Data Analysis with
augmentedRCBD
Aravind, J.1, Mukesh Sankar, S.2, Wankhede, D. P.3, and Kaur, V.4
2024-08-04
Source:vignettes/Data_Analysis_with_augmentedRCBD.Rmd
Data_Analysis_with_augmentedRCBD.Rmd
- Division of Germplasm Conservation, ICAR-National Bureau of Plant Genetic Resources, New Delhi.
- Division of Genetics, ICAR-Indian Agricultural Research Institute, New Delhi.
- Division of Genomic Resources, ICAR-National Bureau of Plant Genetic Resources, New Delhi.
- 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] 23.3.2 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"[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[1] 51.25Information 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] 3It 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’.
[1] "numeric"
str(a) num [1:3] 1 2 3.3
length(a)[1] 3[1] "integer"
str(b) int [1:3] 1 2 3
length(b)[1] 3The vector mode ‘character’ store text.
[1] "character"
str(c) chr [1:3] "one" "two" "three"
length(c)[1] 3The vector mode ‘logical’ stores ‘TRUE’ OR
‘FALSE’ logical data.
[1] "logical"
str(d) logi [1:6] TRUE TRUE TRUE FALSE TRUE FALSE
length(d)[1] 64.3.2 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 2A character, numeric or integer vector can be transformed to a factor
by using the as.factor() function.
[1] "numeric"
str(a) num [1:3] 1 2 3.3[1] "factor"
str(fac_a) Factor w/ 3 levels "1","2","3.3": 1 2 3[1] "integer"
str(b) int [1:3] 1 2 3[1] "factor"
str(fac_b) Factor w/ 3 levels "1","2","3": 1 2 3[1] "character"
str(c) chr [1:3] "one" "two" "three"[1] "factor"
str(fac_c) Factor w/ 3 levels "one","three",..: 1 3 24.3.3 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 44.3.4 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.
[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.
[1] 2.1The 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] 54.4 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.
[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 FALSEInf indicates infinity.
1/0[1] InfNaN (Not a Number) indicates any undefined value.
0/0[1] NaN4.5 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 6.7Consider a matrix 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 matrixa 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 rowb
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 9Consider 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$data L x y z
1 A 1 1 This
2 B 1 2 is
3 C 1 3 a
4 D 1 4 data frameConsider a data frame df.
df L x y z
1 A 1 1 This
2 B 1 2 is
3 C 1 3 a
4 D 1 4 data frame
# Indexing by number
df[,2] # 2nd column of data frame[1] 1 1 1 1
df[2] # 2nd column of data frame x
1 1
2 1
3 1
4 1
df[3,] # 3rd row of data frame L x y z
3 C 1 3 a
df[2:3, 1:3] # rows 2,3 of columns 1,2,3 L x y
2 B 1 2
3 C 1 3
df[2,2] # Element in 2nd column of 2nd row[1] 1
# Indexing by name
df$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
?setwd4.7 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 21132
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().
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.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.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.
- Online tutorials
- Free online courses
-
Rcommunity support- http://stackoverflow.com/
-
Rhelp mailing lists : http://www.r-project.org/mail.html
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
--------------------------------------------------------------------------------
Welcome to augmentedRCBD version 0.1.7.9000
# 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 0.1.7. The previous versions are as follows.
Table 2. Version history of
augmentedRCBD R package.
| Version | Date |
|---|---|
| 0.1.0 | 2018-07-10 |
| 0.1.1 | 2019-07-21 |
| 0.1.2 | 2020-03-19 |
| 0.1.3 | 2020-07-27 |
| 0.1.4 | 2021-02-17 |
| 0.1.5 | 2021-06-12 |
| 0.1.6 | 2023-05-28 |
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.
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.
