1. Division of Germplasm Conservation, ICAR-National Bureau of Plant Genetic Resources, New Delhi.

1. Division of Genetics, ICAR-Indian Agricultural Research Institute, New Delhi.

1. Division of Genomic Resources, ICAR-National Bureau of Plant Genetic Resources, New Delhi.

1. Division of Germplasm Evaluation, ICAR-National Bureau of Plant Genetic Resources, New Delhi.

# 1 Overview

The software augmentedRCBD is built on the R statistical programming language as an add-on (or ‘package’ in the R lingua franca). It performs the analysis of data generated from experiments in augmented randomised complete block design according to Federer, W.T. (1956a, 1956b, 1961; 1976). It also computes analysis of variance, adjusted means, descriptive statistics, genetic variability statistics etc. and includes options for data visualization and report generation.

This tutorial aims to educate the users in utilising this package for performing such analysis. Utilising augmentedRCBD for data analysis requires a basic knowledge of R programming language. However, as many of the intended end-users may not be familiar with R, sections 2 to 4 give a ‘gentle’ introduction to R, especially those aspects which are necessary to get augmentedRCBD up and running for performing data analysis in a Windows environment. Users already familiar with R can feel free to skip to section 5.

# 2 R software

It is a free software environment for statistical computing and graphics. It is free and open source, platform independent (works on Linux, Windows or MacOS), very flexible, comprehensive with robust interfaces for all the popular programming languages as well as databases. It is strengthened by its diverse library of add-on packages extending its ability as well as the incredible community support. It is one of the most popular tools being used in academia today (Tippmann, 2015).

# 3 Getting Started

This section details the steps required to set up the R programming environment under a third-party interface called RStudio in Windows.

## 3.1 Installing R

Download and install R for Windows from http://cran.r-project.org/bin/windows/base/.

Fig. 1: The R download location.

## 3.2 Installing RStudio

The basic command line interface in native R is rather limiting. There are several interfaces which enhance it’s functionality and ease of use, RStudio being one of the most popular among R programmers.

Download and install RStudio for Windows from https://www.rstudio.com/products/rstudio/download/#download

Fig. 2: The RStudio download location.

## 3.3 The RStudio Interface

On opening RStudio, the default interface with four panes/windows is visible as follows. Few panes have different tabs.

Fig. 3: The default RStudio interface with the four panes.

### 3.3.1 Console

This is where the action happens. Here any authentic R code typed after the ‘>’ prompt will be executed after pressing ‘Enter’ to generate the output.

For example, type 1+1 in the console and press ‘Enter’.

1+1
[1] 2

### 3.3.2 Source

This is where R Scripts (collection of code) can be created and edited. R scripts are text files with a .R extension. R Code for analysis can be typed and saved in such R scripts. New scripts can be opened by clicking ‘File|New File’ and selecting ‘R Script’. Code can be selected from R Scripts and sent to console for evaluation by clicking ‘Run’ on the ‘Source’ pane or by pressing ‘Ctrl + Enter’.

### 3.3.3 Environment|History|Connections

The ‘Environment’ tab shows the list of all the ‘objects’ (see section 4.3) defined in the current R session. It has also some buttons up top to open, save and clear the environment as well as few options for import of data under Import Dataset.

The ‘History’ tab shows a history of all the code that was previously evaluated. This is useful, if you want to go back to some code.

The ‘Connections’ tab helps to establish and manage connections with different databases and data sources.

### 3.3.4 Files|Plots|Packages|Help|Viewer

The ‘Files’ tab shows a sleek file browser to access the file directory in the computer with options to manage the working directory (see section 4.1) under the More button.

The ‘Plots’ tab shows all the plots generated in R with buttons to delete unnecessary ones and export useful ones as a pdf file or as an image file.

The ‘Packages’ tab shows a list of all the R add-on packages installed. The check box on the left shows whether they are loaded or not. There are also buttons to install and update R packages.

The ‘Viewer’ tab shows any web content output generated by an R code.

# 4 Some Basics

This section describes some basics to enable the users to have a working knowledge in R in order to use augmentedRCBD.

## 4.1 Working Directory

It is a file path to a folder on the computer which is recognised by R as the default location to read files from or write files to. The code getwd() shows the current working directory, while setwd() can be used to change the existing working directory.

# Print current working directory
getwd()
[1] "C:/Users/Computer/Documents"
# Set new working directory
setwd("C:/Data Analysis/")
getwd()
[1] "C:/Data Analysis/"

One key detail is that file paths in R uses forward slashes (/) as in MacOS or Linux, unlike backward slashes (\) in Windows. This needs to be considered while copying paths from default Windows file explorer.

## 4.2 Expression and Assignment

Expressions are instructions in the form of code to be entered after the > prompt in the console. Expressions can be a constant, an arithmetic or a condition. A more advanced and most useful expression is a function call (see section 4.3).

# Constant
123
[1] 123
# Arithmetic (add two numbers)
1 + 2
[1] 3
# Condition
34 > 25
[1] TRUE
1 == 2
[1] FALSE
# Function call (mean of a series of numbers)
mean(c(25,56,89,35))
[1] 51.25

Information from an expression can be stored as an ‘object’ (see section 4.3) by assigning a name using the operator ‘<-’.

# Assign the result of the expression 1 + 2 to an object 'a'
a <- 1 + 2
a
[1] 3

It is recommended to add comments to explain the code by using the ‘#’ sign. Any code after the ‘#’ sign will be ignored by R.

## 4.3 Objects and Functions

R is an object-oriented programming language (OOP). Any kind or construct created in R is an ‘object’. Each object has a ‘class’ (shown using the class() function) and different ‘attributes’ which defines what operations can be done on that object. There are different types of data structure objects in R such as vectors, matrices, factors, data frames, and lists. A ‘function’ is also an object, which defines a procedure or a sequence of expressions.

### 4.3.1 Vector

A vector is a collection of elements of a single type (or ‘mode’). The common vector modes are ‘numeric’, ‘integer’, ‘character’ and ‘logical’. The c() function is used to create vectors. The functions class(), str() and length() show the attributes of vectors.

Vector modes ‘numeric’ stores real numbers, while ‘integer’ stores integers, which can be enforced by suffixing elements with ‘L’.

# A numeric vector
a <- c(1, 2, 3.3)
class(a)
[1] "numeric"
str(a)
 num [1:3] 1 2 3.3
length(a)
[1] 3
# An integer vector
b <- c(1L, 2L, 3L)
class(b)
[1] "integer"
str(b)
 int [1:3] 1 2 3
length(b)
[1] 3

The vector mode ‘character’ store text.

# A character vector
c <- c("one","two","three")
class(c)
[1] "character"
str(c)
 chr [1:3] "one" "two" "three"
length(c)
[1] 3

The vector mode ‘logical’ stores ‘TRUE’ OR ‘FALSE’ logical data.

#logical vector
d <- c(TRUE,TRUE,TRUE,FALSE,TRUE,FALSE)
class(d)
[1] "logical"
str(d)
 logi [1:6] TRUE TRUE TRUE FALSE TRUE FALSE
length(d)
[1] 6

### 4.3.2 Factor

A ‘factor’ in R stores data from categorical data in variables as different levels.

catg <- c("male","female","female","male","male")
catg
[1] "male"   "female" "female" "male"   "male"  
is.factor(catg)
[1] FALSE
# Apply the factor function
factor_catg <- factor(catg)

factor_catg
[1] male   female female male   male
Levels: female male
is.factor(factor_catg)
[1] TRUE
class(factor_catg)
[1] "factor"
str(factor_catg)
 Factor w/ 2 levels "female","male": 2 1 1 2 2

A character, numeric or integer vector can be transformed to a factor by using the as.factor() function.

