Date:         Tue, 10 Jan 2006 11:16:06 -0800
Reply-To:     David L Cassell <davidlcassell@MSN.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         David L Cassell <davidlcassell@MSN.COM>
Subject:      Re: New to Correlation
In-Reply-To:  <200601092332.k09NQQIb028199@mailgw.cc.uga.edu>
Content-Type: text/plain; format=flowed

machellewilchesky@GMAIL.COM gave some very good advice:
>This is more of a stats question than a SAS question, and as others
>have indicated to you, you can't correlate the type of variables you
>are trying to correlate.

BUT we like stat questions around here.  Well, I do.  And I occasionally
speak
using the royal 'we' when I am off my meds.  :-)

>To find the association between an ordinal (age group) and a nominal
>(mapped value)variable the correct test would be the Krusal-Wallis
>test. This test is also used when looking at a nominal variable with an
>interval or ratio variable if it's markedly non-normal.

Well, that is one option.  I think it important to point out that you have
given
good suggestions, but you have only given one suggestion for one type of
situation in each of  these groups.

>In a nutshell, the decision you make regarding which type of bi-variate
>analyses you perform is a function of the type of variables you have:
>
>1) It they are both Interval/ratio variables, you can use proc corr and
>check the pearson correlation coefficient;

Of course, the Person correlation coefficient is not always appropriate for
numeric data.  The Pearson correlation coefficient looks at the *linear*
relationship.  Sometimes one needs the Spearman correlation coefficient
or other measures.

>2) If they are both ordinal,  or if they are both or one is
>interval/ratio but markedly non-normal, you'd move to the Spearman
>correlation coefficient;

Or just if the relationship is not linear.  They don't have to be ordinal.
With ordinal data, one might opt out of the correlation coefficients
entirely,
and go with one of your sugestions below.

>3) If they are both nominal (i.e. they are categorical  without any
>ordering involved, like colour or ethnicity) then you'd use a
>Chi-square test of independence;

Or log-linear models, or Cochran-Mantel-Haenszel, or ...  It rather depends
on the data and the hypotheses and the goals.

>4) if one is dichotomous (falls into one of 2 values like 'yes' 'no')
>and one is interval/ratio then you'd use a t-test;

..or something which can handle the data if a t-test is not appropriate,
like non-parametric tests.

>5) if one is nominal with more than 2 categories, and the other was
>interval/ratio, you'd use ANOVA

.. unless #6 was more appropriate, or other stat tests...

>and finally,
>
>6) For an Ordinal variable with a Nominal variable, you'd use
>Kruskal-Wallis. As I mentioned above, this test is also used when
>looking at a nominal variable with an interval or ratio variable if the
>latter is markedly non-normal.

But K-W is not the only option here, so be sure to verify that it is what
you want before you dive in.

>IF you wanted to start looking at associations and do modeling, then
>you'd be looking at doing an ordinal logistic regression where:
>
>your ordinal variable (age group) is your dependent variable
>mapped_value would be an independent variable
>and you could add other variables here to your model to check for
>confounding, interaction, and make an attempt to get a precise estimate
>of your effect.

And yet still more options are available, all depending on the data and the
model and the hypotheses and the underlying assumptions and ...

>I know this probably all sounds a bit daunting, but you asked to be
>pointed in the right direction, and as someone else hinted, perhapse
>you might find it helpful to get some statistical analyst support? Grad
>students are usually good at things like this, and will usually be
>happy to earn some extra money to help them during their studies.

And many universities have free stat clinics set up at certain times of day,
to help students and professors in other departments, just for this type
of situation.

>I hope this helped...

I think that it did.  Thanks.

David
--
David L. Cassell
mathematical statistician
Design Pathways
3115 NW Norwood Pl.
Corvallis OR 97330

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