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
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 Means
===============
Treatment Block Means SE r Min Max Adjusted Means
1 84.67 3.84 3 79.00 92.00 84.67
10 3 74.00 <NA> 1 74.00 74.00 77.25
11 1 89.00 <NA> 1 89.00 89.00 86.50
12 1 82.00 <NA> 1 82.00 82.00 79.50
2 79.00 1.15 3 77.00 81.00 79.00
3 82.00 2.65 3 78.00 87.00 82.00
4 83.33 3.93 3 78.00 91.00 83.33
5 2 79.00 <NA> 1 79.00 79.00 78.25
6 3 75.00 <NA> 1 75.00 75.00 78.25
7 1 96.00 <NA> 1 96.00 96.00 93.50
8 3 70.00 <NA> 1 70.00 70.00 73.25
9 2 78.00 <NA> 1 78.00 78.00 77.25
Comparisons
===========
Method : lsd
contrast estimate SE df t.ratio p.value sig
treatment1 - treatment2 5.67 4.24 6 1.336 0.230
treatment1 - treatment3 2.67 4.24 6 0.629 0.553
treatment1 - treatment4 1.33 4.24 6 0.314 0.764
treatment1 - treatment5 6.42 6.36 6 1.009 0.352
treatment1 - treatment6 6.42 6.36 6 1.009 0.352
treatment1 - treatment7 -8.83 6.36 6 -1.389 0.214
treatment1 - treatment8 11.42 6.36 6 1.795 0.123
treatment1 - treatment9 7.42 6.36 6 1.166 0.288
treatment1 - treatment10 7.42 6.36 6 1.166 0.288
treatment1 - treatment11 -1.83 6.36 6 -0.288 0.783
treatment1 - treatment12 5.17 6.36 6 0.812 0.448
treatment2 - treatment3 -3.00 4.24 6 -0.707 0.506
treatment2 - treatment4 -4.33 4.24 6 -1.022 0.346
treatment2 - treatment5 0.75 6.36 6 0.118 0.910
treatment2 - treatment6 0.75 6.36 6 0.118 0.910
treatment2 - treatment7 -14.50 6.36 6 -2.280 0.063
treatment2 - treatment8 5.75 6.36 6 0.904 0.401
treatment2 - treatment9 1.75 6.36 6 0.275 0.792
treatment2 - treatment10 1.75 6.36 6 0.275 0.792
treatment2 - treatment11 -7.50 6.36 6 -1.179 0.283
treatment2 - treatment12 -0.50 6.36 6 -0.079 0.940
treatment3 - treatment4 -1.33 4.24 6 -0.314 0.764
treatment3 - treatment5 3.75 6.36 6 0.590 0.577
treatment3 - treatment6 3.75 6.36 6 0.590 0.577
treatment3 - treatment7 -11.50 6.36 6 -1.808 0.121
treatment3 - treatment8 8.75 6.36 6 1.376 0.218
treatment3 - treatment9 4.75 6.36 6 0.747 0.483
treatment3 - treatment10 4.75 6.36 6 0.747 0.483
treatment3 - treatment11 -4.50 6.36 6 -0.707 0.506
treatment3 - treatment12 2.50 6.36 6 0.393 0.708
treatment4 - treatment5 5.08 6.36 6 0.799 0.455
treatment4 - treatment6 5.08 6.36 6 0.799 0.455
treatment4 - treatment7 -10.17 6.36 6 -1.598 0.161
treatment4 - treatment8 10.08 6.36 6 1.585 0.164
treatment4 - treatment9 6.08 6.36 6 0.956 0.376
treatment4 - treatment10 6.08 6.36 6 0.956 0.376
treatment4 - treatment11 -3.17 6.36 6 -0.498 0.636
treatment4 - treatment12 3.83 6.36 6 0.603 0.569
treatment5 - treatment6 0.00 8.21 6 0.000 1.000
treatment5 - treatment7 -15.25 8.21 6 -1.857 0.113
treatment5 - treatment8 5.00 8.21 6 0.609 0.565
treatment5 - treatment9 1.00 7.34 6 0.136 0.896
treatment5 - treatment10 1.00 8.21 6 0.122 0.907
treatment5 - treatment11 -8.25 8.21 6 -1.005 0.354
treatment5 - treatment12 -1.25 8.21 6 -0.152 0.884
treatment6 - treatment7 -15.25 8.21 6 -1.857 0.113
treatment6 - treatment8 5.00 7.34 6 0.681 0.521
treatment6 - treatment9 1.00 8.21 6 0.122 0.907
