Subject: Re: Attitude responses
From: Marks Nester
Date: Sat, 23 Nov 1996 02:23:39 GMT
On 22 Nov 1996 aacbrown@aol.com wrote:
> Marks Nester in
> writes:
>
> > The data tell you something whether or not you reject
> > the null hypothesis, e.g. the data may tell you that the
> > two groups are quite similar in their attitudes.
>
> If your null hypothesis is that two groups are identical, and you fail to
> reject it, there are two possibilities.
I agree. (Forgetting about validity of statistical assumptions
and appropriateness of the test.)
> The groups may actually be identical
which is generally implausible
> or you may not have enough data to distinguish them. Only the
> second explanation allows you to ask for more money.
Personally if I owned the purse strings I wouldn't want
to fund any project whose sole aim was to determine if two
groups have EXACTLY identical attitudes.
********************************************************
All readers who control budgets take note and save their
money!
********************************************************
I also do not know how one can justify asking for more
money on the basis of a hypothesis test alone. As far as I
can see one would have to take a close look at the
observed means, variances etc. Even though these may have
been used in the original hypothesis test suddenly one
is considering point/interval estimates etc. and this,
I believe, is what one should have done in the first place
instead of bothering with the hypothesis test.
--------------------------------------------------------
All of the above is very interesting but it has not
escaped my attention that my original question
has not been answered.
I said:
It seems quite implausible that two different groups
would share exactly the same attitudes.
So why do a significance test?
Who cares whether or not the two groups
differ significantly?
You said inter alia:
It is often the case that the null hypothesis is implausible,
but it is still a standard technique of classical inference.
I said inter alia:
Then perhaps classical inference is at fault. If the most plausible
position is that the groups differ then why not make that your null
hypothesis. Ask a statistician to design for you a test which has this
as the "null" hypothesis and tell him/her that, on the basis of the test,
you may be prepared to reject this new null hypothesis and concede
that the groups really have IDENTICAL attitudes.
The "inter alias" above relate to the mechanics of hypothesis
testing but do not explain why, in the vast majority of cases,
no sensible person would accept the null hypothesis yet
the null hypothesis is still tested. Why not bypass the
null hypothesis, proceed directly to point/interval
estimates, then make your pronouncements:
there are big differences between groups, or
there are small differences between groups, or
we can't really tell yet because of large variation, or
whatever.
Kind regards
Marks R. Nester
Subject: Re: Outliers
From: pfv2@cornell.edu (Paul Velleman)
Date: Sat, 23 Nov 1996 00:56:50 -0500
In article , Bill
Simpson wrote:
> Several people are mentioning the use of robust statistical methods. This
> is essentially what I said.
>
> For example, using "robust regression" amounts to an assumption that the
> errors have a double exponential (Laplace) distribution. (Since robust
> regression minimizes the absolute errors, which is the way to get the MLE
> for a model with Laplace distributed errors)
>
There are, in fact, many better robust regression methods than least
absolute residuals. Some are maximum liklihood for some error model, but
many are not.
-- Paul Velleman
Subject: Re: Attitude responses
From: emetrics@ix.netcom.com(Jason C McLoney)
Date: 23 Nov 1996 05:49:15 GMT
In market research it is not uncommon to assume that some types of
ordinal data can be treated as interval. It seems to me that the test
is whether the group male, female differ with respect to the question..
There are 2 approaches I would reccommend. One is a Chi test (if you
are using a contgency table then you may need to decompose the chi if
the predictor variable (independent) has more than 2 levels). A second
approach is the use of the non-parametric test statistics of
Mann-Whitney (though there are some issues that arise when ranks have
multiple ties and data sets are small) I am unfamiliar with SAS but
SPSS allows you to do all these tests under the various menu commands.
In <56ioti$frb@www.umsmed.edu> Warren writes:
>
>Nick,
>
>Unless you have reason to believe the categories are equally spaced, I
>would worry a little about numbering just as you said. And the
general
>test of association may not tell you what you need to know...how do
the
>proportions relate to each other on an ordinal scale.
>
>You have a couple of options, I would think.
>
>In PROC FREQ in SAS, you can select scores different from 1,2,3,4
(CMH),
>but you don't seem to have any strong belief in how much distance
there
>is between categories.
>
>You could use ridits which assign scores that take into account the
>number in each category...but I think we are back to numbering the
>categories if I remember the ridit procedure...it does some kind of
>midranking as I recall.
>
>You could use a straight ranking
>procedure...like Kruskal-Wallis-Mann-Whitney.