# Conversion of numeric to factor
a <- c(1, 2, 3.3)
class(a)
[1] "numeric"
str(a)
 num [1:3] 1 2 3.3
fac_a <- as.factor(a)
class(fac_a)
[1] "factor"
str(fac_a)
 Factor w/ 3 levels "1","2","3.3": 1 2 3
# Conversion of integer to factor
b <- c(1L, 2L, 3L)
class(b)
[1] "integer"
str(b)
 int [1:3] 1 2 3
fac_b <- as.factor(b)
class(fac_b)
[1] "factor"
str(fac_b)
 Factor w/ 3 levels "1","2","3": 1 2 3
# Conversion of character to factor
c <- c("one","two","three")
class(c)
[1] "character"
str(c)
 chr [1:3] "one" "two" "three"
fac_c <- as.factor(c)
class(fac_c)
[1] "factor"
str(fac_c)
 Factor w/ 3 levels "one","three",..: 1 3 2

### 4.3.3 Matrix

A ‘matrix’ in R is a vector with the attributes ‘nrow’ and ‘ncol’.

# Generate 5 * 4 numeric matrix
m <- matrix(1:20, nrow = 5, ncol = 4)
m
     [,1] [,2] [,3] [,4]
[1,]    1    6   11   16
[2,]    2    7   12   17
[3,]    3    8   13   18
[4,]    4    9   14   19
[5,]    5   10   15   20
class(m)
[1] "matrix" "array" 
typeof(m)
[1] "integer"
# Dimensions of m
dim(m) 
[1] 5 4

### 4.3.4 List

A ‘list’ is a container containing different objects. The contents of list need not be of the same type or mode. A list can encompass a mixture of data types such as vectors, matrices, data frames, other lists or any other data structure.

w <- list(a, m, d, list(b, c))
class(w)
[1] "list"
str(w)
List of 4
$: num [1:3] 1 2 3.3$ : int [1:5, 1:4] 1 2 3 4 5 6 7 8 9 10 ...
$: logi [1:6] TRUE TRUE TRUE FALSE TRUE FALSE$ :List of 2
..$: int [1:3] 1 2 3 ..$ : chr [1:3] "one" "two" "three"

### 4.3.5 Data Frame

A ‘data frame’ in R is a special kind of list with every element having equal length. It is very important for handling tabular data in R. It is a array like structure with rows and columns. Each column needs to be of a single data type, however data type can vary between columns.

L <- LETTERS[1:4]
y <- 1:4
z <- c("This", "is", "a", "data frame")
df <- data.frame(L, x = 1, y, z)
df
  L x y          z
1 A 1 1       This
2 B 1 2         is
3 C 1 3          a
4 D 1 4 data frame
str(df)
'data.frame':   4 obs. of  4 variables:
$L: chr "A" "B" "C" "D"$ x: num  1 1 1 1
$y: int 1 2 3 4$ z: chr  "This" "is" "a" "data frame"
attributes(df)
$names [1] "L" "x" "y" "z"$class
[1] "data.frame"

$row.names [1] 1 2 3 4 rownames(df) [1] "1" "2" "3" "4" colnames(df) [1] "L" "x" "y" "z" ### 4.3.6 Functions All of the work in R is done by functions. It is an object defining a procedure which takes one or more objects as input (or ‘arguments’), performs some action on them and finally gives a new object as output (or ‘return’). class(), mean(), getwd(), +, etc. are all functions. For example the function mean() takes a numeric vector as argument and returns the mean as a numeric vector. a <- c(1, 2, 3.3) mean(a) [1] 2.1 The user can also create custom functions. For example the function foo adds two numbers and gives the result. foo <- function(n1, n2) { out <- n1 + n2 return(out) } foo(2,3) [1] 5 ## 4.4 Special Elements In addition to numbers and text, there are some special elements which can be included in different data objects. NA (not available) indicates missing data. x <- c(2.5, NA, 8.6) y <- c(TRUE, FALSE, NA) z <- c("k", NA, "m", "n", "o") is.na(x) [1] FALSE TRUE FALSE is.na(z) [1] FALSE TRUE FALSE FALSE FALSE anyNA(x) [1] TRUE a [1] 1.0 2.0 3.3 is.na(a) [1] FALSE FALSE FALSE Inf indicates infinity. 1/0 [1] Inf NaN (Not a Number) indicates any undefined value. 0/0 [1] NaN ## 4.5 Indexing The [ function is used to extract elements of an object by indexing (numeric or logical). Named elements in lists and data frames can be extracted by using the $ operator.

Consider a vector a.

a <- c(1, 2, 3.3, 2.8, 6.7)
# Numeric indexing
# Extract first element
a[1]
[1] 1
# Extract elements 2:3
a[2:3]
[1] 2.0 3.3
# Logical indexing
a[a > 3]
[1] 3.3 6.7

Consider a matrix m.

m <- matrix(1:9, nrow = 3, ncol = 3, byrow = TRUE)
colnames(m) <- c('a', 'b', 'c')
m
     a b c
[1,] 1 2 3
[2,] 4 5 6
[3,] 7 8 9
# Extract elements
m[,2] # 2nd column of matrix
[1] 2 5 8
m[3,] # 3rd row of matrix
a b c
7 8 9 
m[2:3, 1:3] # rows 2,3 of columns 1,2,3 
     a b c
[1,] 4 5 6
[2,] 7 8 9
m[2,2] # Element in 2nd column of 2nd row
b
5 
m[, 'b'] # Column 'b'
[1] 2 5 8
m[, c('a', 'c')] # Column 'a' and 'c'
     a c
[1,] 1 3
[2,] 4 6
[3,] 7 9

Consider a list w.

w <- list(vec = a, mat = m, data = df, alist = list(b, c))

