Date:         Sat, 10 Dec 2005 22:34:26 -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: Normality Assumption for Pearson Product Moment Correlation
In-Reply-To:  <200512110108.jBB0pnPx001749@mailgw.cc.uga.edu>
Content-Type: text/plain; format=flowed

walker.627@OSU.EDU wrote:
>Could someone comment on whether or how Normality is assumed in the
>calculation of Pearson Product Moment Correlations, as can be calculated
>in proc corr?  What is the implication if Normality is violated for either
>the Dependent or Independent variables?

There's no normality assumption at all in the *calculation* of the Pearson
r.  The
assumption comes in later, when you use that r and do the hypothesis test of
H0: rho = 0.  If you assume bivariate normality (and independence, and
equally
distributed) then r is the best way to assess the strength of the
relationship
between the two variables.  That's because the bivariate normality
guarantees
a linear relationship between the variables, and r is a parametric measure
of rho.

As soon as you drop one or more of these assumptions, then things fall
apart.
If one or both are not normal, then you suddenly have a situation where you
may not have a nice linear relationship described by a simple parameter in
the
bivariate density function.  In fact, you may have a situation where
Spearman's
nonparametric estimate works nicer.

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

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