Confuse-a-Cat [General Sta­tis­tics]

posted by Helmut Homepage – Vienna, Austria, 2020-06-30 14:27 (294 d 22:23 ago) – Posting: # 21620
Views: 2,968

Hi ElMaestro,

» I am sorry that I am once again not able to tell what I am looking for :-D.

No, I’m sorry that I’m not able to comprehend your message. As you know, walnut-sized brain.

» 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?

I think:
» 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.

Go back to my script and

med.spl <- aggregate(xs[, 2], list(sample = xs$sample), median)
plot(mean.spl$x, med.spl$x)
cor(mean.spl$x, med.spl$x)

» Independence?

No. Both are measures of the location of the data. IMHO, that would not be suitable to construct a test as stated at the end of this post.

» 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.

Oh dear!

» Or Cmax and AUCt (which I guess are correlated and dependent(?), …

Correlated, yes. Highly sometimes. In some cases not so much (recall that one). Why? Duno. Though correlation  causation.
Actually there are hidden ([image] confounding) variables – the entire PK stuff – which drives the apparent correlation. So are they dependent even with a high correlation? I would say no. Both depend on the underlying PK.

» … 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.

Already the ones you mentioned gave me headaches.

» Without debating to much about the specific cases, how do we generally approach it to define two (outcomes of) functions as being independent?

See above. Maybe I’m completely wrong.

» 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.

Sorry, again.

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:

 Admin contact
21,419 posts in 4,475 threads, 1,510 registered users;
online 6 (0 registered, 6 guests [including 2 identified bots]).
Forum time: Wednesday 12:51 CEST (Europe/Vienna)

In the Middles Ages the lingua franca of science was Latin.
Nowadays the language of science is bad English.    Anonymous

The Bioequivalence and Bioavailability Forum is hosted by
BEBAC Ing. Helmut Schütz