Timeline for Can a statistic depend on a parameter?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Mar 17, 2019 at 20:06 | answer | added | Eric Gilleland | timeline score: 1 | |
| Mar 13, 2019 at 20:33 | history | edited | kjetil b halvorsen♦ | CC BY-SA 4.0 |
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| Apr 7, 2016 at 14:57 | vote | accept | An old man in the sea. | ||
| Mar 24, 2016 at 20:54 | comment | added | whuber♦ | That sounds like a fair description. I think it's close to what @dsaxton writes in an answer in referring to $\mu_0$ as a "hypothesized value" of $\mu$. It might become even clearer when you consider a one-sided t-test, where the "hypothesized value" isn't a value at all: it's an entire (half-infinite) interval, either $(-\infty,\mu_0]$ or $[\mu_0, \infty)$. Technically, the null hypothesis is a set of distributions. This might reinforce the conceptual distinction between it and the particular distribution that actually governs the data. | |
| Mar 24, 2016 at 20:42 | comment | added | An old man in the sea. | @whuber I think I get it. $\mu_0$ is the value $H_0$ states for the $\mu$ that governs the population. $\mu_0$ 's value may not be equal to the value of the parameter($\mu$) of the DGP. correct? | |
| Mar 24, 2016 at 20:33 | comment | added | whuber♦ | $\mu_0$ is not a property of the population: it has no role at all in generating $\bar X$. Therefore it is not a parameter. The acid test of a parameter is this: if, no matter what value you give to it, the (theoretical underlying) distribution of the data is unchanged, then it is not a parameter. | |
| Mar 24, 2016 at 20:33 | comment | added | An old man in the sea. | @whuber $t_{\mu_0}(\mathbf{X})=\frac{\bar X - \mu_0}{s(\mathbf{X})}$ I'm referring to $\mu_0$ | |
| Mar 24, 2016 at 19:53 | comment | added | whuber♦ | Please be specific: exactly what parameter of the population are you referring to? I'm afraid I cannot detect any part of the formula for a t statistic that involves any property of the population: all parts of it refer directly to the sample and the hypothesis: the sample mean, the sample SD, the sample size, and the hypothesized value. | |
| Mar 24, 2016 at 19:47 | comment | added | An old man in the sea. | @whuber From Casella and Berger, parameters are variables whose different values will result in different distributions. Well, in my perspective, I would say the t-stat depends on a variable, not observed, that can alter the distribution of t-stat, when evaluated at a value other than the one under the null... | |
| Mar 24, 2016 at 18:28 | answer | added | dsaxton | timeline score: 9 | |
| Mar 24, 2016 at 18:28 | comment | added | whuber♦ | In what sense do you understand a t-statistic as depending on a parameter? Let's be concrete about this: I have a dataset of numbers $2,3,4$ and I wish to use a t-test to compare its mean to the value $5$. Could you please indicate precisely where in the formula for the t-statistic a parameter appears? | |
| Mar 24, 2016 at 18:22 | history | asked | An old man in the sea. | CC BY-SA 3.0 |