[R] ANOVA for nested design

[Jinsong Zhao]

Hi there,

The following is a simple design. A and B are factors with their levels 
randomly selected. In other words, A and B are random.

The data is recorded in "abc", as:
 > dput(abc)
structure(list(water = c(12.1, 12.1, 12.8, 12.8, 14.4, 14.4,
14.7, 14.5, 23.1, 23.4, 28.1, 28.8), A = structure(c(1L, 1L,
1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L), .Label = c("1", "2",
"3"), class = "factor"), B = structure(c(1L, 1L, 2L, 2L, 3L,
3L, 4L, 4L, 5L, 5L, 6L, 6L), .Label = c("1", "2", "3", "4", "5",
"6"), class = "factor")), .Names = c("water", "A", "B"), row.names = c(NA,
-12L), class = "data.frame")

I run ems from afex package:

 > ems(n ~ A*B, nested="A/B", random="AB")
       VarianceComponent
Effect e B A
      A 1 n nb
      B 1 n
      e 1
attr(,"terms")
[1] n a b

So, the ANOVA for this design is something like:

 > summary(aov(water ~ A + Error(B), abc))

Error: B
           Df Sum Sq Mean Sq F value Pr(>F)
A          2  416.8  208.39   22.68 0.0155 *
Residuals  3   27.6    9.19
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Error: Within
           Df Sum Sq Mean Sq F value Pr(>F)
Residuals  6   0.31 0.05167
 > summary(aov(water ~ B + Error(A), abc))

Error: A
   Df Sum Sq Mean Sq
B  2  416.8   208.4

Error: Within
           Df Sum Sq Mean Sq F value   Pr(>F)
B          3  27.57   9.190   177.9 2.99e-06 ***
Residuals  6   0.31   0.052
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
 >

Is it possible to write the above two aov(...) into one aov(...)?

Any suggestions will be really appreciated. Thanks in advance.

Best regards,
Jinsong