```Date: Sat, 10 Dec 2005 22:34:26 -0800 Reply-To: David L Cassell Sender: "SAS(r) Discussion" From: David L Cassell 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 _________________________________________________________________ On the road to retirement? Check out MSN Life Events for advice on how to get there! http://lifeevents.msn.com/category.aspx?cid=Retirement ```

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