Timeline for How to prove statistically that mean jumps when a parameter crosses an unknown threshold value?
Current License: CC BY-SA 4.0
30 events
| when toggle format | what | by | license | comment | |
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| Aug 29, 2022 at 3:41 | answer | added | zhaokg | timeline score: 2 | |
| S Jul 25, 2022 at 15:47 | history | bounty ended | Roman | ||
| S Jul 25, 2022 at 15:47 | history | notice removed | Roman | ||
| Jul 25, 2022 at 10:58 | comment | added | Sextus Empiricus | @Roman a problem with the 'false advertising' is that the long introduction about a random number generator is distracting. You pose a statistical question by embedding it in a made up story about some device, that can often lead to confusion. Good statisticians will ask you more about that background of the question and you end up in a situation that is similar to the xy-problem where the people that are supposed to help you with your problem are not understanding your problem. If the physical device is not real then better not tell about it. | |
| Jul 25, 2022 at 8:17 | comment | added | Roman | @dipetkov, It is not clear to me, what is not clear to you. If you can formulate your confusion as a question, I will be happy to answer this question. My data is just a set of pairs: (t_i, v_i). Where t_i and v_i are real numbers. More details I do not have and they are not relevant. | |
| Jul 25, 2022 at 8:13 | comment | added | dipetkov | What data? From my reading (which I think was careful enough), it's not clear what data you actually have. | |
| Jul 25, 2022 at 8:07 | comment | added | Roman | @dipetkov, just read the question carefully. I did not ask anything about physical functioning of the device. I had a specific question about analysis of the data. People have a tendency not to answer what was asked. Instead they "question the question". | |
| Jul 24, 2022 at 0:04 | answer | added | civilstat | timeline score: 3 | |
| Jul 22, 2022 at 9:37 | comment | added | dipetkov | I don't understand why the false advertising. Why make up a fun story about a physical device and freezing temperatures and then say "hey, it doesn't exist; I made all of it up!" You dedicate three paragraphs to this made-up story and then let people down with the denouement. | |
| Jul 22, 2022 at 9:21 | answer | added | Sextus Empiricus | timeline score: 1 | |
| Jul 20, 2022 at 18:00 | history | tweeted | twitter.com/StackStats/status/1549816419499610119 | ||
| Jul 20, 2022 at 11:22 | answer | added | user4422 | timeline score: 1 | |
| Jul 19, 2022 at 16:08 | comment | added | user225256 | Another approach is to look for two clusters in the graph of temperatures and random numbers. | |
| Jul 18, 2022 at 8:34 | comment | added | mkt | There are many relevant threads with the change-point tag. For e.g.: stats.stackexchange.com/questions/395078/… | |
| S Jul 18, 2022 at 8:18 | history | bounty started | Roman | ||
| S Jul 18, 2022 at 8:18 | history | notice added | Roman | Draw attention | |
| Jul 18, 2022 at 8:16 | history | edited | Roman | CC BY-SA 4.0 |
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| Jul 18, 2022 at 8:14 | comment | added | Roman | @mkt, would it be so obvious, I would not ask the question. My problem is high noise or, in other words, lack of data. Nothing is obvious there. We are far from the situation where we can see something with eyes. We are not sure that effect is real and, therefore, would like to have a statistical test that provides a reliable estimation. | |
| Jul 15, 2022 at 13:58 | comment | added | mkt | I don't think the existence of an interaction negates the existence of a discontinuity. But this begins to stray too far from the question at hand. | |
| Jul 15, 2022 at 13:53 | comment | added | Frank Harrell | But even the point of freezing of water is not discontinuous with respect to temperature (interacts with amount of contaminants in water). | |
| Jul 15, 2022 at 13:20 | history | edited | whuber♦ |
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| Jul 15, 2022 at 13:19 | comment | added | whuber♦ | Even classical physical laws lead to all kinds of discontinuous behavior. This, in part, is what chaos theory was invented to help explain. For numerous practical examples, check out any stress-strain study in engineering that seeks to estimate breaking points of materials or look at any phase diagram of a chemical system. | |
| Jul 15, 2022 at 12:17 | history | edited | mkt |
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| Jul 15, 2022 at 12:16 | comment | added | mkt | My general recommendation in response to your situation would be: first plot all values as a function of temperature. If there is a strong discontinuity, it should be identifiable a good visualisation. | |
| Jul 15, 2022 at 12:14 | comment | added | mkt | @Roman It would help if you edited your question to make clear that this is a made-up example and not an actual device. If you include details like this, it's natural for readers to question the details. Explain your actual underlying question/situation in addition to your hypothetical example. | |
| Jul 15, 2022 at 12:12 | comment | added | mkt | @FrankHarrell I don't follow your argument. Bimetallic strips in a variety of appliances are used to force temperature-dependent discontinuities. Phase transitions of matter are a natural physical discontinuity. Why wouldn't these be possible causes of such a change? | |
| Jul 15, 2022 at 12:06 | comment | added | Frank Harrell | That does not make sense to me. You said when the temperature outside is high something happens. High is a matter of degree. A zero-order discontinuity is unlikely in your example. | |
| Jul 15, 2022 at 11:29 | comment | added | Roman | @FrankHarrell, sorry but it was not my question. The question is not about physics, but about mathematical problem. The "device" does not exist. I made this example just to demonstrate the mathematical problem that i have. | |
| Jul 15, 2022 at 11:20 | comment | added | Frank Harrell | You would need to find a principle in physics that would justify the conclusion of a zero-order discontinuity at a single temperature point. Such discontinuities are almost never found in nature. To demonstrate the existence of such a jump you'd need in my estimation to fit a spline function in temperature with plenty of knots, demonstrate that the function is not flat (global test of all temperature parameters combined), then demonstrate that at some point there is a massive sudden change. What you are more likely to find is a gradual change with temperature. | |
| Jul 15, 2022 at 9:19 | history | asked | Roman | CC BY-SA 4.0 |