Re: Interpreting uncentered product terms

If you fail to center before multiplying A x B then the AB interaction
term will be correlated with A and with B. However, centering does not
change the correlation between A and B. For instance, if your data
came from a simple two-level factorial design in variables A and B, and
if you center A and B before multiplying AxB, then the correlation
coefficients among A, B, and AxB will all be zero. If you fail to
center, then there will be correlations between A and AxB and with B
and AxB. As a consequence of this the t-ratios on A and B will be
influenced and cannot be interpreted in the usual way... their values
depend on the "centering constants" you used for A and for B. Try
using different centering constants (including no centering... same as
subtracting zero, subtracting the appropriate averages from A and from
B, and some constants between those.

Some think that both centering and scaling by division is required. Not
to. Centering alone is necessary if you are entertaining any kind of
2nd-order terms (interactions, quadratics, etc.)

.