# Partial Correlations

Thu Nov 9 01:22:02 EST 1995

```HI,

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 cruzio.com

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