treatment6 - treatment10 1.00 7.34 6 0.136 0.896
treatment6 - treatment11 -8.25 8.21 6 -1.005 0.354
treatment6 - treatment12 -1.25 8.21 6 -0.152 0.884
treatment7 - treatment8 20.25 8.21 6 2.466 0.049 *
treatment7 - treatment9 16.25 8.21 6 1.979 0.095
treatment7 - treatment10 16.25 8.21 6 1.979 0.095
treatment7 - treatment11 7.00 7.34 6 0.953 0.377
treatment7 - treatment12 14.00 7.34 6 1.906 0.105
treatment8 - treatment9 -4.00 8.21 6 -0.487 0.643
treatment8 - treatment10 -4.00 7.34 6 -0.545 0.606
treatment8 - treatment11 -13.25 8.21 6 -1.614 0.158
treatment8 - treatment12 -6.25 8.21 6 -0.761 0.475
treatment9 - treatment10 -0.00 8.21 6 -0.000 1.000
treatment9 - treatment11 -9.25 8.21 6 -1.126 0.303
treatment9 - treatment12 -2.25 8.21 6 -0.274 0.793
treatment10 - treatment11 -9.25 8.21 6 -1.126 0.303
treatment10 - treatment12 -2.25 8.21 6 -0.274 0.793
treatment11 - treatment12 7.00 7.34 6 0.953 0.377
Treatment Groups
================
Method : lsd
Treatment Adjusted Means SE df lower.CL upper.CL Group
8 73.25 5.61 6 59.52 86.98 1
9 77.25 5.61 6 63.52 90.98 12
10 77.25 5.61 6 63.52 90.98 12
5 78.25 5.61 6 64.52 91.98 12
6 78.25 5.61 6 64.52 91.98 12
2 79.00 3.00 6 71.66 86.34 12
12 79.50 5.61 6 65.77 93.23 12
3 82.00 3.00 6 74.66 89.34 12
4 83.33 3.00 6 76.00 90.67 12
1 84.67 3.00 6 77.33 92.00 12
11 86.50 5.61 6 72.77 100.23 12
7 93.50 5.61 6 79.77 107.23 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 1718 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 1717 286
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
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 Means
===============
Treatment Block Means SE r Min Max Adjusted Means
1 256.00 3.06 3 250.00 260.00 256.00
10 3 450.00 <NA> 1 450.00 450.00 437.67
11 1 300.00 <NA> 1 300.00 300.00 299.42
12 1 289.00 <NA> 1 289.00 289.00 288.42
2 228.00 6.11 3 220.00 240.00 228.00
3 247.67 10.17 3 237.00 268.00 247.67
4 264.00 18.68 3 227.00 287.00 264.00
5 2 281.00 <NA> 1 281.00 281.00 293.92
6 3 395.00 <NA> 1 395.00 395.00 382.67
7 1 347.00 <NA> 1 347.00 347.00 346.42
8 3 226.00 <NA> 1 226.00 226.00 213.67
9 2 311.00 <NA> 1 311.00 311.00 323.92
Comparisons
===========
Method : lsd
contrast estimate SE df t.ratio p.value sig
treatment1 - treatment2 28.00 13.81 6 2.027 0.089
treatment1 - treatment3 8.33 13.81 6 0.603 0.568
treatment1 - treatment4 -8.00 13.81 6 -0.579 0.584
treatment1 - treatment5 -37.92 20.72 6 -1.830 0.117
treatment1 - treatment6 -126.67 20.72 6 -6.113 0.001 ***
treatment1 - treatment7 -90.42 20.72 6 -4.363 0.005 **
treatment1 - treatment8 42.33 20.72 6 2.043 0.087
treatment1 - treatment9 -67.92 20.72 6 -3.278 0.017 *
treatment1 - treatment10 -181.67 20.72 6 -8.767 0.000 ***
treatment1 - treatment11 -43.42 20.72 6 -2.095 0.081
treatment1 - treatment12 -32.42 20.72 6 -1.564 0.169
treatment2 - treatment3 -19.67 13.81 6 -1.424 0.204
treatment2 - treatment4 -36.00 13.81 6 -2.606 0.040 *
treatment2 - treatment5 -65.92 20.72 6 -3.181 0.019 *
treatment2 - treatment6 -154.67 20.72 6 -7.464 0.000 ***
