Timeline for Error estimation during measurements with high standard deviation
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 22, 2018 at 21:38 | comment | added | Zlelik | and when climate folks tell me, temperature rises 0.5C±0.1 with standard deviation 2C, then it is a little bit strange for me :) | |
| Sep 22, 2018 at 21:36 | comment | added | Zlelik | But still, what this 0.6cm means from physical point of view? standard deviation is clear, when I write 120±20cm (20 cm is standard deviation), that means if I do any measurements, then with 65% probability value will be from 100cm to 140 cm. but what is 0.6cm? Or what would you do in this example: today average water level h=(123.3±0.6)cm in the sense that you explain, then tomorrow it becomes h=(125.3±0.6)cm and in both cases, the standard deviation is 20cm, then would you declare a flood and start evacuating the people or you would do nothing? | |
| Sep 22, 2018 at 2:04 | comment | added | rob♦ | When climate folks talk about observing several centimeters of sea-level rise over the past twenty years, they are making exactly the sort of analysis you suggest in your comment. The sea has rapid waves which are much taller than a few centimeters, and tides which are much taller than typical rapid waves, so if you go the beach and take one photograph you will probably observe the water level more than a meter above or below the "mean" level. However, with many observations, it's possible to confirm that the mean sea level is significantly different today than it was in the 1990s. | |
| Sep 21, 2018 at 21:58 | comment | added | Zlelik | It is a little bit more clear, but still not 100% clear. If we tell that today average water level h=(123.3±0.6)cm in the sense that you explain, then tomorrow it becomes h=(125.3±0.6)cm and in both cases, the standard deviation is 20cm, then should we declare a flood or it is just random deviation and does not mean anything? In other words what 0.6cm means from the physical point of view, not from pure statistics? | |
| Sep 21, 2018 at 14:08 | comment | added | rob♦ | I was trying to distinguish between what you can say about any individual measurement and what you can say about an ensemble of measurements. Perhaps the edit will clarify things. | |
| Sep 21, 2018 at 14:07 | history | edited | rob♦ | CC BY-SA 4.0 |
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| Sep 21, 2018 at 7:22 | comment | added | Zlelik | Thanks for a good answer. I only did not get what means error 0.6cm in your example. If I have a normal distribution σ=20cm, that means with probability 65% value is between 100 and 140 cm. But when I do 1000 measurements and the standard deviation is the same 20cm, what is this 0.6cm? I think it does not matter how many measurements I did, but probability will be the same 65% to find the value between 100 and 140 cm and if I tell 123.3±0.6cm with standard deviation 20cm, then the probability that value is between 122.7 and 123.9 cm is very small, maybe <1%. | |
| Sep 21, 2018 at 6:09 | history | answered | rob♦ | CC BY-SA 4.0 |