Timeline for Instrument accuracy necessary to distinguish two values
Current License: CC BY-SA 4.0
29 events
| when toggle format | what | by | license | comment | |
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| S Feb 13, 2020 at 12:09 | history | bounty ended | KAE | ||
| S Feb 13, 2020 at 12:09 | history | notice removed | KAE | ||
| Feb 13, 2020 at 1:08 | vote | accept | KAE | ||
| Feb 12, 2020 at 18:27 | comment | added | KAE | @NuclearWang In the real-world problem that I am (over) simplifying here, repeated measurements are not possible, but this would indeed be a good approach. | |
| Feb 12, 2020 at 16:53 | comment | added | whuber♦ | @Nuclear Thank you for your comment, which is to the point. I just wish to observe that the Normality assumption is unnecessary; having a finite measurement variance suffices. And if one uses the median of the measurements, then literally any distribution with a (unique) median of zero will do. | |
| Feb 12, 2020 at 16:46 | comment | added | Nuclear Hoagie | @whuber raises a great point about repeated measurements. If your error term is normally distributed and centered on zero, your measurement tool can be as imprecise as you want, so long as you take enough measurements - the mean of the measurements will approach the true size with enough repeated measures. Repeated applications of an accurate but imprecise tool will essentially fix the precision problem. | |
| Feb 12, 2020 at 16:38 | comment | added | Firebug | @whuber true, I'll keep that in mind as well, hadn't looked at it from that perspective | |
| Feb 12, 2020 at 16:36 | comment | added | whuber♦ | @Firebug Thank you for finding those. The benefit of a new tag is that we can make it a synonym of the others (which I will do) and from then on, anyone who wants to tag their post with "metrology" will be able to do so, but the tag will link to the synonymous tags. | |
| Feb 12, 2020 at 16:31 | history | edited | Firebug |
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| Feb 12, 2020 at 16:31 | comment | added | Firebug | @whuber does it warrant a new tag anyways? Specially when we have measurement-error and measurement? | |
| Feb 12, 2020 at 16:30 | history | rollback | whuber♦ |
Rollback to Revision 6
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| Feb 12, 2020 at 16:24 | history | edited | Firebug |
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| Feb 12, 2020 at 14:57 | answer | added | usεr11852 | timeline score: 3 | |
| Feb 10, 2020 at 16:30 | comment | added | usεr11852 | @KAE, is that what you are asking though? I would view it as an incomplete answer as it stands. :) | |
| Feb 9, 2020 at 16:29 | comment | added | usεr11852 | Assuming we can have to accept the "rounded low quality estimate" as our estimate then the maximum deviation we can accept is $0.2551$ on the sense that $1.95996*0.2551 < 0.5$. | |
| Feb 6, 2020 at 18:00 | history | tweeted | twitter.com/StackStats/status/1225479411492958209 | ||
| S Feb 5, 2020 at 12:57 | history | bounty started | KAE | ||
| S Feb 5, 2020 at 12:57 | history | notice added | KAE | Draw attention | |
| Jan 27, 2020 at 18:24 | comment | added | KAE | @whuber Let's say the group of shoes was previously measured with a master reference instrument, which has an error which is an order of magnitude lower than that of my lower-quality instrument, and all had sizes that were exact integers. Then the size labels fell off so the actual shoe sizes are unknown. | |
| Jan 27, 2020 at 18:24 | history | edited | KAE | CC BY-SA 4.0 |
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| Jan 27, 2020 at 16:03 | comment | added | Ed V | Of course you are absolutely correct! The shoes cannot be exactly integer sizes and nothing is stated about the measurement noise distribution. So I just assumed this was a toy model, assumed normally distributed measurement error and tacitly assumed a reasonably accurate estimate of sigma was available. But I think it best to delete my previous comment. Thanks! | |
| Jan 27, 2020 at 15:34 | comment | added | whuber♦ | @Ed There are several pitfalls there. The first is that the measurement error is unknown: it has been estimated from a calibration experiment. The second is that it's unlikely all shoe sizes are exact integers--that would be assuming a manufacturing process with no variability at all, which is not plausible. | |
| Jan 27, 2020 at 15:31 | history | edited | KAE | CC BY-SA 4.0 |
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| Jan 27, 2020 at 13:14 | comment | added | KAE | @whuber (1) I would like my distinctions to be correct often, say 95% of the time. (2) I will measure a given shoe once. (3) I estimated my instrument's error previously as the RMS difference between my instrument and the master instrument on a set of objects of known sizes. Let's assume my instrument's error is randomly distributed around the real size and not a systematic bias such as always measuring 0.2 cm too high. I removed the reference to accuracy in the last line. | |
| Jan 27, 2020 at 13:10 | history | edited | KAE | CC BY-SA 4.0 |
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| Jan 25, 2020 at 0:59 | history | edited | Firebug |
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| Jan 24, 2020 at 22:28 | comment | added | whuber♦ | (1) How reliable do you want your distinctions to be? (2) How many times are you willing to measure a given shoe? (3) Please be aware of the difference between precision and accuracy. Your reference to the latter at the end of your question suggests there may be some systematic error in the measurement system: is that the case? | |
| Jan 24, 2020 at 21:44 | history | edited | KAE | CC BY-SA 4.0 |
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| Jan 24, 2020 at 20:19 | history | asked | KAE | CC BY-SA 4.0 |