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 > > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code.