Experiment designs for Agriculture

July 25, 2017
By

(This article was first published on R tutorial for Spatial Statistics, and kindly contributed to R-bloggers)

This post is more for personal use than anything else. It is just a collection of code and functions to produce some of the most used experimental designs in agriculture and animal science. 
I will not go into details about these designs. If you want to know more about what to use in which situation you can find material at the following links:
Design of Experiments (Penn State): https://onlinecourses.science.psu.edu/stat503/node/5

Statistical Methods for Bioscience (Wisconsin-Madison): http://www.stat.wisc.edu/courses/st572-larget/Spring2007/

R Packages to create several designs are presented here: https://cran.r-project.org/web/views/ExperimentalDesign.html
A very good tutorial about the use of the package Agricolae can be found here:
https://cran.r-project.org/web/packages/agricolae/vignettes/tutorial.pdf

Complete Randomized Design

This is probably the most common design, and it is generally used when conditions are uniform, so we do not need to account for variations due for example to soil conditions. 
In R we can create a simple CRD with the function expand.grid and then with some randomization:
 TR.Structure = expand.grid(rep=1:3, Treatment1=c("A","B"), Treatment2=c("A","B","C"))  
Data.CRD = TR.Structure[sample(1:nrow(TR.Structure),nrow(TR.Structure)),]

Data.CRD = cbind(PlotN=1:nrow(Data.CRD), Data.CRD[,-1])

write.csv(Data.CRD, "CompleteRandomDesign.csv", row.names=F)
The first line create a basic treatment structure, with rep that identifies the number of replicate, that looks like this:

 > TR.Structure  
rep Treatment1 Treatment2
1 1 A A
2 2 A A
3 3 A A
4 1 B A
5 2 B A
6 3 B A
7 1 A B
8 2 A B
9 3 A B
10 1 B B
11 2 B B
12 3 B B
13 1 A C
14 2 A C
15 3 A C
16 1 B C
17 2 B C
18 3 B C

The second line randomizes the whole data.frame to obtain a CRD, then we add with cbind a column at the beginning with an ID for the plot, while also eliminating the columns with rep.

Add Control

To add a Control we need to write two separate lines, one for the treatment structure and the other for the control:
 TR.Structure = expand.grid(rep=1:3, Treatment1=c("A","B"), Treatment2=c("A","B","C"))  
CR.Structure = expand.grid(rep=1:3, Treatment1=c("Control"), Treatment2=c("Control"))

Data.CCRD = rbind(TR.Structure, CR.Structure)
This will generate the following table:

 > Data.CCRD  
rep Treatment1 Treatment2
1 1 A A
2 2 A A
3 3 A A
4 1 B A
5 2 B A
6 3 B A
7 1 A B
8 2 A B
9 3 A B
10 1 B B
11 2 B B
12 3 B B
13 1 A C
14 2 A C
15 3 A C
16 1 B C
17 2 B C
18 3 B C
19 1 Control Control
20 2 Control Control
21 3 Control Control

As you can see the control is totally excluded from the rest. Now we just need to randomize, again using the function sample:

 Data.CCRD = Data.CCRD[sample(1:nrow(Data.CCRD),nrow(Data.CCRD)),]  

Data.CCRD = cbind(PlotN=1:nrow(Data.CCRD), Data.CCRD[,-1])

write.csv(Data.CCRD, "CompleteRandomDesign_Control.csv", row.names=F)

Block Design with Control

The starting is the same as before. The difference starts when we need to randomize, because in CRD we randomize over the entire table, but with blocks, we need to do it by block.
 TR.Structure = expand.grid(Treatment1=c("A","B"), Treatment2=c("A","B","C"))  
CR.Structure = expand.grid(Treatment1=c("Control"), Treatment2=c("Control"))

Data.CBD = rbind(TR.Structure, CR.Structure)

Block1 = Data.CBD[sample(1:nrow(Data.CBD),nrow(Data.CBD)),]
Block2 = Data.CBD[sample(1:nrow(Data.CBD),nrow(Data.CBD)),]
Block3 = Data.CBD[sample(1:nrow(Data.CBD),nrow(Data.CBD)),]

Data.CBD = rbind(Block1, Block2, Block3)

BlockID = rep(1:nrow(Block1),3)

Data.CBD = cbind(Block = BlockID, Data.CBD)

write.csv(Data.CBD, "BlockDesign_Control.csv", row.names=F)
As you can see from the code above, we’ve created three objects, one for each block, where we used the function sample to randomize.