treatment2 - treatment7 -118.42 20.72 6 -5.715 0.001 **
treatment2 - treatment8 14.33 20.72 6 0.692 0.515
treatment2 - treatment9 -95.92 20.72 6 -4.629 0.004 **
treatment2 - treatment10 -209.67 20.72 6 -10.118 0.000 ***
treatment2 - treatment11 -71.42 20.72 6 -3.447 0.014 *
treatment2 - treatment12 -60.42 20.72 6 -2.916 0.027 *
treatment3 - treatment4 -16.33 13.81 6 -1.182 0.282
treatment3 - treatment5 -46.25 20.72 6 -2.232 0.067
treatment3 - treatment6 -135.00 20.72 6 -6.515 0.001 ***
treatment3 - treatment7 -98.75 20.72 6 -4.766 0.003 **
treatment3 - treatment8 34.00 20.72 6 1.641 0.152
treatment3 - treatment9 -76.25 20.72 6 -3.680 0.010 *
treatment3 - treatment10 -190.00 20.72 6 -9.169 0.000 ***
treatment3 - treatment11 -51.75 20.72 6 -2.497 0.047 *
treatment3 - treatment12 -40.75 20.72 6 -1.967 0.097
treatment4 - treatment5 -29.92 20.72 6 -1.444 0.199
treatment4 - treatment6 -118.67 20.72 6 -5.727 0.001 **
treatment4 - treatment7 -82.42 20.72 6 -3.977 0.007 **
treatment4 - treatment8 50.33 20.72 6 2.429 0.051
treatment4 - treatment9 -59.92 20.72 6 -2.892 0.028 *
treatment4 - treatment10 -173.67 20.72 6 -8.381 0.000 ***
treatment4 - treatment11 -35.42 20.72 6 -1.709 0.138
treatment4 - treatment12 -24.42 20.72 6 -1.178 0.283
treatment5 - treatment6 -88.75 26.75 6 -3.318 0.016 *
treatment5 - treatment7 -52.50 26.75 6 -1.963 0.097
treatment5 - treatment8 80.25 26.75 6 3.000 0.024 *
treatment5 - treatment9 -30.00 23.93 6 -1.254 0.257
treatment5 - treatment10 -143.75 26.75 6 -5.374 0.002 **
treatment5 - treatment11 -5.50 26.75 6 -0.206 0.844
treatment5 - treatment12 5.50 26.75 6 0.206 0.844
treatment6 - treatment7 36.25 26.75 6 1.355 0.224
treatment6 - treatment8 169.00 23.93 6 7.063 0.000 ***
treatment6 - treatment9 58.75 26.75 6 2.196 0.070
treatment6 - treatment10 -55.00 23.93 6 -2.299 0.061
treatment6 - treatment11 83.25 26.75 6 3.112 0.021 *
treatment6 - treatment12 94.25 26.75 6 3.523 0.012 *
treatment7 - treatment8 132.75 26.75 6 4.962 0.003 **
treatment7 - treatment9 22.50 26.75 6 0.841 0.433
treatment7 - treatment10 -91.25 26.75 6 -3.411 0.014 *
treatment7 - treatment11 47.00 23.93 6 1.964 0.097
treatment7 - treatment12 58.00 23.93 6 2.424 0.052
treatment8 - treatment9 -110.25 26.75 6 -4.121 0.006 **
treatment8 - treatment10 -224.00 23.93 6 -9.362 0.000 ***
treatment8 - treatment11 -85.75 26.75 6 -3.205 0.018 *
treatment8 - treatment12 -74.75 26.75 6 -2.794 0.031 *
treatment9 - treatment10 -113.75 26.75 6 -4.252 0.005 **
treatment9 - treatment11 24.50 26.75 6 0.916 0.395
treatment9 - treatment12 35.50 26.75 6 1.327 0.233
treatment10 - treatment11 138.25 26.75 6 5.168 0.002 **
treatment10 - treatment12 149.25 26.75 6 5.579 0.001 **
treatment11 - treatment12 11.00 23.93 6 0.460 0.662
Treatment Groups
================
Method : lsd
Treatment Adjusted Means SE df lower.CL upper.CL Group
8 213.67 18.27 6 168.95 258.38 12
2 228.00 9.77 6 204.10 251.90 1
3 247.67 9.77 6 223.76 271.57 123
1 256.00 9.77 6 232.10 279.90 1234
4 264.00 9.77 6 240.10 287.90 234
12 288.42 18.27 6 243.70 333.13 345
5 293.92 18.27 6 249.20 338.63 345
