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Can p's involving slopes of z on x, z on y, & z on (x,y) appear in
same Bonferroni ranking?
Posted:
Aug 12, 2012 2:07 PM
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Suppose the two simple linear regressions
z on x
z on y
and the multiple linear regression
z on (x,y).
In another thread, Ray (Koopman) has warned me that it's not legit to
t-test slopes or intercepts from z on x against slopes or intercepts
from z on (x,y), nor to t-test slopes or intercepts from z on y
against slopes or intercepts from z on (x,y). In particular, he
observed that you can't do this because, for example, the slope of the
regression line involving the x variable for z on (x,y) is not
independent of the slope of the regression line for z on x.
But suppose now that one has:
i) a p resulting from t-testing two sets of slopes of z on x, where
the two sets are obtained in two different "data selection frames"
using the same 20 samples in each frame.
ii) a p resulting from t-testing two sets of the "x-slopes" of z on
(x,y), where the two sets are obtained in the same two "data
selection frames" using the same 20 samples as in (i) above.
Can both of these p's appear in the same Bonferroni ranking, since no
property of z on x was ever t-tested against any property of z on
(x,y) in order to develop each of these p's?
Or does the nature of the Bonferroni correction also rule out allowing
these two p's to appear in the same ranking?
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