## Worded differently [General Statistics]

Hi Hötzi,

OK.

I am fully aware that when we simulate a normal dist. with some mean and some variance, then that defines their expected estimates in a sample. I.e. if a sample has a mean that is higher than the simulated mean, then that does not necessarily mean the sampled sd is higher (or lower, for that matter, that was where I was going with "perturbation"). It sounds right to think of the two as independent, in that case. Now, how about the general case, for example if we know nothing about the nature of the sample, but just look at any two functions of the sample? What property would we look for in those two functions to think they are independent?

A general understanding of the idea of independence of any two quantities derived from a sample, that is what I am looking for; point #3 above defines my question.

❝ Completely confused. Can you try again, please?

OK.

- Let us look at the wikipedia page for the t test:

"Most test statistics have the form t = Z/s, where Z and s are functions of the data."

- For the t-distribution, here Z=sample mean - mean and s=sd/sqrt(n)

- Why are Z and s independent in this case? Or more generally, and for me much more importantly, if we have two functions (f and g, or Z and s), then which properties of such functions or their input would render them independent??

I am fully aware that when we simulate a normal dist. with some mean and some variance, then that defines their expected estimates in a sample. I.e. if a sample has a mean that is higher than the simulated mean, then that does not necessarily mean the sampled sd is higher (or lower, for that matter, that was where I was going with "perturbation"). It sounds right to think of the two as independent, in that case. Now, how about the general case, for example if we know nothing about the nature of the sample, but just look at any two functions of the sample? What property would we look for in those two functions to think they are independent?

A general understanding of the idea of independence of any two quantities derived from a sample, that is what I am looking for; point #3 above defines my question.

—

Pass or fail!

ElMaestro

Pass or fail!

ElMaestro

### Complete thread:

- Statistical independence, what is it? I mean really, what is it?? ElMaestro 2020-06-27 21:35 [General Statistics]
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- Die don’t remember the last roll. Really. ElMaestro 2020-06-28 14:45
- Die don’t remember the last roll. Really. Helmut 2020-06-28 15:36
- Still none the wiser ElMaestro 2020-06-28 18:20
- You’ve lost me now. Helmut 2020-06-28 21:55
- Worded differentlyElMaestro 2020-06-29 08:30
- Still not sure what you are aiming at… Helmut 2020-06-29 16:46
- Still not sure what you are aiming at… ElMaestro 2020-06-30 00:55
- Confuse-a-Cat Helmut 2020-06-30 11:33
- Confuse-a-Cat ElMaestro 2020-06-30 13:07
- Confuse-a-Cat Helmut 2020-06-30 14:27
- pseudorandom and linear independence mittyri 2020-07-01 00:04

- Confuse-a-Cat ElMaestro 2020-06-30 13:07

- Confuse-a-Cat Helmut 2020-06-30 11:33

- Still not sure what you are aiming at… ElMaestro 2020-06-30 00:55

- Still not sure what you are aiming at… Helmut 2020-06-29 16:46

- Worded differentlyElMaestro 2020-06-29 08:30

- You’ve lost me now. Helmut 2020-06-28 21:55

- Still none the wiser ElMaestro 2020-06-28 18:20

- Die don’t remember the last roll. Really. Helmut 2020-06-28 15:36

- Die don’t remember the last roll. Really. ElMaestro 2020-06-28 14:45
- Statistical independence, what is it? I mean really, what is it?? martin 2020-07-01 08:40
- Statistical independence, what is it? I mean really, what is it?? ElMaestro 2020-07-01 09:42
- Statistical independence, what is it? I mean really, what is it?? martin 2020-07-01 10:07

- Statistical independence, what is it? I mean really, what is it?? ElMaestro 2020-07-01 09:42

- Die don’t remember the last roll. Really. Helmut 2020-06-28 13:35