11 299.42 18.27 6 254.70 344.13 45
9 323.92 18.27 6 279.20 368.63 56
7 346.42 18.27 6 301.70 391.13 56
6 382.67 18.27 6 337.95 427.38 67
10 437.67 18.27 6 392.95 482.38 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"
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
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 Means
===============
Treatment Block Means SE r Min Max Adjusted Means
1 84.67 3.84 3 79.00 92.00 84.67
10 3 74.00 <NA> 1 74.00 74.00 77.25
11 1 89.00 <NA> 1 89.00 89.00 86.50
12 1 82.00 <NA> 1 82.00 82.00 79.50
2 79.00 1.15 3 77.00 81.00 79.00
3 82.00 2.65 3 78.00 87.00 82.00
4 83.33 3.93 3 78.00 91.00 83.33
5 2 79.00 <NA> 1 79.00 79.00 78.25
6 3 75.00 <NA> 1 75.00 75.00 78.25
7 1 96.00 <NA> 1 96.00 96.00 93.50
8 3 70.00 <NA> 1 70.00 70.00 73.25
9 2 78.00 <NA> 1 78.00 78.00 77.25
Comparisons
===========
Method : lsd
contrast estimate SE df t.ratio p.value sig
treatment1 - treatment2 5.67 4.24 6 1.336 0.230
treatment1 - treatment3 2.67 4.24 6 0.629 0.553
treatment1 - treatment4 1.33 4.24 6 0.314 0.764
treatment1 - treatment5 6.42 6.36 6 1.009 0.352
treatment1 - treatment6 6.42 6.36 6 1.009 0.352
treatment1 - treatment7 -8.83 6.36 6 -1.389 0.214
treatment1 - treatment8 11.42 6.36 6 1.795 0.123
treatment1 - treatment9 7.42 6.36 6 1.166 0.288
treatment1 - treatment10 7.42 6.36 6 1.166 0.288
treatment1 - treatment11 -1.83 6.36 6 -0.288 0.783
treatment1 - treatment12 5.17 6.36 6 0.812 0.448
treatment2 - treatment3 -3.00 4.24 6 -0.707 0.506
treatment2 - treatment4 -4.33 4.24 6 -1.022 0.346
treatment2 - treatment5 0.75 6.36 6 0.118 0.910
treatment2 - treatment6 0.75 6.36 6 0.118 0.910
treatment2 - treatment7 -14.50 6.36 6 -2.280 0.063
treatment2 - treatment8 5.75 6.36 6 0.904 0.401
treatment2 - treatment9 1.75 6.36 6 0.275 0.792
treatment2 - treatment10 1.75 6.36 6 0.275 0.792
treatment2 - treatment11 -7.50 6.36 6 -1.179 0.283
treatment2 - treatment12 -0.50 6.36 6 -0.079 0.940
treatment3 - treatment4 -1.33 4.24 6 -0.314 0.764
treatment3 - treatment5 3.75 6.36 6 0.590 0.577
treatment3 - treatment6 3.75 6.36 6 0.590 0.577
treatment3 - treatment7 -11.50 6.36 6 -1.808 0.121
treatment3 - treatment8 8.75 6.36 6 1.376 0.218
treatment3 - treatment9 4.75 6.36 6 0.747 0.483
treatment3 - treatment10 4.75 6.36 6 0.747 0.483
treatment3 - treatment11 -4.50 6.36 6 -0.707 0.506
treatment3 - treatment12 2.50 6.36 6 0.393 0.708
treatment4 - treatment5 5.08 6.36 6 0.799 0.455
treatment4 - treatment6 5.08 6.36 6 0.799 0.455
treatment4 - treatment7 -10.17 6.36 6 -1.598 0.161
treatment4 - treatment8 10.08 6.36 6 1.585 0.164
treatment4 - treatment9 6.08 6.36 6 0.956 0.376
treatment4 - treatment10 6.08 6.36 6 0.956 0.376
treatment4 - treatment11 -3.17 6.36 6 -0.498 0.636
treatment4 - treatment12 3.83 6.36 6 0.603 0.569
treatment5 - treatment6 0.00 8.21 6 0.000 1.000
treatment5 - treatment7 -15.25 8.21 6 -1.857 0.113
treatment5 - treatment8 5.00 8.21 6 0.609 0.565
treatment5 - treatment9 1.00 7.34 6 0.136 0.896
treatment5 - treatment10 1.00 8.21 6 0.122 0.907