# Indexing by number
w[2] # As list structure
$mat a b c [1,] 1 2 3 [2,] 4 5 6 [3,] 7 8 9 w[[2]] # Without list structure  a b c [1,] 1 2 3 [2,] 4 5 6 [3,] 7 8 9 # Indexing by name w$vec
[1] 1.0 2.0 3.3 2.8 6.7
w$data  L x y z 1 A 1 1 This 2 B 1 2 is 3 C 1 3 a 4 D 1 4 data frame Consider a data frame df. df  L x y z 1 A 1 1 This 2 B 1 2 is 3 C 1 3 a 4 D 1 4 data frame # Indexing by number df[,2] # 2nd column of data frame [1] 1 1 1 1 df[2] # 2nd column of data frame  x 1 1 2 1 3 1 4 1 df[3,] # 3rd row of data frame  L x y z 3 C 1 3 a df[2:3, 1:3] # rows 2,3 of columns 1,2,3   L x y 2 B 1 2 3 C 1 3 df[2,2] # Element in 2nd column of 2nd row [1] 1 # Indexing by name df$L
[1] "A" "B" "C" "D"
df$z [1] "This" "is" "a" "data frame" ## 4.6 Help Documentation The help documentation regarding any function can be viewed using the ? or help() function. The help documentation shows the default usage of the function including, the arguments that are taken by the function and the type of output object returned (‘Value’). ?ls help(ls) ?mean ?setwd ## 4.7 Packages Packages in R are collections of R functions, data, and compiled code in a well-defined format. They are add-ons which extend the functionality of R and at present, there are 17425 packages available for deployment and use at the official repository, the Comprehensive R Archive Network (CRAN). Valid packages from CRAN can be installed by using the install.packages() command. # Install the package 'readxl' for importing data from excel install.packages(readxl) Installed packages can be loaded using the function library(). # Install the package 'readxl' for importing data from excel library(readxl) ## 4.8 Importing and Exporting Tabular Data Tabular data from a spreadsheet can be imported into R in different ways. Consider some data such as in Table 1. Copy this data in to a spreadsheet editor such as MS Excel and save it as augdata.csv, a comma-separated-value file and augdata.xlsx, an Excel file in the working directory (getwd()). Table 1: Example data from an experiment in augmented RCBD design. blk trt y1 y2 I 1 92 258 I 2 79 224 I 3 87 238 I 4 81 278 I 7 96 347 I 11 89 300 I 12 82 289 II 1 79 260 II 2 81 220 II 3 81 237 II 4 91 227 II 5 79 281 II 9 78 311 III 1 83 250 III 2 77 240 III 3 78 268 III 4 78 287 III 8 70 226 III 6 75 395 III 10 74 450 The augdata.csv file can be imported into R using the read.csv() function or the read_csv() function in the readr package. data <- read.csv(file = "augdata.csv") str(data) 'data.frame': 20 obs. of 4 variables:$ blk: Factor w/ 3 levels "I","II","III": 1 1 1 1 1 1 1 2 2 2 ...
$trt: num 1 2 3 4 7 11 12 1 2 3 ...$ y1 : num  92 79 87 81 96 89 82 79 81 81 ...
$y2 : num 258 224 238 278 347 300 289 260 220 237 ... The argument stringsAsFactors = FALSE reads the text columns as of type character instead of the default factor. data <- read.csv(file = "augdata.csv", stringsAsFactors = FALSE) str(data) 'data.frame': 20 obs. of 4 variables:$ blk: chr  "I" "I" "I" "I" ...
$trt: num 1 2 3 4 7 11 12 1 2 3 ...$ y1 : num  92 79 87 81 96 89 82 79 81 81 ...
$y2 : num 258 224 238 278 347 300 289 260 220 237 ... The augdata.xlsx file can be imported into R using the read_excel() function in the readxl package. library(readxl) data <- read_excel(path = "augdata.xlsx") 'data.frame': 20 obs. of 4 variables:$ blk: chr  "I" "I" "I" "I" ...
$trt: num 1 2 3 4 7 11 12 1 2 3 ...$ y1 : num  92 79 87 81 96 89 82 79 81 81 ...
$y2 : num 258 224 238 278 347 300 289 260 220 237 ... The tabular data can be exported from R to a .csv (comma-separated-value) file by the write.csv() function. write.csv(x = data, file = "augdata.csv") ## 4.9 Additional Resources To learn more about R, there are umpteen number of online tutorials as well as free courses available. Queries about various aspects can be put to the active and vibrant R community online. # 5 Installation of augmentedRCBD The package augmentedRCBD can be installed using the following functions. # Install from CRAN install.packages('augmentedRCBD', dependencies=TRUE) # Install development version from Github if (!require('devtools')) install.packages('devtools') library(devtools) install_github("aravind-j/augmentedRCBD") The stable release is hosted in CRAN (see section 4.7), while the under-development version is hosted as a Github repository. To install from github, you need to use the install_github() function from devtools package. Then the package can be loaded using the function library(augmentedRCBD)  -------------------------------------------------------------------------------- Welcome to augmentedRCBD version 0.1.4.9000 # To know how to use this package type: browseVignettes(package = 'augmentedRCBD') for the package vignette. # To know whats new in this version type: news(package='augmentedRCBD') for the NEWS file. # To cite the methods in the package type: citation(package='augmentedRCBD') # To suppress this message use: suppressPackageStartupMessages(library(augmentedRCBD)) -------------------------------------------------------------------------------- The current version of the package is 0.1.4. The previous versions are as follows. Table 2. Version history of augmentedRCBD R package. [1] "Packages 'RCurl', 'httr' and 'XML' are required to generate this table" To know detailed history of changes use news(package='augmentedRCBD'). # 6 Data Format Certain details need to be considered for arranging experimental data for analysis using the augmentedRCBD package. The data should be in long/vertical form, where each row has the data from one genotype per block. For example, consider the following data (Table 3) recorded for a trait from an experiment laid out in an augmented block design with 3 blocks and 12 genotypes(or treatment) with 6 to 7 genotypes/block. 8 genotypes (Test, G 5 to G 12) are not replicated, while 4 genotypes (Check, G 1 to G 4) are replicated. Table 3: Data from an experiment in augmented RCBD design.  Block I G12 G4 G11 G2 G1 G7 G3 82 81 89 79 92 96 87 Block II G5 G9 – G3 G1 G2 G4 79 78 – 81 79 81 91 Block III G4 G2 G1 G6 G10 G3 G8 78 77 83 75 74 78 70 This data needs to be arranged with columns showing block, genotype (or treatment) and the data of the trait for each genotype per block (Table 4). Table 4: Data from an experiment in augmented RCBD design arranged in long-form. Block Treatment Trait Block I G 1 92 Block I G 2 79 Block I G 3 87 Block I G 4 81 Block I G 7 96 Block I G 11 89 Block I G 12 82 Block II G 1 79 Block II G 2 81 Block II G 3 81 Block II G 4 91 Block II G 5 79 Block II G 9 78 Block III G 1 83 Block III G 2 77 Block III G 3 78 Block III G 4 78 Block III G 8 70 Block III G 6 75 Block III G 10 74 The data for block and genotype (or treatment) can also be depicted as numbers (Table 5). Table 5: Data from an experiment in augmented RCBD design arranged in long-form (Block and Treatment as numbers). Block Treatment Trait 1 1 92 1 2 79 1 3 87 1 4 81 1 7 96 1 11 89 1 12 82 2 1 79 2 2 81 2 3 81 2 4 91 2 5 79 2 9 78 3 1 83 3 2 77 3 3 78 3 4 78 3 8 70 3 6 75 3 10 74 Multiple traits can be added as additional columns (Table 6). Table 6: Data from an experiment in augmented RCBD design arranged in long-form (Multiple traits). Block Treatment Trait1 Trait2 Block I G 1 92 258 Block I G 2 79 224 Block I G 3 87 238 Block I G 4 81 278 Block I G 7 96 347 Block I G 11 89 300 Block I G 12 82 289 Block II G 1 79 260 Block II G 2 81 220 Block II G 3 81 237 Block II G 4 91 227 Block II G 5 79 281 Block II G 9 78 311 Block III G 1 83 250 Block III G 2 77 240 Block III G 3 78 268 Block III G 4 78 287 Block III G 8 70 226 Block III G 6 75 395 Block III G 10 74 450 Data should preferably be balanced i.e. all the check genotypes should be present in all the blocks. If not, a warning is issued. The number of test genotypes can vary within a block. There should not be any missing values. Rows of genotypes with missing values for one or more