[R] Ask for help on Error() model

[Jinsong Zhao]

Hi there,

I have a experimental design as following:

     P A B           Y
1   1 1 1 -0.18524045
2   1 1 2 -1.64226232
3   2 2 1 -0.51342697
4   2 2 2 -0.29684874
5   3 3 1  0.71566733
6   3 3 2 -1.06097480
7   4 4 1  0.05772670
8   4 4 2  0.99316677
9   5 1 1 -0.61860414
10  5 1 2  0.50257548
11  6 2 1 -0.33761079
12  6 2 2  0.43147661
13  7 3 1  0.06946383
14  7 3 2  0.85383454
15  8 4 1  0.90484162
16  8 4 2 -0.51943748
17  9 1 1  0.65379758
18  9 1 2  0.08579220
19 10 2 1 -1.71654785
20 10 2 2 -1.35651463
21 11 3 1  0.78819475
22 11 3 2  0.50247178
23 12 4 1 -0.44911823
24 12 4 2 -1.48756811

here, P is the block randomly choose from a large experimental site. A 
and B are the two factors. Y is the result of experiment, here just 
random number using rnorm(24).

As being told, this experimental design is: A and B are crossed; and 
Plot is nested in A and crossed with B.

I try to analyze the data using aov():

aov(Y~A*B + Error(P%in%A), data =df)

it give the following message:
Estimated effects may be unbalanced
Warning message:
In aov(Y ~ A * B + Error(P %in% A), data = df) : Error() model is singular

However, when I using the following code:

aov(Y~A*B + Error(P), data =df)

it gives the same result, but doesn't give the warning.

I hope to know what's the difference between the two formula.

Any suggestions or comments will be really appreciated. Thanks in advance.

Regards,
Jinsong