treatment5 - treatment11 -8.25 8.21 6 -1.005 0.354
treatment5 - treatment12 -1.25 8.21 6 -0.152 0.884
treatment6 - treatment7 -15.25 8.21 6 -1.857 0.113
treatment6 - treatment8 5.00 7.34 6 0.681 0.521
treatment6 - treatment9 1.00 8.21 6 0.122 0.907
treatment6 - treatment10 1.00 7.34 6 0.136 0.896
treatment6 - treatment11 -8.25 8.21 6 -1.005 0.354
treatment6 - treatment12 -1.25 8.21 6 -0.152 0.884
treatment7 - treatment8 20.25 8.21 6 2.466 0.049 *
treatment7 - treatment9 16.25 8.21 6 1.979 0.095
treatment7 - treatment10 16.25 8.21 6 1.979 0.095
treatment7 - treatment11 7.00 7.34 6 0.953 0.377
treatment7 - treatment12 14.00 7.34 6 1.906 0.105
treatment8 - treatment9 -4.00 8.21 6 -0.487 0.643
treatment8 - treatment10 -4.00 7.34 6 -0.545 0.606
treatment8 - treatment11 -13.25 8.21 6 -1.614 0.158
treatment8 - treatment12 -6.25 8.21 6 -0.761 0.475
treatment9 - treatment10 -0.00 8.21 6 -0.000 1.000
treatment9 - treatment11 -9.25 8.21 6 -1.126 0.303
treatment9 - treatment12 -2.25 8.21 6 -0.274 0.793
treatment10 - treatment11 -9.25 8.21 6 -1.126 0.303
treatment10 - treatment12 -2.25 8.21 6 -0.274 0.793
treatment11 - treatment12 7.00 7.34 6 0.953 0.377
Treatment Groups
================
Method : lsd
Treatment Adjusted Means SE df lower.CL upper.CL Group
8 73.25 5.61 6 59.52 86.98 1
9 77.25 5.61 6 63.52 90.98 12
10 77.25 5.61 6 63.52 90.98 12
5 78.25 5.61 6 64.52 91.98 12
6 78.25 5.61 6 64.52 91.98 12
2 79.00 3.00 6 71.66 86.34 12
12 79.50 5.61 6 65.77 93.23 12
3 82.00 3.00 6 74.66 89.34 12
4 83.33 3.00 6 76.00 90.67 12
1 84.67 3.00 6 77.33 92.00 12
11 86.50 5.61 6 72.77 100.23 12
7 93.50 5.61 6 79.77 107.23 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 1718 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 1717 286
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
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 Means
===============
Treatment Block Means SE r Min Max Adjusted Means
1 256.00 3.06 3 250.00 260.00 256.00
10 3 450.00 <NA> 1 450.00 450.00 437.67
11 1 300.00 <NA> 1 300.00 300.00 299.42
12 1 289.00 <NA> 1 289.00 289.00 288.42
2 228.00 6.11 3 220.00 240.00 228.00
3 247.67 10.17 3 237.00 268.00 247.67
4 264.00 18.68 3 227.00 287.00 264.00
5 2 281.00 <NA> 1 281.00 281.00 293.92
6 3 395.00 <NA> 1 395.00 395.00 382.67
7 1 347.00 <NA> 1 347.00 347.00 346.42
8 3 226.00 <NA> 1 226.00 226.00 213.67
9 2 311.00 <NA> 1 311.00 311.00 323.92
Comparisons
===========
Method : lsd
contrast estimate SE df t.ratio p.value sig
treatment1 - treatment2 28.00 13.81 6 2.027 0.089
treatment1 - treatment3 8.33 13.81 6 0.603 0.568
treatment1 - treatment4 -8.00 13.81 6 -0.579 0.584
treatment1 - treatment5 -37.92 20.72 6 -1.830 0.117
treatment1 - treatment6 -126.67 20.72 6 -6.113 0.001 ***
treatment1 - treatment7 -90.42 20.72 6 -4.363 0.005 **
treatment1 - treatment8 42.33 20.72 6 2.043 0.087
treatment1 - treatment9 -67.92 20.72 6 -3.278 0.017 *
treatment1 - treatment10 -181.67 20.72 6 -8.767 0.000 ***
treatment1 - treatment11 -43.42 20.72 6 -2.095 0.081
treatment1 - treatment12 -32.42 20.72 6 -1.564 0.169