traits should be removed. Such a tabular data should be imported (see section 7.8) into R as a data frame object (see section 4.3.5). The columns with the block and treatment categorical data should of the type factor (see section 4.3.2), while the column(s) with the trait data should be of the type integer or numeric (see section 4.3.1). # 7 Data Analysis for a Single Trait Analysis of data for a single trait can be performed by using augmentedRCBD function. It generates an object of class augmentedRCBD. Such an object can then be taken as input by the several functions to print the results to console (print.augmentedRCBD), generate descriptive statistics from adjusted means (describe.augmentedRCBD), plot frequency distribution (freqdist.augmentedRCBD) and computed genetic variability statistics (gva.augmentedRCBD). All these outputs can also be exported as a MS Word report using the report.augmentedRCBD function. [1] "package 'diagram' is required to generate this figure" Fig. 4. Workflow for analysis of single traits with augmentedRCBD. ## 7.1 augmentedRCBD() Consider the data in Table 1. The data can be imported into R as vectors as follows. blk <- c(1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3) trt <- c(1, 2, 3, 4, 7, 11, 12, 1, 2, 3, 4, 5, 9, 1, 2, 3, 4, 8, 6, 10) y1 <- c(92, 79, 87, 81, 96, 89, 82, 79, 81, 81, 91, 79, 78, 83, 77, 78, 78, 70, 75, 74) y2 <- c(258, 224, 238, 278, 347, 300, 289, 260, 220, 237, 227, 281, 311, 250, 240, 268, 287, 226, 395, 450) The blk and trt vectors with the block and treatment data need to be converted into factors as follows before analysis. # Convert block and treatment to factors blk <- as.factor(blk) trt <- as.factor(trt) With the data in appropriate format, the analysis can be performed as follows for the trait y1 as follows. out1 <- augmentedRCBD(blk, trt, y1, method.comp = "lsd", alpha = 0.05, group = TRUE, console = TRUE)  Augmented Design Details ======================== Number of blocks "3" Number of treatments "12" Number of check treatments "4" Number of test treatments "8" Check treatments "1, 2, 3, 4" ANOVA, Treatment Adjusted ========================= Df Sum Sq Mean Sq F value Pr(>F) Block (ignoring Treatments) 2 360.1 180.04 6.675 0.0298 * Treatment (eliminating Blocks) 11 285.1 25.92 0.961 0.5499 Treatment: Check 3 52.9 17.64 0.654 0.6092 Treatment: Test and Test vs. Check 8 232.2 29.02 1.076 0.4779 Residuals 6 161.8 26.97 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ANOVA, Block Adjusted ===================== Df Sum Sq Mean Sq F value Pr(>F) Treatment (ignoring Blocks) 11 575.7 52.33 1.940 0.215 Treatment: Check 3 52.9 17.64 0.654 0.609 Treatment: Test 7 505.9 72.27 2.679 0.125 Treatment: Test vs. Check 1 16.9 16.87 0.626 0.459 Block (eliminating Treatments) 2 69.5 34.75 1.288 0.342 Residuals 6 161.8 26.97 Treatment Means =============== Treatment Block Means SE r Min Max Adjusted Means 1 1 84.66667 3.844188 3 79 92 84.66667 2 10 3 74.00000 NA 1 74 74 77.25000 3 11 1 89.00000 NA 1 89 89 86.50000 4 12 1 82.00000 NA 1 82 82 79.50000 5 2 79.00000 1.154701 3 77 81 79.00000 6 3 82.00000 2.645751 3 78 87 82.00000 7 4 83.33333 3.929942 3 78 91 83.33333 8 5 2 79.00000 NA 1 79 79 78.25000 9 6 3 75.00000 NA 1 75 75 78.25000 10 7 1 96.00000 NA 1 96 96 93.50000 11 8 3 70.00000 NA 1 70 70 73.25000 12 9 2 78.00000 NA 1 78 78 77.25000 Coefficient of Variation ======================== 6.372367 Overall Adjusted Mean ===================== 81.0625 Standard Errors =================== Std. Error of Diff. CD (5%) Control Treatment Means 4.240458 10.37603 Two Test Treatments (Same Block) 7.344688 17.97180 Two Test Treatments (Different Blocks) 8.211611 20.09309 A Test Treatment and a Control Treatment 6.704752 16.40594 Treatment Groups ================== Method : lsd Treatment Adjusted Means SE df lower.CL upper.CL Group 8 8 73.25000 5.609598 6 59.52381 86.97619 1 9 9 77.25000 5.609598 6 63.52381 90.97619 12 10 10 77.25000 5.609598 6 63.52381 90.97619 12 5 5 78.25000 5.609598 6 64.52381 91.97619 12 6 6 78.25000 5.609598 6 64.52381 91.97619 12 2 2 79.00000 2.998456 6 71.66304 86.33696 12 12 12 79.50000 5.609598 6 65.77381 93.22619 12 3 3 82.00000 2.998456 6 74.66304 89.33696 12 4 4 83.33333 2.998456 6 75.99637 90.67029 12 1 1 84.66667 2.998456 6 77.32971 92.00363 12 11 11 86.50000 5.609598 6 72.77381 100.22619 12 7 7 93.50000 5.609598 6 79.77381 107.22619 2 class(out1) [1] "augmentedRCBD" Similarly the analysis for the trait y2 can be computed as follows. out2 <- augmentedRCBD(blk, trt, y2, method.comp = "lsd", alpha = 0.05, group = TRUE, console = TRUE)  Augmented Design Details ======================== Number of blocks "3" Number of treatments "12" Number of check treatments "4" Number of test treatments "8" Check treatments "1, 2, 3, 4" ANOVA, Treatment Adjusted ========================= Df Sum Sq Mean Sq F value Pr(>F) Block (ignoring Treatments) 2 7019 3510 12.261 0.007597 ** Treatment (eliminating Blocks) 11 58965 5360 18.727 0.000920 *** Treatment: Check 3 2150 717 2.504 0.156116 Treatment: Test and Test vs. Check 8 56815 7102 24.810 0.000473 *** Residuals 6 1717 286 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ANOVA, Block Adjusted ===================== Df Sum Sq Mean Sq F value Pr(>F) Treatment (ignoring Blocks) 11 64708 5883 20.550 0.000707 *** Treatment: Check 3 2150 717 2.504 0.156116 Treatment: Test 7 34863 4980 17.399 0.001366 ** Treatment: Test vs. Check 1 27694 27694 96.749 6.36e-05 *** Block (eliminating Treatments) 2 1277 639 2.231 0.188645 Residuals 6 1718 286 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Treatment Means =============== Treatment Block Means SE r Min Max Adjusted Means 1 1 256.0000 3.055050 3 250 260 256.0000 2 10 3 450.0000 NA 1 450 450 437.6667 3 11 1 300.0000 NA 1 300 300 299.4167 4 12 1 289.0000 NA 1 289 289 288.4167 5 2 228.0000 6.110101 3 220 240 228.0000 6 3 247.6667 10.170764 3 237 268 247.6667 7 4 264.0000 18.681542 3 227 287 264.0000 8 5 2 281.0000 NA 1 281 281 293.9167 9 6 3 395.0000 NA 1 395 395 382.6667 10 7 1 347.0000 NA 1 347 347 346.4167 11 8 3 226.0000 NA 1 226 226 213.6667 12 9 2 311.0000 NA 1 311 311 323.9167 Coefficient of Variation ======================== 6.057617 Overall Adjusted Mean ===================== 298.4792 Standard Errors =================== Std. Error of Diff. CD (5%) Control Treatment Means 13.81424 33.80224 Two Test Treatments (Same Block) 23.92697 58.54719 Two Test Treatments (Different Blocks) 26.75117 65.45775 A Test Treatment and a Control Treatment 21.84224 53.44603 Treatment Groups ================== Method : lsd Treatment Adjusted Means SE df lower.CL upper.CL Group 8 8 213.6667 18.274527 6 168.9505 258.3828 12 2 2 228.0000 9.768146 6 204.0982 251.9018 1 3 3 247.6667 9.768146 6 223.7649 271.5685 123 1 1 256.0000 9.768146 6 232.0982 279.9018 1234 4 4 264.0000 9.768146 6 240.0982 287.9018 234 12 12 288.4167 18.274527 6 243.7005 333.1328 345 5 5 293.9167 18.274527 6 249.2005 338.6328 345 11 11 299.4167 18.274527 6 254.7005 344.1328 45 9 9 323.9167 18.274527 6 279.2005 368.6328 56 7 7 346.4167 18.274527 6 301.7005 391.1328 56 6 6 382.6667 18.274527 6 337.9505 427.3828 67 10 10 437.6667 18.274527 6 392.9505 482.3828 7 class(out2) [1] "augmentedRCBD" The data can also be imported as a data frame and then used for analysis. Consider the data frame data imported from Table 1 according to the instructions in section 4.8. str(data) 'data.frame': 20 obs. of 4 variables:$ blk: Factor w/ 3 levels "1","2","3": 1 1 1 1 1 1 1 2 2 2 ...
$trt: Factor w/ 12 levels "1","2","3","4",..: 1 2 3 4 7 11 12 1 2 3 ...$ y1 : num  92 79 87 81 96 89 82 79 81 81 ...
$y2 : num 258 224 238 278 347 300 289 260 220 237 ... # Convert block and treatment to factors data$blk <- as.factor(data$blk) data$trt <- as.factor(data$trt) # Results for variable y1 out1 <- augmentedRCBD(data$blk, data$trt, data$y1, method.comp = "lsd",
alpha = 0.05, group = TRUE, console = TRUE)

