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Re: Idempotence and "Replication Insensitivity" are equivalent ?

From: vc <boston103_at_hotmail.com>
Date: 26 Sep 2006 20:31:14 -0700
Message-ID: <1159327874.108737.273580@m73g2000cwd.googlegroups.com>


pamelafluente_at_libero.it wrote:
> vc ha scritto:
>
> > pamelaflue..._at_libero.it wrote:
> > > vc ha scritto:
> > > Since we are here (cdt), they could be the values that you find in the
> > > records
> > > for a given field. For instance, your records are variables observed on
> > >
> > > your students and the field of interest could be the number of members
> > > of their family. You could be interested in the Median family size *of
> > > your
> > > students*... You could be interested in other statistics as well, Mean,
> > > std, etc. ...
> >
> > OK, so you are saying that the collection {1,2,3} is in fact a random
> > sample realization, let's say the number of children in a family,
> > which leads us to the original question. What grounds do you have for
> > stating that having one, two or three children is equally probable ?
> > You visited three households and are now trying to extrapolate your
> > experience for say the entire city ?
> >
>
> You insist with the random sample story.
>

I insist on nothing. You said yourself that the collection is a random sample.

> Forget about random samples.
>
> I have 4 students not belonging to the same family and I want to know
> *their* median
> family size { 1 5 2 7 }.

That set *is* a random sample consisting of four elements.

>I do not want to make inference about the
> whole world. Just interested in *that* set. They do not represent, to
> me, any other set in which they are contained.

If the members of your collection are randomly chosen they do represent some population. If they are not randomly chosen, but are somehow deterministically selected, then the collection has got nothing to do with any kind of statistic, descriptive or otherwise.

>That set is all my word,
> and I want to describe only that set. The whole population is know.
>
> Is it clear? There is no inferential aim. Only description. That's why
> it's called *Descriptive Statistics*.
>You are talking of another branch
> of statistics: Statistical Inference.
>
> I repeat. I am saying that computing the median of { 1 5 2 7 }

There is no "median of {1,5,2,7}". There can be either a probability density function distribution median, or a sample distribution median.   Which is it gonna be ?

>
> * is like *
>
> computing the median of a discrete random variable X that takes
> the values 1,5,2,7 each with probability 1/4.

So where does 1/4 come from if the collection does not consist of random numbers? From heavens ?

>
> What do find hard to get in this *analogy* ?

What "analogy" is that ?

>
> I have also specified Median family size *of your students*, not any
> other (container) set.
> After that I do not know any other way to tell you.
Received on Tue Sep 26 2006 - 22:31:14 CDT

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