R help - Jun 2017 - How to code the factor for ANOVA

Hi there,

I have a experimental design related question. I have done a experiment 
with 3 factors. The design matrix is similar to:
> data.frame(Factor.1 = rep(rep(0:2, each = 3),3), Factor.2 = 
rep(c("U","S","N"), 9), Factor.3 = rep(0:2, each =
9))
    Factor.1 Factor.2 Factor.3
1         0        U        0
2         0        S        0
3         0        N        0
4         1        U        0
5         1        S        0
6         1        N        0
7         2        U        0
8         2        S        0
9         2        N        0
10        0        U        1
11        0        S        1
12        0        N        1
13        1        U        1
14        1        S        1
15        1        N        1
16        2        U        1
17        2        S        1
18        2        N        1
19        0        U        2
20        0        S        2
21        0        N        2
22        1        U        2
23        1        S        2
24        1        N        2
25        2        U        2
26        2        S        2
27        2        N        2

The Factor.2 indicates the type of a fertilizer, such as urea, and the 
Factor.3 indicates the weight of the fertilizer. So the treatments with 
Factor.3 == 0 at each levels of Factor.1 are same. That means No.1, No.2 
and No.3 are same, No.4, No.5 and No.6 are same, and No.7, No.8 and No.9 
are same. Thus, in the real experiment, those treatments were not 
performed as stated in the design matrix. For instance, only No.1, No.5 
and No.9 are performed.

In the case, how to code the factor for ANOVA? I really appreciate any 
comments and suggestions. Thanks in advance.

Best regards,
Jinsong

You really really need to go through one of the many R (web) tutorials
where this is discussed in detail. Or see the Intro to R tutorial that
ships with R. This is not the proper venue for learning how R handles
linear models and how its formula interface works. A terse treatment
can be found in ?lm, ?aov, and ?formula and links therein, but a
suitable tutorial would probably be a better alternative.

Cheers,
Bert


Bert Gunter

"The trouble with having an open mind is that people keep coming along
and sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )


On Sun, Jun 25, 2017 at 10:05 PM, Jinsong Zhao <jszhao at yeah.net>
wrote:
> Hi there,
>
> I have a experimental design related question. I have done a experiment
with
> 3 factors. The design matrix is similar to:
>
>> data.frame(Factor.1 = rep(rep(0:2, each = 3),3), Factor.2 >
> rep(c("U","S","N"), 9), Factor.3 = rep(0:2,
each = 9))
>    Factor.1 Factor.2 Factor.3
> 1         0        U        0
> 2         0        S        0
> 3         0        N        0
> 4         1        U        0
> 5         1        S        0
> 6         1        N        0
> 7         2        U        0
> 8         2        S        0
> 9         2        N        0
> 10        0        U        1
> 11        0        S        1
> 12        0        N        1
> 13        1        U        1
> 14        1        S        1
> 15        1        N        1
> 16        2        U        1
> 17        2        S        1
> 18        2        N        1
> 19        0        U        2
> 20        0        S        2
> 21        0        N        2
> 22        1        U        2
> 23        1        S        2
> 24        1        N        2
> 25        2        U        2
> 26        2        S        2
> 27        2        N        2
>
> The Factor.2 indicates the type of a fertilizer, such as urea, and the
> Factor.3 indicates the weight of the fertilizer. So the treatments with
> Factor.3 == 0 at each levels of Factor.1 are same. That means No.1, No.2
and
> No.3 are same, No.4, No.5 and No.6 are same, and No.7, No.8 and No.9 are
> same. Thus, in the real experiment, those treatments were not performed as
> stated in the design matrix. For instance, only No.1, No.5 and No.9 are
> performed.
>
> In the case, how to code the factor for ANOVA? I really appreciate any
> comments and suggestions. Thanks in advance.
>
> Best regards,
> Jinsong
>
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