Augmented Design Details
========================

Number of blocks           "3"
Number of treatments       "12"
Number of check treatments "4"
Number of test treatments  "8"
Check treatments           "1, 2, 3, 4"

=========================
Df Sum Sq Mean Sq F value Pr(>F)
Block (ignoring Treatments)           2  360.1  180.04   6.675 0.0298 *
Treatment (eliminating Blocks)       11  285.1   25.92   0.961 0.5499
Treatment: Check                    3   52.9   17.64   0.654 0.6092
Treatment: Test and Test vs. Check  8  232.2   29.02   1.076 0.4779
Residuals                             6  161.8   26.97
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

=====================
Df Sum Sq Mean Sq F value Pr(>F)
Treatment (ignoring Blocks)    11  575.7   52.33   1.940  0.215
Treatment: Check              3   52.9   17.64   0.654  0.609
Treatment: Test               7  505.9   72.27   2.679  0.125
Treatment: Test vs. Check     1   16.9   16.87   0.626  0.459
Block (eliminating Treatments)  2   69.5   34.75   1.288  0.342
Residuals                       6  161.8   26.97

Treatment Means
===============
Treatment Block    Means       SE r Min Max Adjusted Means
1          1       84.66667 3.844188 3  79  92       84.66667
2         10     3 74.00000       NA 1  74  74       77.25000
3         11     1 89.00000       NA 1  89  89       86.50000
4         12     1 82.00000       NA 1  82  82       79.50000
5          2       79.00000 1.154701 3  77  81       79.00000
6          3       82.00000 2.645751 3  78  87       82.00000
7          4       83.33333 3.929942 3  78  91       83.33333
8          5     2 79.00000       NA 1  79  79       78.25000
9          6     3 75.00000       NA 1  75  75       78.25000
10         7     1 96.00000       NA 1  96  96       93.50000
11         8     3 70.00000       NA 1  70  70       73.25000
12         9     2 78.00000       NA 1  78  78       77.25000

Coefficient of Variation
========================
6.372367

=====================
81.0625

Standard Errors
===================
Std. Error of Diff.  CD (5%)
Control Treatment Means                             4.240458 10.37603
Two Test Treatments (Same Block)                    7.344688 17.97180
Two Test Treatments (Different Blocks)              8.211611 20.09309
A Test Treatment and a Control Treatment            6.704752 16.40594

Treatment Groups
==================

Method : lsd

Treatment Adjusted Means       SE df lower.CL  upper.CL Group
8          8       73.25000 5.609598  6 59.52381  86.97619    1
9          9       77.25000 5.609598  6 63.52381  90.97619    12
10        10       77.25000 5.609598  6 63.52381  90.97619    12
5          5       78.25000 5.609598  6 64.52381  91.97619    12
6          6       78.25000 5.609598  6 64.52381  91.97619    12
2          2       79.00000 2.998456  6 71.66304  86.33696    12
12        12       79.50000 5.609598  6 65.77381  93.22619    12
3          3       82.00000 2.998456  6 74.66304  89.33696    12
4          4       83.33333 2.998456  6 75.99637  90.67029    12
1          1       84.66667 2.998456  6 77.32971  92.00363    12
11        11       86.50000 5.609598  6 72.77381 100.22619    12
7          7       93.50000 5.609598  6 79.77381 107.22619     2
class(out1)
[1] "augmentedRCBD"
# Results for variable y2
out2 <- augmentedRCBD(data$blk, data$trt, data$y2, method.comp = "lsd", alpha = 0.05, group = TRUE, console = TRUE)  Augmented Design Details ======================== Number of blocks "3" Number of treatments "12" Number of check treatments "4" Number of test treatments "8" Check treatments "1, 2, 3, 4" ANOVA, Treatment Adjusted ========================= Df Sum Sq Mean Sq F value Pr(>F) Block (ignoring Treatments) 2 7019 3510 12.261 0.007597 ** Treatment (eliminating Blocks) 11 58965 5360 18.727 0.000920 *** Treatment: Check 3 2150 717 2.504 0.156116 Treatment: Test and Test vs. Check 8 56815 7102 24.810 0.000473 *** Residuals 6 1717 286 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ANOVA, Block Adjusted ===================== Df Sum Sq Mean Sq F value Pr(>F) Treatment (ignoring Blocks) 11 64708 5883 20.550 0.000707 *** Treatment: Check 3 2150 717 2.504 0.156116 Treatment: Test 7 34863 4980 17.399 0.001366 ** Treatment: Test vs. Check 1 27694 27694 96.749 6.36e-05 *** Block (eliminating Treatments) 2 1277 639 2.231 0.188645 Residuals 6 1718 286 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Treatment Means =============== Treatment Block Means SE r Min Max Adjusted Means 1 1 256.0000 3.055050 3 250 260 256.0000 2 10 3 450.0000 NA 1 450 450 437.6667 3 11 1 300.0000 NA 1 300 300 299.4167 4 12 1 289.0000 NA 1 289 289 288.4167 5 2 228.0000 6.110101 3 220 240 228.0000 6 3 247.6667 10.170764 3 237 268 247.6667 7 4 264.0000 18.681542 3 227 287 264.0000 8 5 2 281.0000 NA 1 281 281 293.9167 9 6 3 395.0000 NA 1 395 395 382.6667 10 7 1 347.0000 NA 1 347 347 346.4167 11 8 3 226.0000 NA 1 226 226 213.6667 12 9 2 311.0000 NA 1 311 311 323.9167 Coefficient of Variation ======================== 6.057617 Overall Adjusted Mean ===================== 298.4792 Standard Errors =================== Std. Error of Diff. CD (5%) Control Treatment Means 13.81424 33.80224 Two Test Treatments (Same Block) 23.92697 58.54719 Two Test Treatments (Different Blocks) 26.75117 65.45775 A Test Treatment and a Control Treatment 21.84224 53.44603 Treatment Groups ================== Method : lsd Treatment Adjusted Means SE df lower.CL upper.CL Group 8 8 213.6667 18.274527 6 168.9505 258.3828 12 2 2 228.0000 9.768146 6 204.0982 251.9018 1 3 3 247.6667 9.768146 6 223.7649 271.5685 123 1 1 256.0000 9.768146 6 232.0982 279.9018 1234 4 4 264.0000 9.768146 6 240.0982 287.9018 234 12 12 288.4167 18.274527 6 243.7005 333.1328 345 5 5 293.9167 18.274527 6 249.2005 338.6328 345 11 11 299.4167 18.274527 6 254.7005 344.1328 45 9 9 323.9167 18.274527 6 279.2005 368.6328 56 7 7 346.4167 18.274527 6 301.7005 391.1328 56 6 6 382.6667 18.274527 6 337.9505 427.3828 67 10 10 437.6667 18.274527 6 392.9505 482.3828 7 class(out2) [1] "augmentedRCBD" Check genotypes are inferred by default on the basis of number of replications. However, if some test genotypes are also replicated, they may also be falsely detected as checks. To avoid this, the checks can be specified by the checks argument. # Results for variable y1 (checks specified) out1 <- augmentedRCBD(data$blk, data$trt, data$y1, method.comp = "lsd",
alpha = 0.05, group = TRUE, console = TRUE,
checks = c("1", "2", "3", "4"))

