Timeline for Why is the population standard deviation approximated as the sample standard deviation?
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| when toggle format | what | by | license | comment | |
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| Sep 16, 2024 at 12:29 | comment | added | Christoph Hanck | Related: stats.stackexchange.com/questions/646690/… | |
| Sep 16, 2024 at 11:18 | answer | added | Dammalapati Sai Krishna | timeline score: 1 | |
| Nov 2, 2020 at 7:05 | answer | added | lamplamp | timeline score: 1 | |
| Nov 2, 2020 at 6:46 | history | edited | lamplamp | CC BY-SA 4.0 |
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| Jun 16, 2019 at 16:30 | comment | added | Michael Hardy | @jsk : "When a class shifts from teaching a z test with population standard deviation known to a t test using the sample standard deviation, sometimes unfortunate language like this is used that creates a seemingly illogical inconsistency between how the mean and standard deviation are described and used." $${}$$ Unfortunate language like WHAT? If I had any idea specifically what "language" you had in mind, I might be able to understand what you're saying. | |
| Jun 16, 2019 at 16:25 | comment | added | Michael Hardy | You wrote "However, we don't make the same assumption that the mean of the population is the approximately equal to the mean of the sample." That is simply not true. If you could tell us what caused you to think we do not use the sample mean to estimate the population mean, maybe your question could be understood. | |
| Jun 16, 2019 at 9:01 | history | tweeted | twitter.com/StackStats/status/1140182502314860545 | ||
| Jun 16, 2019 at 7:28 | history | edited | Richard Hardy |
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| Jun 16, 2019 at 4:24 | comment | added | Sigma | “I just don’t find that satisfying”. It is not satisfying, indeed. The problem is that the text you’re using is not advanced enough to formally justify/prove the statement. You will find proofs for statements like those in mathematical statistics textbooks. Check, for example, Statistical Inference by Casella & Berger. | |
| Jun 16, 2019 at 1:55 | comment | added | jsk | @Michael When a class shifts from teaching a z test with population standard deviation known to a t test using the sample standard deviation, sometimes unfortunate language like this is used that creates a seemingly illogical inconsistency between how the mean and standard deviation are described and used. The treatment of the sd as a nuisance parameter when testing a mean seems to further the confusion. Some of the handwaving done to transition from the ztest to the ttest without getting into technical details likely leads to confusion as well. | |
| Jun 16, 2019 at 1:31 | comment | added | user3391564 | I've wondered the same thing. We may consider the sample mean the best available estimate of the population mean. But we know it's not perfect, so we want to quantify our uncertainty with a p-value or CI. So we do so by estimating the standard error, with the very same data we don't entirely "trust". | |
| Jun 16, 2019 at 1:21 | answer | added | develarist | timeline score: -3 | |
| Jun 16, 2019 at 1:16 | comment | added | Michael Hardy | "why is the sample standard deviation a good approximation of the population standard deviation, but the sample mean is not a good approximation of the population mean?" Where have you seen it asserted that the sample mean is not a good approximation of the population mean? It is often used as an estimator of a population mean. | |
| Jun 16, 2019 at 0:40 | review | First posts | |||
| Jun 16, 2019 at 1:42 | |||||
| Jun 16, 2019 at 0:39 | history | asked | lamplamp | CC BY-SA 4.0 |