Other Designs with Agricolae

The package agricolae includes many designs, which I am sure will cover all your needs in terms of setting up field and lab experiments.
We will look at some of them, so first let’s install the package:
 install.packages("agricolae")  
library(agricolae)

The main syntax for design in agricolae is the following:

 Trt1 = c("A","B","C")  
design.crd(trt=Trt1, r=3)

The result is the output below:

 > design.crd(trt=Trt1, r=3)  
$parameters
$parameters$design
[1] "crd"

$parameters$trt
[1] "A" "B" "C"

$parameters$r
[1] 3 3 3

$parameters$serie
[1] 2

$parameters$seed
[1] 1572684797

$parameters$kinds
[1] "Super-Duper"

$parameters[[7]]
[1] TRUE


$book
plots r Trt1
1 101 1 A
2 102 1 B
3 103 2 B
4 104 2 A
5 105 1 C
6 106 3 A
7 107 2 C
8 108 3 C
9 109 3 B

As you can see the function takes only one argument for treatments and another for replicates. Therefore, if we need to include a more complex treatment structure we first need to work on them:

 Trt1 = c("A","B","C")  
Trt2 = c("1","2")
Trt3 = c("+","-")

TRT.tmp = as.vector(sapply(Trt1, function(x){paste0(x,Trt2)}))
TRT = as.vector(sapply(TRT.tmp, function(x){paste0(x,Trt3)}))
TRT.Control = c(TRT, rep("Control", 3))

As you can see we have now three treatments, which are merged into unique strings within the function sapply:

 > TRT  
[1] "A1+" "A1-" "A2+" "A2-" "B1+" "B1-" "B2+" "B2-" "C1+" "C1-" "C2+" "C2-"

Then we need to include the control, and then we can use the object TRT.Control with the function design.crd, from which we can directly obtain the data.frame with $book:

 > design.crd(trt=TRT.Control, r=3)$book  
plots r TRT.Control
1 101 1 A2+
2 102 1 B1+
3 103 1 Control
4 104 1 B2+
5 105 1 A1+
6 106 1 C2+
7 107 2 A2+
8 108 1 C2-
9 109 2 Control
10 110 1 B2-
11 111 3 Control
12 112 1 Control
13 113 2 C2-
14 114 2 Control
15 115 1 C1+
16 116 2 C1+
17 117 2 B2-
18 118 1 C1-
19 119 2 C2+
20 120 3 C2-
21 121 1 A2-
22 122 2 C1-
23 123 2 A1+
24 124 3 C1+
25 125 1 B1-
26 126 3 Control
27 127 3 A1+
28 128 2 B1+
29 129 2 B2+
30 130 3 B2+
31 131 1 A1-
32 132 2 B1-
33 133 2 A2-
34 134 1 Control
35 135 3 C2+
36 136 2 Control
37 137 2 A1-
38 138 3 B1+
39 139 3 Control
40 140 3 A2-
41 141 3 A1-
42 142 3 A2+
43 143 3 B2-
44 144 3 C1-
45 145 3 B1-

Other possible designs are:

 #Random Block Design  
design.rcbd(trt=TRT.Control, r=3)$book

#Incomplete Block Design
design.bib(trt=TRT.Control, r=7, k=3)

#Split-Plot Design
design.split(Trt1, Trt2, r=3, design=c("crd"))

#Latin Square
design.lsd(trt=TRT.tmp)$sketch

Others not included above are: Alpha designs, Cyclic designs, Augmented block designs, Graeco – latin square designs, Lattice designs, Strip Plot Designs, Incomplete Latin Square Design

Final Note

For repeated measures and crossover designs I think we can create designs simply using again the function expand.grid and including time and subjects, as I did in my previous post about Power Analysis. However, there is also the package Crossover that deals specifically with crossover design and on this page you can find more packages that deal with clinical designs: https://cran.r-project.org/web/views/ClinicalTrials.html

To leave a comment for the author, please follow the link and comment on their blog: R tutorial for Spatial Statistics.

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