Augmented Design Details
========================

Number of blocks           "3"
Number of treatments       "12"
Number of check treatments "4"
Number of test treatments  "8"
Check treatments           "1, 2, 3, 4"

=========================
Df Sum Sq Mean Sq F value Pr(>F)
Block (ignoring Treatments)           2  360.1  180.04   6.675 0.0298 *
Treatment (eliminating Blocks)       11  285.1   25.92   0.961 0.5499
Treatment: Check                    3   52.9   17.64   0.654 0.6092
Treatment: Test and Test vs. Check  8  232.2   29.02   1.076 0.4779
Residuals                             6  161.8   26.97
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

=====================
Df Sum Sq Mean Sq F value Pr(>F)
Treatment (ignoring Blocks)    11  575.7   52.33   1.940  0.215
Treatment: Check              3   52.9   17.64   0.654  0.609
Treatment: Test               7  505.9   72.27   2.679  0.125
Treatment: Test vs. Check     1   16.9   16.87   0.626  0.459
Block (eliminating Treatments)  2   69.5   34.75   1.288  0.342
Residuals                       6  161.8   26.97

Treatment Means
===============
Treatment Block    Means       SE r Min Max Adjusted Means
1          1       84.66667 3.844188 3  79  92       84.66667
2         10     3 74.00000       NA 1  74  74       77.25000
3         11     1 89.00000       NA 1  89  89       86.50000
4         12     1 82.00000       NA 1  82  82       79.50000
5          2       79.00000 1.154701 3  77  81       79.00000
6          3       82.00000 2.645751 3  78  87       82.00000
7          4       83.33333 3.929942 3  78  91       83.33333
8          5     2 79.00000       NA 1  79  79       78.25000
9          6     3 75.00000       NA 1  75  75       78.25000
10         7     1 96.00000       NA 1  96  96       93.50000
11         8     3 70.00000       NA 1  70  70       73.25000
12         9     2 78.00000       NA 1  78  78       77.25000

Coefficient of Variation
========================
6.372367

=====================
81.0625

Standard Errors
===================
Std. Error of Diff.  CD (5%)
Control Treatment Means                             4.240458 10.37603
Two Test Treatments (Same Block)                    7.344688 17.97180
Two Test Treatments (Different Blocks)              8.211611 20.09309
A Test Treatment and a Control Treatment            6.704752 16.40594

Treatment Groups
==================

Method : lsd

Treatment Adjusted Means       SE df lower.CL  upper.CL Group
8          8       73.25000 5.609598  6 59.52381  86.97619    1
9          9       77.25000 5.609598  6 63.52381  90.97619    12
10        10       77.25000 5.609598  6 63.52381  90.97619    12
5          5       78.25000 5.609598  6 64.52381  91.97619    12
6          6       78.25000 5.609598  6 64.52381  91.97619    12
2          2       79.00000 2.998456  6 71.66304  86.33696    12
12        12       79.50000 5.609598  6 65.77381  93.22619    12
3          3       82.00000 2.998456  6 74.66304  89.33696    12
4          4       83.33333 2.998456  6 75.99637  90.67029    12
1          1       84.66667 2.998456  6 77.32971  92.00363    12
11        11       86.50000 5.609598  6 72.77381 100.22619    12
7          7       93.50000 5.609598  6 79.77381 107.22619     2
# Results for variable y2 (checks specified)
out2 <- augmentedRCBD(data$blk, data$trt, data$y2, method.comp = "lsd", alpha = 0.05, group = TRUE, console = TRUE, checks = c("1", "2", "3", "4"))  Augmented Design Details ======================== Number of blocks "3" Number of treatments "12" Number of check treatments "4" Number of test treatments "8" Check treatments "1, 2, 3, 4" ANOVA, Treatment Adjusted ========================= Df Sum Sq Mean Sq F value Pr(>F) Block (ignoring Treatments) 2 7019 3510 12.261 0.007597 ** Treatment (eliminating Blocks) 11 58965 5360 18.727 0.000920 *** Treatment: Check 3 2150 717 2.504 0.156116 Treatment: Test and Test vs. Check 8 56815 7102 24.810 0.000473 *** Residuals 6 1717 286 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ANOVA, Block Adjusted ===================== Df Sum Sq Mean Sq F value Pr(>F) Treatment (ignoring Blocks) 11 64708 5883 20.550 0.000707 *** Treatment: Check 3 2150 717 2.504 0.156116 Treatment: Test 7 34863 4980 17.399 0.001366 ** Treatment: Test vs. Check 1 27694 27694 96.749 6.36e-05 *** Block (eliminating Treatments) 2 1277 639 2.231 0.188645 Residuals 6 1718 286 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Treatment Means =============== Treatment Block Means SE r Min Max Adjusted Means 1 1 256.0000 3.055050 3 250 260 256.0000 2 10 3 450.0000 NA 1 450 450 437.6667 3 11 1 300.0000 NA 1 300 300 299.4167 4 12 1 289.0000 NA 1 289 289 288.4167 5 2 228.0000 6.110101 3 220 240 228.0000 6 3 247.6667 10.170764 3 237 268 247.6667 7 4 264.0000 18.681542 3 227 287 264.0000 8 5 2 281.0000 NA 1 281 281 293.9167 9 6 3 395.0000 NA 1 395 395 382.6667 10 7 1 347.0000 NA 1 347 347 346.4167 11 8 3 226.0000 NA 1 226 226 213.6667 12 9 2 311.0000 NA 1 311 311 323.9167 Coefficient of Variation ======================== 6.057617 Overall Adjusted Mean ===================== 298.4792 Standard Errors =================== Std. Error of Diff. CD (5%) Control Treatment Means 13.81424 33.80224 Two Test Treatments (Same Block) 23.92697 58.54719 Two Test Treatments (Different Blocks) 26.75117 65.45775 A Test Treatment and a Control Treatment 21.84224 53.44603 Treatment Groups ================== Method : lsd Treatment Adjusted Means SE df lower.CL upper.CL Group 8 8 213.6667 18.274527 6 168.9505 258.3828 12 2 2 228.0000 9.768146 6 204.0982 251.9018 1 3 3 247.6667 9.768146 6 223.7649 271.5685 123 1 1 256.0000 9.768146 6 232.0982 279.9018 1234 4 4 264.0000 9.768146 6 240.0982 287.9018 234 12 12 288.4167 18.274527 6 243.7005 333.1328 345 5 5 293.9167 18.274527 6 249.2005 338.6328 345 11 11 299.4167 18.274527 6 254.7005 344.1328 45 9 9 323.9167 18.274527 6 279.2005 368.6328 56 7 7 346.4167 18.274527 6 301.7005 391.1328 56 6 6 382.6667 18.274527 6 337.9505 427.3828 67 10 10 437.6667 18.274527 6 392.9505 482.3828 7 In case the large number of treatments or genotypes, it is advisable to avoid treatment comparisons with the group = FALSE argument as it will be memory and processor intensive. Further it is advised to simplify output with simplify = TRUE in order to reduce output object size. ## 7.3 describe.augmentedRCBD() The descriptive statistics such as count, mean, standard error, minimum, maximum, skewness ( with p-value from D’Agostino test of skewness (D’Agostino (1970))) and kurtosis (with p-value from Anscombe-Glynn test of kurtosis (Anscombe and Glynn (1983))) for the adjusted means from the results in an object of class augmentedRCBD can be computed as follows. # Descriptive statistics for variable y1 describe.augmentedRCBD(out1) $Count
[1] 12