treatment2 - treatment3 -19.67 13.81 6 -1.424 0.204
treatment2 - treatment4 -36.00 13.81 6 -2.606 0.040 *
treatment2 - treatment5 -65.92 20.72 6 -3.181 0.019 *
treatment2 - treatment6 -154.67 20.72 6 -7.464 0.000 ***
treatment2 - treatment7 -118.42 20.72 6 -5.715 0.001 **
treatment2 - treatment8 14.33 20.72 6 0.692 0.515
treatment2 - treatment9 -95.92 20.72 6 -4.629 0.004 **
treatment2 - treatment10 -209.67 20.72 6 -10.118 0.000 ***
treatment2 - treatment11 -71.42 20.72 6 -3.447 0.014 *
treatment2 - treatment12 -60.42 20.72 6 -2.916 0.027 *
treatment3 - treatment4 -16.33 13.81 6 -1.182 0.282
treatment3 - treatment5 -46.25 20.72 6 -2.232 0.067
treatment3 - treatment6 -135.00 20.72 6 -6.515 0.001 ***
treatment3 - treatment7 -98.75 20.72 6 -4.766 0.003 **
treatment3 - treatment8 34.00 20.72 6 1.641 0.152
treatment3 - treatment9 -76.25 20.72 6 -3.680 0.010 *
treatment3 - treatment10 -190.00 20.72 6 -9.169 0.000 ***
treatment3 - treatment11 -51.75 20.72 6 -2.497 0.047 *
treatment3 - treatment12 -40.75 20.72 6 -1.967 0.097
treatment4 - treatment5 -29.92 20.72 6 -1.444 0.199
treatment4 - treatment6 -118.67 20.72 6 -5.727 0.001 **
treatment4 - treatment7 -82.42 20.72 6 -3.977 0.007 **
treatment4 - treatment8 50.33 20.72 6 2.429 0.051
treatment4 - treatment9 -59.92 20.72 6 -2.892 0.028 *
treatment4 - treatment10 -173.67 20.72 6 -8.381 0.000 ***
treatment4 - treatment11 -35.42 20.72 6 -1.709 0.138
treatment4 - treatment12 -24.42 20.72 6 -1.178 0.283
treatment5 - treatment6 -88.75 26.75 6 -3.318 0.016 *
treatment5 - treatment7 -52.50 26.75 6 -1.963 0.097
treatment5 - treatment8 80.25 26.75 6 3.000 0.024 *
treatment5 - treatment9 -30.00 23.93 6 -1.254 0.257
treatment5 - treatment10 -143.75 26.75 6 -5.374 0.002 **
treatment5 - treatment11 -5.50 26.75 6 -0.206 0.844
treatment5 - treatment12 5.50 26.75 6 0.206 0.844
treatment6 - treatment7 36.25 26.75 6 1.355 0.224
treatment6 - treatment8 169.00 23.93 6 7.063 0.000 ***
treatment6 - treatment9 58.75 26.75 6 2.196 0.070
treatment6 - treatment10 -55.00 23.93 6 -2.299 0.061
treatment6 - treatment11 83.25 26.75 6 3.112 0.021 *
treatment6 - treatment12 94.25 26.75 6 3.523 0.012 *
treatment7 - treatment8 132.75 26.75 6 4.962 0.003 **
treatment7 - treatment9 22.50 26.75 6 0.841 0.433
treatment7 - treatment10 -91.25 26.75 6 -3.411 0.014 *
treatment7 - treatment11 47.00 23.93 6 1.964 0.097
treatment7 - treatment12 58.00 23.93 6 2.424 0.052
treatment8 - treatment9 -110.25 26.75 6 -4.121 0.006 **
treatment8 - treatment10 -224.00 23.93 6 -9.362 0.000 ***
treatment8 - treatment11 -85.75 26.75 6 -3.205 0.018 *
treatment8 - treatment12 -74.75 26.75 6 -2.794 0.031 *
treatment9 - treatment10 -113.75 26.75 6 -4.252 0.005 **
treatment9 - treatment11 24.50 26.75 6 0.916 0.395
treatment9 - treatment12 35.50 26.75 6 1.327 0.233
treatment10 - treatment11 138.25 26.75 6 5.168 0.002 **
treatment10 - treatment12 149.25 26.75 6 5.579 0.001 **
treatment11 - treatment12 11.00 23.93 6 0.460 0.662
Treatment Groups
================
Method : lsd
Treatment Adjusted Means SE df lower.CL upper.CL Group
