[R-sig-ME] To interpret the interaction between treatment factors in lme4

[Likan Zhan]

Hi all,

If both A and B are three levels treatment factors:
A:1,2,3;
B:1,2,3

And we use the following model to fit our data:
model=lmer(response~A*B+(1|subject)+(1|trial),data=xx)

and the following is the result of the fixed-effects:

Fixed-effects

(Intercept)    t=100, p<.000
  A2           t=1.0, p<.9
  A3           t=1.0, p<.9
  B2           t=10,  p<.008
  B3           t=1.0, p<.9
  A2:B3        t=100, p<.000   <===
  A3:B3        t=1.8, p<.6
  A3:B2        t=1.0, p<.7
  A3:B3        t=1.0, p<.6

How could we interpret the significant effect of "A2:B3",
what is the null hypothesis of it?

Thank you very much.

Likan