$Mean [1] 81.0625$Std.Error
[1] 1.547002

$Std.Deviation [1] 5.358973$Min
[1] 73.25

$Max [1] 93.5$Skewness(statistic)
skew         z
0.9250344 1.6745760

$Skewness(p.value) [1] 0.09401746$Kurtosis(statistic)
kurt        z
3.522807 1.282305

$Kurtosis(p.value) [1] 0.1997357 # Descriptive statistics for variable y2 describe.augmentedRCBD(out2) $Count
[1] 12

$Mean [1] 298.4792$Std.Error
[1] 18.92257

$Std.Deviation [1] 65.5497$Min
[1] 213.6667

$Max [1] 437.6667$Skewness(statistic)
skew         z
0.7449405 1.3680211

$Skewness(p.value) [1] 0.1713055$Kurtosis(statistic)
kurt        z
2.787997 0.536812

$Kurtosis(p.value) [1] 0.5913975 ## 7.4 freqdist.augmentedRCBD() The frequency distribution of the adjusted means from the results in an object of class augmentedRCBD can be plotted as follows. # Frequency distribution for variable y1 freq1 <- freqdist.augmentedRCBD(out1, xlab = "Trait 1") Warning: Removed 2 rows containing missing values (geom_bar). plot(freq1) # Frequency distribution for variable y2 freq2 <- freqdist.augmentedRCBD(out2, xlab = "Trait 2") Warning: Removed 2 rows containing missing values (geom_bar). plot(freq2) The colours for the check values may be specified using the argument check.col. colset <- c("red3", "green4", "purple3", "darkorange3") # Frequency distribution for variable y1 freq1 <- freqdist.augmentedRCBD(out1, xlab = "Trait 1", check.col = colset) Warning: Removed 2 rows containing missing values (geom_bar). plot(freq1) # Frequency distribution for variable y2 freq2 <- freqdist.augmentedRCBD(out2, xlab = "Trait 2", check.col = colset) Warning: Removed 2 rows containing missing values (geom_bar). plot(freq2) The default the check highlighting can be avoided using the argument highlight.check = FALSE. # Frequency distribution for variable y1 freq1 <- freqdist.augmentedRCBD(out1, xlab = "Trait 1", highlight.check = FALSE) Warning: Removed 2 rows containing missing values (geom_bar). plot(freq1) # Frequency distribution for variable y2 freq2 <- freqdist.augmentedRCBD(out2, xlab = "Trait 2", highlight.check = FALSE) Warning: Removed 2 rows containing missing values (geom_bar). plot(freq2) ## 7.5 gva.augmentedRCBD() The genetic variability statistics such as mean, phenotypic, genotypic and environmental variation (Federer and Searle (1976)), phenotypic, genotypic and environmental coefficient of variation (Burton (1951), Burton (1952)), category of phenotypic and genotypic coefficient of variation according to Sivasubramaniam and Madhavamenon (1973), broad-sense heritability (H2) (Lush (1940)), H2 category according to Robinson (1966), Genetic advance (GA), genetic advance as per cent of mean (GAM) and GAM category according to Johnson et al. (1955) are computed from an object of class augmentedRCBD as follows. # Genetic variability statistics for variable y1 gva.augmentedRCBD(out1) $Mean
[1] 81.0625

$PV [1] 72.26786$GV
[1] 45.29563

$EV [1] 26.97222$GCV
[1] 8.302487

$GCV category [1] "Low"$PCV
[1] 10.48703

$PCV category [1] "Medium"$ECV
[1] 6.406759

$hBS [1] 62.67743$hBS category
[1] "High"

$GA [1] 10.99216$GAM
[1] 13.5601

$GAM category [1] "Medium" # Genetic variability statistics for variable y2 gva.augmentedRCBD(out2) $Mean
[1] 298.4792

$PV [1] 4980.411$GV
[1] 4694.161

$EV [1] 286.25$GCV
[1] 22.95435

$GCV category [1] "High"$PCV
[1] 23.64387

$PCV category [1] "High"$ECV
[1] 5.668377

$hBS [1] 94.25248$hBS category
[1] "High"

$GA [1] 137.2223$GAM
[1] 45.97382

$GAM category [1] "High" ## 7.5 report.augmentedRCBD() The results generated by the analysis can be exported to a MS Word file as follows. # MS word report for variable y1 report.augmentedRCBD(aug = out1, target = file.path(tempdir(), "augmentedRCBD output - y1.docx")) # MS word report for variable y2 report.augmentedRCBD(aug = out1, target = file.path(tempdir(), "augmentedRCBD output - y2.docx")) Fig. 6: MS Word report generated with report.agumentedRCBD function. # 8 Data Analysis for a Multiple Traits Analysis of data for a multiple traits simultaneously can be performed by using augmentedRCBD.bulk function. It generates an object of class augmentedRCBD.bulk. Such an object can then be taken as input by print.augmentedRCBD.bulk to print the results to console. The results can also be exported as a MS Word report using the report.augmentedRCBD.bulk function. [1] "package 'diagram' is required to generate this figure" Fig. 7. Workflow for analysis of multiple traits with augmentedRCBD. ## 8.1 augmentedRCBD.bulk() Consider the data frame data imported from Table 1 according to the instructions in section 4.8. str(data) 'data.frame': 20 obs. of 4 variables:$ blk: Factor w/ 3 levels "1","2","3": 1 1 1 1 1 1 1 2 2 2 ...
$trt: Factor w/ 12 levels "1","2","3","4",..: 1 2 3 4 7 11 12 1 2 3 ...$ y1 : num  92 79 87 81 96 89 82 79 81 81 ...
$y2 : num 258 224 238 278 347 300 289 260 220 237 ... # Convert block and treatment to factors data$blk <- as.factor(data$blk) data$trt <- as.factor(data\$trt)

Rather than performing the analysis individually for each variable/trait separately using augmentedRCBD, the analysis can be performed simultaneously for for both the traits using augmentedRCBD.bulk function. It is a wrapper around the augmentedRCBD core function and its associated helper functions.

However in this case treatment comparisons/grouping by least significant difference or Tukey’s honest significant difference method is not computed. Also the output object size is reduced using the simplify = TRUE argument in the augmentedRCBD function.