>
>Another technique for analyzing these data (your example fits the
classic
>mold very well) is something called a "proportional odds model." It
>would be the best choice if the assumptions are met. SAS will do this
>type of model using PROC LOGISTIC and test the "PO" assumption. If
the
>proportional odds assumption isn't reasonable, you can do a
"generalized
>logits" model using PROC CATMOD...you could compare the "not at all"
>group to all the rest. Agresti would be a good place to look for
>references, but Agresti isn't a good "elementary" text...I haven't
seen
>his new book but it might be a little more "elementary". All of these
>would require a little reading on your part concerning the
assumptions.
>
>
>n.w.nelson@education.leeds.ac.uk (nick nelson) wrote:
>>Say I have responses on an attitude scale
>>
>>eg Do you like this? lots / some / a little / not at all
>>
>>and two groups eg men and women. What is the best way to
>>establish whethere the two groups differ significantly?
>>
>>On approach I have seen involves numbering the responses 4,3,2,1
>>and working with the means, but this seems dubious due to the
>>non-interval nature of the scale.
>>
>>Alternatively you could cast the reponses in a 4x2 table and do
>>a chi2 on it, but this ignores the order information altogether.
>>
>>Is there a middle path?
>>
>>Nick.
>
>
Subject: Re: Strange model in nonparametric stats
From: thomas lumley
Date: Sat, 23 Nov 1996 11:41:44 -0800
On 22 Nov 1996, Randall C. Poe wrote:
> I'm reading a couple of statistics papers that have to do with nonparametric estimation
> in a setting with correlated measurement errors. I find the model used for the
> errors to be very strange, and I wonder if somebody could help me
> understand it intuitively.
>
> The errors e_i are taken to be samples from a stochastic process
> Z(t) with autocovariance function g(t). The i-th error is
> Z(a*x_i), where a is a scaling parameter. Large a corresponds
> to e_i widely spaced in the stochastic process (covariance
> g(a*(x_i - x_j)) and therefore not very highly correlated.
>
> Here's what I find peculiar: the parameter a also -> oo, at
> rate either faster than n (a/n -> oo), slower than n (a/n -> 0)
> or the same rate as n (a/n -> constant). The different rates
> supposedly model different correlation regimes (termed
> asymptotically independent, long-range correlation, and
> short-range correlation).
The idea of a sequence of models with n and a increasing is not intended
to be taken at face value as a description of an actual experiment. In
any real experiment a and n are both particular finite numbers, not
sequences. The authors are trying to answer the question "What are the
properties of this model for particular finite a and n if a is not small
compared to n".
As exact analysis of this problem is presumably infeasible they simplify
the problem by saying "Let n be very large and a be much smaller than/same
size as/much larger than n". In standard mathematical theory this requires
the analysis of a sequence of models which have a and n increasing to
infinity at the specified rates. The idea is that quantities proportional
to, say, a/n can be ignored in the first case but not in the second or
third case. Suppose your estimator has a bias which is roughly a/n. The
usual theory for ARMA models assumes that terms like are small enough to
be ignored, but if a and n are of comparable size in your data this may be
untrue.
A simpler example to understand comes from linear regression. Suppose we
have n observations on p variables. We all know that if n is large and p
is small the least squares estimators are good, but that if p is nearly
as big as n the estimators may be very poor. If you wanted to have some
idea of how big p could be compared to n you could study sequences of
models in which, for example, p was proportional to n or to the square root
of n or some such. Suppose you got consistent estimators when n was of
order p^2. If you know from experience that in a certain setting with
n=100 and p=10 you get good estimation you would be able to say that you
should get similarly good estimation with n=400 and p=20 in the same sort
of data.
thomas lumley
UW biostatistics
Subject: Re: Attitude responses
From: aacbrown@aol.com
Date: 24 Nov 1996 00:50:38 GMT
Marks Nester in
writes:
> Why not bypass the null hypothesis, proceed directly
> to point/interval estimates
There are many statisticians who agree with you. In particular, many
Bayesians lean toward this point of view. However I think the solid
majority of statisticians find classical hypothesis testing, which usually
includes implausible null hypotheses, to be useful.
It's really more a question of the reporting of results than of
statistical technique. I can say that "a 95% confidence interval for x is
1 to 2" or "I reject the null hypothesis that x=0 at the 5% significance
level." The first statement gives more information, the second is often
more useful for communicating results.
But if you don't like hypothesis testing, don't do it.
Aaron C. Brown
New York, NY
Subject: Question about GG distribution
From: Igor Kozintsev
Date: Sat, 23 Nov 1996 20:13:03 -0600
Hello,
The following distribution is called Generalized Gaussian
and is widely used in image processing:
\begin{equation}
f_{X}(x)=\left[\frac{\nu \eta (\nu ,\sigma )}{2\Gamma (1 / \nu)}\right]
\exp (-[\eta (\nu ,\sigma ) |x|]^\nu ),
\end{equation}
where
\begin{equation}
\eta = \eta(\nu ,\sigma ) = {\sigma}^{-1}
\left[\frac{\Gamma (3/\nu )}{\Gamma (1/\nu)}\right]^{1/2}.
