On Tue, 25 Apr 2000, Simon, Steve, PhD wrote:
> I'm helping out someone taking a Statistics class and her instructor is
> drawing a distinction between "part correlation" and "partial
> correlation". I had never heard of the term "part correlation" before.
Neither had I until I found myself teaching it, because it was part of
the extensive chapter on correlation in Glass & Stanley (1970). As
Dennis has pointed out, the "part correlation" is also called the
"semipartial correlation", which is perhaps more descriptive if you come
at the idea via partial correlation initially.
> As best I understand it, If you have three variables, A, B, C, then you
> can compute residuals for A (call it A-A') for a regression model using
> A as the dependent variable and C as the independent variable. You can
> also compute the residuals for B (call it B-B') using B as the dependent
> variable and C as the independent variable.
> The definition of partial correlation between A and B adjusting for C is
> the correlation between (A-A') and (B-B').
Right, although I've edited out the "s" you'd put on "correlation". It's
symmetrical in A and B and there's only one of it.
> The definition of part correlation between A and B adjusting for C is
> the correlation between (A-A') and B.
Not quite. The part correlation is unsymmetrical. Glass & Hopkins
(1984) use the notation r with subscript 1(2.3) for the part
correlation of variable 1 with the residuals on variable 2 having been
predicted by variable 3; and r_1(2.3) is not in general equal to
r_2(1.3). The part correlation you describe above would be r_B(A.C),
and in words one would say "between B and A with A adjusted for C"
or "of B with the residuals on A having been predicted by C" (G&H's
usage).
> The instructor claims that the part correlation is usually better
> (more interpretable?) ...
Whether "better", let alone "usually", depends highly on the context(s)
in which one practices statistics. I never found much use for the thing
myself, but then I don't have all that much use for correlation
coefficients anyway, being far more interested in the variables being
related (and in the models, linear and otherwise, relating them) than in
coefficients that are subject to so many slings and arrows of outrageous
fortune. For some purposes, as Dennis points out, it is arguably
preferable (which is not necessarily a synonym for "better"!); and G&H
(section 8.12, pp 128-130) give an interesting example involving the
correlation between a measure of intelligence (= your B) and achievement
gains during an instructional unit (pretest = C, posttest = A).
> but that SPSS and other software will not compute such a correlation.
As Dennis indicated, this is nonsense. Deponent either doesn't
understand SPSS, doesn't understand data, or doesn't understand part
correlation, or more than one of the above. What she probably (?) means
is, "SPSS doesn't have a canned routine that will produce part
correlations on demand, untouched (as Heidi Kass used to like to say) by
the human mind." Or, in different terms, an explicit call to the usual
formula for a part correlation in terms of zero-order correlations.
G&H's equation (8.11):
r_1(2.3) = (r_12 - r_13*r_23)/SQRT(1 - r^2_23)
But there is nothing whatever to prevent one from carrying out the simple
linear regression of A on C, storing the residual therefrom, and politely
asking SPSS for the correlation of that residual with B.
> Does any of this make sense? Why would you ever want to use a part
> correlation?
Ah. For _that_, you'd probably get more interesting answers from your
client's instructor than from me. I don't even believe in residualized
gain scores (used in G&H's sole example of part correlation).
-- Don.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
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