NetNews Usenet Archive 1992 #18/NN_1992_18.iso/spool/sci/math/stat/1696

Text File | 1992-08-18 | 4.0 KB | 79 lines

Newsgroups: sci.math.stat
Path: sparky!uunet!munnari.oz.au!metro!sunb!laurel.ocs.mq.edu.au!wskelly
From: [e-mail] (William Skelly)
Subject: Re: Standard Deviation.
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Date: Tue, 18 Aug 1992 21:47:11 GMT
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In article <[e-mail]> [e-mail] (Bill Venables) writes:

[with regard to the n vs. n-1 thread...]

>What surprises me is how this quaint little thread got going at all.  The
>elementary books are wrong if they make a big issue of unbiasedness, period.

There is definitely a group of us following this list from many scientific
disciplines who use statistics, but certaintly are not up to your (and
many others on this list level of competence in the field).  Needless to
say, we are using (responsibly I hope) this list as a sounding board as we
learn our own way through unfamiliar concepts.  Having said that an
engineer was responsible for starting this thread, bless every one of them:-)
>
>In this context the *two* important quantities are (a) the sum of squares,
>since it is the squared length of the orthogonal projection of the
>observation vector onto the residual space,

Heeding my previous comment, what the hell is an "orthogonal projection of
the observation vector onto the residual space?"  I thought the Sum of
Squares was just that, x_1^2 + x_2^2 + ....?

> and (b) the degrees of freedom,
>which is the dimension of the residual space.  This latter number is
>sometimes n-1, but more often n-p where p is somewhat larger than 1.  These
>two quantities, *separately*, are what you need for virtually all
>inferential procedures, like testing and confidence intervals.  Whether you
>divide one by the other to give an estimate of the variance is up to you.
>Incidently, if you do, it turns out to be unbiased, but "so what?", really.

Bang on!  Yes, I think I see light.  This concept "degrees of freedom"
is probably a much more confusing concept.  Made even more confusing to
non-statistians, because a lot of us are thinking "n" sample size...
i.e. the number of observations we have, rather than the more abstract
(right term?) concepts of sample or residual "space."

>In my opinion statistical inference is all about reliably capturing
>information from data (and elsewhere if you are a Bayesian); it's not
>really about coming up with a number from a data set that you can show will
>be "close" to an unknown parameter value, in some special sense of "close".

I am not sure I follow you.  From my applications I only want to test
some null-hypothesis (perhaps a narrow application...but very useful!).
Generally I want to know if two samples are from the same population.
Isn't this just asking whether or not the two sample means are close?

>The trouble with many elementary books is that they get hung up on a narrow
>definition of "estimation" and elevate unbiasedness to an importance far in
>excess of what is warranted, at the same time not mentioning sufficiency,
>say, a far more important concept, (but harder to describe, of course).

Is "estimation" part of inferential or descriptive statistical anlysis
(serious question)?  It is not "elementary books" that are the problem
although I'm always looking for a better book.  The problem is that any
paper you read states that there is some assumption of "biasedness/
unbiasedness" in the methods used.  Therefore, it is important to know
and understand what these terms mean, or are you implying that such
assumptions need not be stated because they are unimportant?

I'd be interested in your definition of "sufficiency".  I've just
found an excellent text by Griffith and Amrhein (1991), I will
pass along a full reference and their definition of sufficiency,
when I get a chance.

Cheers,
Chris