |