## Confuse-a-Cat [General Statistics]

Hi ElMaestro,

» OK, I try again.

THX for your patience.

» I give you two functions of a sample x, call the functions f and g (or Z and s, or alpha and beta, or apple and banana). Symbols not important. How do we determine that f and g are independent?

Feel like a cat.

In the OP (and now?) you were talking about a

» […] how about generally, when f and g are not necessarily mean and dispersion indicators of the x-sample from a normal distribution?

Are you not happy with existing tests (questioning the independence) and are trying to develop a

Slowly I get the feeling that I can’t follow your arguments and I’m not qualified to answer your question. Sorry.

» OK, I try again.

THX for your patience.

» I give you two functions of a sample x, call the functions f and g (or Z and s, or alpha and beta, or apple and banana). Symbols not important. How do we determine that f and g are independent?

Feel like a cat.

In the OP (and now?) you were talking about a

*test*and whether the numerator and denominator constructing it are independent functions of \(x\).$$t=\frac{Z}{s},\; Z=f(x)\:\wedge\:s=g(x)$$Somehow I have the feeling that the discussion moves towards transformations. Another cup of tea.`x <- seq(1, 2, length.out = 100)`

fun <- data.frame(f.1 = sin(x), f.2 = sin(x+1), f.3 = cos(x),

f.4 = x^2, f.5 = sqrt(x), f.6 = tan(x))

corr <- data.frame(f.1 = rep(NA, 6), f.2 = NA, f.3 = NA,

f.4 = NA, f.5 = NA, f.6 = NA)

colnames(corr) <- rownames(corr) <- c("sin(x)", "sin(x+1)", "cos(x)",

"x^2", "sqrt(x)", "tan(x)")

for (j in 1:nrow(corr)) {

for (k in 1:ncol(corr)) {

if (k < j) {

corr[k, j] <- sprintf("%+7.5f", cor(fun[, j], fun[, k]))

}

}

}

corr[is.na(corr)] <- ""

corr[-nrow(corr), ]

» […] how about generally, when f and g are not necessarily mean and dispersion indicators of the x-sample from a normal distribution?

Are you not happy with existing tests (questioning the independence) and are trying to develop a

*new*one? How does the “perturbation on the data” come into play?Slowly I get the feeling that I can’t follow your arguments and I’m not qualified to answer your question. Sorry.

—

Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

*Dif-tor heh smusma*🖖Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

### 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-CatHelmut 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-CatHelmut 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