## Confuse-a-Cat [General Statistics]

Hi Helmut,

I am sorry that I am once again not able to tell what I am looking for . I am not talking about simulations and not about transformations either.

Two functions, generally, and the key word is really

We can think of f=mean(x) and g=median(x). I guess we can easily do a mental picture of plotting means versus medians, often seeing the strong relationship. Visually appealing. Independence?

OK then let us say f=range(x) and g=sine function of the range (x).

Or an F statistics with a variance in both f=numerator and g=denominator in an unbalanced anova.

Or Cmax and AUCt (which I guess are correlated and dependent(?), but the example is not great in my perspective since the two functions are not applied to a random sample but to a time series).

There is no end to the possible examples.

And so forth. Without debating to much about the specific cases, how do we generally approach it to define two (outcomes of) functions as being independent? Which mathematical/algebraic/statistical/whatever properties of functions render them mutually independent? When I understand it, I think or hope I will understand the nature of independence.

For inspiration: Are estimates of any two statistical moments independent? If yes, why? Is it only the first and second? Why? Is it generally so? Why? Etc. I am looking for the

I am sorry that I am once again not able to tell what I am looking for . I am not talking about simulations and not about transformations either.

Two functions, generally, and the key word is really

**generally**, when are they (or their results) to be considered independent?We can think of f=mean(x) and g=median(x). I guess we can easily do a mental picture of plotting means versus medians, often seeing the strong relationship. Visually appealing. Independence?

OK then let us say f=range(x) and g=sine function of the range (x).

Or an F statistics with a variance in both f=numerator and g=denominator in an unbalanced anova.

Or Cmax and AUCt (which I guess are correlated and dependent(?), but the example is not great in my perspective since the two functions are not applied to a random sample but to a time series).

There is no end to the possible examples.

And so forth. Without debating to much about the specific cases, how do we generally approach it to define two (outcomes of) functions as being independent? Which mathematical/algebraic/statistical/whatever properties of functions render them mutually independent? When I understand it, I think or hope I will understand the nature of independence.

For inspiration: Are estimates of any two statistical moments independent? If yes, why? Is it only the first and second? Why? Is it generally so? Why? Etc. I am looking for the

**general**clarity.—

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