Partial Correlations

Nadine Nemec & Peter Wilde nadpete at
Thu Nov 9 01:22:02 EST 1995


   Partial correlations are based on the model that a dependent variable (y) is 
correlated with a set of independent variables (x1,x2,..xn).  Each partial 
correlation measures the correlation of y with a given xi, with the other 
independent variables held constant - the correlation with just that independent 
variable alone.  A good discussion can be found in Zar, Biostatistics.

   A significant negative partial correlation means that y varies inversely with the 
given xi  (i.e., as xi increases, y decreases and vica versa).  In other words, 
there may be a linear relationship between the variables with a negative slope. So, 
a significant negative partial correlation means the same as a positive one, just 
that the sign of the relationship is negative.  A non-significant, or zero, partial 
correlation is just that:  statistically, there is no correlation between the y and 
xi - variation in xi is not reflected with a variation in y.

  The preceeding is best stated in terms of null hypotheses.  See the texts for 
that.  An important point with correlation is that a non-zero correlation between 
two variables does not imply there is a causal relationship between the two, only 
that they vary together in a linear way.  

Pete Wilde
Kinnetic Laboratories, Inc.
kinnetic at

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