[R] Basic question about three factor Anova

[Bogdan Lataianu]

 Read the data using scan():
#
#          a1               a2               a3               a4
#     -------------    -------------    -------------    -------------
#     b1   b2   b3     b1   b2   b3     b1   b2   b3     b1   b2   b3
#     ---  ---  ---    ---  ---  ---    ---  ---  ---    ---  ---  ---
#
# c1:
#     4.1  4.6  3.7    4.9  5.2  4.7    5.0  6.1  5.5    3.9  4.4  3.7
#     4.3  4.9  3.9    4.6  5.6  4.7    5.4  6.2  5.9    3.3  4.3  3.9
#     4.5  4.2  4.1    5.3  5.8  5.0    5.7  6.5  5.6    3.4  4.7  4.0
#     3.8  4.5  4.5    5.0  5.4  4.5    5.3  5.7  5.0    3.7  4.1  4.4
#     4.3  4.8  3.9    4.6  5.5  4.7    5.4  6.1  5.9    3.3  4.2  3.9
#
# c2:
#     4.8  5.6  5.0    4.9  5.9  5.0    6.0  6.0  6.1    4.1  4.9
4.3
#     4.5  5.8  5.2    5.5  5.3  5.4    5.7  6.3  5.3    3.9  4.7  4.1
#     5.0  5.4  4.6    5.5  5.5  4.7    5.5  5.7  5.5    4.3  4.9  3.8
#     4.6  6.1  4.9    5.3  5.7  5.1    5.7  5.9  5.8    4.0  5.3  4.7
#     5.0  5.4  4.7    5.5  5.5  4.9    5.5  5.7  5.6    4.3  4.3  3.8
#
# NOTE: Cut and paste the numbers without the leading # or labels
#

> Y <- scan()
> A <- gl(4,3, 4*3*2*5, labels=c("a1","a2","a3","a4"));
> B <- gl(3,1, 4*3*2*5, labels=c("b1","b2","b3"));
> C <- gl(2,60, 4*3*2*5, labels=c("c1","c2"));
> anova(lm(Y~A*B*C))   # all effects and interactions



In the above example, why the number of replications for A is 3, for B
is 1 and for C is 60?
And why 4*3*2*5? Is the 5 because there are 5 lines in each 4*3*2
group?
What is the logic behind this?