I am writing to ask a clarification when I am trying to use "lme4" package in R.
If in our experiment, 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:
(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
Could you tell me what is the meaning of the significant effect of "A2:B3",
what is the null hypothesis of it?