The logical arguments describe, freqdist and gva can be used to specify whether to generate the descriptive statistics, frequency distribution plots and genetic variability statistics respectively. If gva = TRUE, then plots to compare phenotypic and genotypic coefficient of variation, broad sense heritability and genetic advance over mean between traits are also generated.

bout <- augmentedRCBD.bulk(data = data, block = "blk",
treatment = "trt", traits = c("y1", "y2"),
checks = NULL, alpha = 0.05, describe = TRUE,
freqdist = TRUE, gva = TRUE,
check.col = c("brown", "darkcyan",
"forestgreen", "purple"),
console = TRUE)

ANOVA for y1 computed (1/2)

ANOVA for y2 computed (2/2)

Augmented Design Details
========================

Number of blocks           "3"
Number of treatments       "12"
Number of check treatments "4"
Number of test treatments  "8"
Check treatments           "1, 2, 3, 4"
Number of traits           "2"
Traits                     "y1, y2"

=========================
Source Df         y1          y2
1        Block (ignoring Treatments)  2 180.04 *   3509.67 **
2     Treatment (eliminating Blocks) 11  25.92 ns  5360.49 **
3                   Treatment: Check  3  17.64 ns   716.75 ns
4 Treatment: Test and Test vs. Check  8  29.02 ns  7101.89 **
5                          Residuals  6  26.97      286.25

=====================
Source Df        y1           y2
1    Treatment (ignoring Blocks) 11 52.33 ns    5882.5 **
2               Treatment: Check  3 17.64 ns    716.75 ns
3      Treatment: Test vs. Check  1 16.87 ns  27694.41 **
4                Treatment: Test  7 72.27 ns   4980.41 **
5 Block (eliminating Treatments)  2 34.75 ns    638.58 ns
6                      Residuals  6 26.97       286.25

Coefficient of Variation
========================
Trait   CV
1    y1 6.37
2    y2 6.06

=====================
1    y1                 81.06
2    y2                298.48

Standard Errors
===================
Comparison   y1    y2
1 A Test Treatment and a Control Treatment  6.7 21.84
2                  Control Treatment Means 4.24 13.81
3   Two Test Treatments (Different Blocks) 8.21 26.75
4         Two Test Treatments (Same Block) 7.34 23.93

Critical Difference
===================
alpha = 0.05                                Comparison    y1    y2
1 A Test Treatment and a Control Treatment 16.41 53.45
2                  Control Treatment Means 10.38  33.8
3   Two Test Treatments (Different Blocks) 20.09 65.46
4         Two Test Treatments (Same Block) 17.97 58.55

Descriptive Statistics
===================
Trait Count   Mean Std.Error Std.Deviation    Min    Max Skewness
skew...1    y1    12  81.06      1.55          5.36  73.25   93.5 0.93 ns
skew...2    y2    12 298.48     18.92         65.55 213.67 437.67 0.74 ns
Kurtosis
skew...1 3.52 ns
skew...2 2.79 ns

Genetic Variability Analysis
===================
Trait   Mean      PV      GV     EV   GCV GCV.category   PCV PCV.category
1    y1  81.06   72.27    45.3  26.97   8.3          Low 10.49       Medium
2    y2 298.48 4980.41 4694.16 286.25 22.95         High 23.64         High
ECV   hBS hBS.category     GA   GAM GAM.category
1 6.41 62.68         High  10.99 13.56       Medium
2 5.67 94.25         High 137.22 45.97         High

Warning Messages
===================
y1
Removed 2 rows containing missing values (geom_bar).
y2
Removed 2 rows containing missing values (geom_bar).

Treatment Means
===============
Treatment    y1     y2
1          1 84.67    256
2         10 77.25 437.67
3         11  86.5 299.42
4         12  79.5 288.42
5          2    79    228
6          3    82 247.67
7          4 83.33    264
8          5 78.25 293.92
9          6 78.25 382.67
10         7  93.5 346.42
11         8 73.25 213.67
12         9 77.25 323.92

## 8.3 report.augmentedRCBD.bulk()

The results generated by the analysis can be exported to a MS Word file as follows.

# MS word report
report.augmentedRCBD.bulk(aug.bulk = bout,
target = file.path(tempdir(),
"augmentedRCBD bulk output.docx"))

Fig. 8: MS Word report generated with report.agumentedRCBD.bulk function.

# 9 Citing augmentedRCBD


To cite the R package 'augmentedRCBD' in publications use:

Aravind, J., Mukesh Sankar, S., Wankhede, D. P., and Kaur, V. (2021).
augmentedRCBD: Analysis of Augmented Randomised Complete Block
Designs. R package version 0.1.4.9000,
https://aravind-j.github.io/augmentedRCBD/https://cran.r-project.org/package=augmentedRCBD.

A BibTeX entry for LaTeX users is

@Manual{,
title = {augmentedRCBD: Analysis of Augmented Randomised Complete Block Designs},
author = {J. Aravind and S. {Mukesh Sankar} and Dhammaprakash Pandhari Wankhede and Vikender Kaur},
year = {2021},
note = {R package version 0.1.4.9000},
note = {https://aravind-j.github.io/augmentedRCBD/},
note = {https://cran.r-project.org/package=augmentedRCBD},
}

This free and open-source software implements academic research by the
authors and co-workers. If you use it, please support the project by
citing the package.

# 10 Session Info

sessionInfo()
R version 4.0.5 (2021-03-31)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Catalina 10.15.7

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base

other attached packages:
[1] augmentedRCBD_0.1.4.9000

loaded via a namespace (and not attached):
[1] Rcpp_1.0.6         mvtnorm_1.1-1      lattice_0.20-41    multcompView_0.1-8
[5] zoo_1.8-9          rprojroot_2.0.2    digest_0.6.27      utf8_1.2.1
[9] plyr_1.8.6         R6_2.5.0           evaluate_0.14      httr_1.4.2
[13] ggplot2_3.3.3      highr_0.8          pillar_1.6.0       Rdpack_2.1.1
[17] gdtools_0.2.3      rlang_0.4.10       multcomp_1.4-16    uuid_0.1-4
[21] data.table_1.14.0  jquerylib_0.1.3    Matrix_1.3-2       flextable_0.6.5
[25] rmarkdown_2.7      pkgdown_1.6.1      labeling_0.4.2     moments_0.14
[29] textshaping_0.3.1  desc_1.3.0         splines_4.0.5      stringr_1.4.0
[33] munsell_0.5.0      compiler_4.0.5     xfun_0.22          pkgconfig_2.0.3
[37] systemfonts_1.0.1  base64enc_0.1-3    htmltools_0.5.1.1  tidyselect_1.1.0
[41] tibble_3.1.0       codetools_0.2-18   fansi_0.4.2        crayon_1.4.1
[45] dplyr_1.0.5        MASS_7.3-53.1      rbibutils_2.1      grid_4.0.5
[49] jsonlite_1.7.2     xtable_1.8-4       gtable_0.3.0       lifecycle_1.0.0
[53] magrittr_2.0.1     scales_1.1.1       zip_2.1.1          estimability_1.3
[57] stringi_1.5.3      cachem_1.0.4       farver_2.1.0       reshape2_1.4.4
[61] fs_1.5.0           xml2_1.3.2         bslib_0.2.4        ellipsis_0.3.1
[65] ragg_1.1.1         generics_0.1.0     vctrs_0.3.7        sandwich_3.0-0
[69] TH.data_1.0-10     tools_4.0.5        glue_1.4.2         officer_0.3.18
[73] purrr_0.3.4        emmeans_1.5.5-1    fastmap_1.1.0      survival_3.2-10
[77] yaml_2.2.1         colorspace_2.0-0   memoise_2.0.0      knitr_1.32
[81] sass_0.3.1        

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