\end{equation}
(sorry for this latex code)
I need to generate random numbers for this distribution
and evaluate first three moments of the distribution (conditioned
on variable to be in some interval) on the computer.
Could anybody help me with this?
I will appreciate your advice and/or reference.
Thank you,
----------------------------------------------------------------------------
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_/ _/ _/ _/ | University of Illinois
_/ _/_/_/ _/_/_/_/ | 405 N. Mathews Ave.
_/ _/ _/ | Urbana, IL 61801
_/ _/ _/ |
|
Igor Kozintsev | igor@ifp.uiuc.edu
Graduate student | Ph. (217)-244-1089
Electrical and Computer Engineering | FAX: (217)-244-8371
Image Formation & Processing Group | http://www.ifp.uiuc.edu
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Subject: Re: Occam's razor & WDB2T [was Decidability question]
From: kenneth paul collins
Date: Sat, 23 Nov 1996 21:41:46 -0500
Bob Massey wrote:
> [...] real computers can only compute a finite number
> of cycling(rational) outputs even if run forever!
Yeah. But such does not constitute a limit upon that which
is computable (via machine, or otherwise).
A machine that is designed so that it can "divide & conquer"
can render such infinities irrelevant. Basically, such a
machine transforms all problems into Geometry, and, instead
of "algorithms", use cross-correlation among continuua to
arrive at solutions.
In such an approach, an infinity can be represented on a
continuum... the "end points" are superfluous because the
continuum represents "all there is of a particular
'quality'". Then calculation can "orient" within "all there
is" within the "infinity" in question by simply "sliding"
along the continuum. "Infinities" are easily dealt with in
this way. Real solutions with respect to such are possible
in short computational periods.
There is one "caveat", however. "Solutions" that are
produced are only as accurate as are the correlations
between the continuua and the "infinities" that they
represent. This caveat is dealt with by imbuing such a
computational system with "intelligence" with respect to
such correlateions. That is, within every problem-solving
activity that occurs within such a system, there exists a
parallel continuum-correlation-with-infinity convergence
dynamic. And when one looks, one finds that such constitutes
the essence of that which is referred to as "intelligence".
What's actually happening is that the system strives
continuously to climb the gradient that is what's described
by 2nd Thermo (WDB2T).
Given a means to assess the continuum-infinity-correlations,
accuracy can be increased to any desired degree, and
reasonable accuracy can be converged upon within
relatively-short time frames. And it's easy to imbue such
systems with the capacity to "recognize" advantageous "tool"
inventions, and to produce outputs that will tell of such
tools. That is, to imbue the system with the ability to
invent the tools it needs to increase the correlations...
the machine would recognize the usefulness of lenses, for
instance, because encounters with lenses would result
in the useful increase of correlations... this'd lead to the
invention of magnifying glasses, microscopes and telescopes.
And so forth.
Our nervous systems work in precisely this fashion. I've
explored computer math using such a Geometrical approach,
and know of no problems that it doesn't handle in
straight-forward fashions.
Such systems incorporate no "tree"-like structures. They
"just" do their continuua-"sliding" cross-correlation stuff.
Coincidences among continuua in a converged "state" form a
the closest thing that this sort of system has to a
"tree"-like structure. But such is not very "tree"-like
because new continuua can be added continually, and each new
continuum makes possible formerly non-existent
"tree"-branching analogues. This means that the "tree"-like
structure is capable of growing everywhere, This renders the
conceptalization of "branching" nonsensical, hence "trees",
and their finite "time" & "space" (physical memory), are
rendered nonsensical, too. (Note, of course some physical
memory is required, and the "resolving power" of a
"continuum machine" will increase in some proportion to
physical memory. But even small "continuum machines" can
solve seemingly-"intractable" problems.)
[I apologize if this msg seems a bit "cryptic". I'm
exhausted, and close to accepting that no one will ever be
able to come and play with me. So why bother to "translate"?
What's here is here because I'm obliged to make it
available.] ken collins
Subject: Re: Occam's razor & WDB2T [was Decidability question]
From: jono@cse.ucsc.edu (Jonathan Gibbs)
Date: 24 Nov 1996 06:33:33 GMT
kenneth paul collins (KPCollins@postoffice.worldnet.att.net) wrote:
: A machine that is designed so that it can "divide & conquer"
: can render such infinities irrelevant. Basically, such a
: machine transforms all problems into Geometry, and, instead
: of "algorithms", use cross-correlation among continuua to
: arrive at solutions.
[tons snipped]
Sounds very facinating ken, can you point me to a good reference on
this stuff? Perhaps a journal paper...
--jono
--
"The human mind is a dangerous plaything, boys. When it's used for evil,
watch out! But when it's used for good, then things are much nicer."
-- The Tick
