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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


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 ttest slopes or intercepts from z on x against slopes or intercepts from z on (x,y), nor to ttest 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 ttesting 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 ttesting two sets of the "xslopes" 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 ttested 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?



