
Hi, I am turning to you with a (hopefully simple?) stats question. I would
like to test equality of two correlation coefficients in a setting with
three variables X,Y,Z, i.e. equality of r(X,Y) and r(Z,Y). I have found a
formula to transform the "2 dependent correlations difference" to
t-distribution with N-3 df:
t = (rxy - rzy)* SQRT[{(n - 3)(1 + rxz)}/ {2(1 - rxy^2 - rxz^2 - rzy^2 +
2rxy*rxz*rzy)}]
(Blalock, H., 1972. Social Statistics. NY: McGraw-Hill. Page 406-7). Am
actually not sure whether this is exact or approximate (even given normality
assumption, the Fisher's Z-transform which this is - I assume - based on, is
approximate, right?).
But to make it a bit more complicated, Shapiro-Wilks test of normality gives
p=0.022 for variable X. Therefore assuming normality may not be safe
(justifiable) at all? What do I do then? Do I report this test as
"assymptotically valid", or do I run some other test?

Any ideas? Many thanks in advance,
Jaroslav

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