8 213.67 18.27 6 168.95 258.38 12
2 228.00 9.77 6 204.10 251.90 1
3 247.67 9.77 6 223.76 271.57 123
1 256.00 9.77 6 232.10 279.90 1234
4 264.00 9.77 6 240.10 287.90 234
12 288.42 18.27 6 243.70 333.13 345
5 293.92 18.27 6 249.20 338.63 345
11 299.42 18.27 6 254.70 344.13 45
9 323.92 18.27 6 279.20 368.63 56
7 346.42 18.27 6 301.70 391.13 56
6 382.67 18.27 6 337.95 427.38 67
10 437.67 18.27 6 392.95 482.38 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"
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
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 Means
===============
Treatment Block Means SE r Min Max Adjusted Means
1 84.67 3.84 3 79.00 92.00 84.67
10 3 74.00 <NA> 1 74.00 74.00 77.25
11 1 89.00 <NA> 1 89.00 89.00 86.50
12 1 82.00 <NA> 1 82.00 82.00 79.50
2 79.00 1.15 3 77.00 81.00 79.00
3 82.00 2.65 3 78.00 87.00 82.00
4 83.33 3.93 3 78.00 91.00 83.33
5 2 79.00 <NA> 1 79.00 79.00 78.25
6 3 75.00 <NA> 1 75.00 75.00 78.25
7 1 96.00 <NA> 1 96.00 96.00 93.50
8 3 70.00 <NA> 1 70.00 70.00 73.25
9 2 78.00 <NA> 1 78.00 78.00 77.25
Comparisons
===========
Method : lsd
contrast estimate SE df t.ratio p.value sig
treatment1 - treatment2 5.67 4.24 6 1.336 0.230
treatment1 - treatment3 2.67 4.24 6 0.629 0.553
treatment1 - treatment4 1.33 4.24 6 0.314 0.764
treatment1 - treatment5 6.42 6.36 6 1.009 0.352
treatment1 - treatment6 6.42 6.36 6 1.009 0.352
treatment1 - treatment7 -8.83 6.36 6 -1.389 0.214
treatment1 - treatment8 11.42 6.36 6 1.795 0.123
treatment1 - treatment9 7.42 6.36 6 1.166 0.288
treatment1 - treatment10 7.42 6.36 6 1.166 0.288
treatment1 - treatment11 -1.83 6.36 6 -0.288 0.783
treatment1 - treatment12 5.17 6.36 6 0.812 0.448
treatment2 - treatment3 -3.00 4.24 6 -0.707 0.506
treatment2 - treatment4 -4.33 4.24 6 -1.022 0.346
treatment2 - treatment5 0.75 6.36 6 0.118 0.910
treatment2 - treatment6 0.75 6.36 6 0.118 0.910
treatment2 - treatment7 -14.50 6.36 6 -2.280 0.063
treatment2 - treatment8 5.75 6.36 6 0.904 0.401
treatment2 - treatment9 1.75 6.36 6 0.275 0.792
treatment2 - treatment10 1.75 6.36 6 0.275 0.792
treatment2 - treatment11 -7.50 6.36 6 -1.179 0.283
treatment2 - treatment12 -0.50 6.36 6 -0.079 0.940
treatment3 - treatment4 -1.33 4.24 6 -0.314 0.764
treatment3 - treatment5 3.75 6.36 6 0.590 0.577
treatment3 - treatment6 3.75 6.36 6 0.590 0.577
treatment3 - treatment7 -11.50 6.36 6 -1.808 0.121
treatment3 - treatment8 8.75 6.36 6 1.376 0.218
treatment3 - treatment9 4.75 6.36 6 0.747 0.483
treatment3 - treatment10 4.75 6.36 6 0.747 0.483
treatment3 - treatment11 -4.50 6.36 6 -0.707 0.506
treatment3 - treatment12 2.50 6.36 6 0.393 0.708
treatment4 - treatment5 5.08 6.36 6 0.799 0.455
treatment4 - treatment6 5.08 6.36 6 0.799 0.455
treatment4 - treatment7 -10.17 6.36 6 -1.598 0.161
treatment4 - treatment8 10.08 6.36 6 1.585 0.164
treatment4 - treatment9 6.08 6.36 6 0.956 0.376
treatment4 - treatment10 6.08 6.36 6 0.956 0.376
treatment4 - treatment11 -3.17 6.36 6 -0.498 0.636
treatment4 - treatment12 3.83 6.36 6 0.603 0.569
treatment5 - treatment6 0.00 8.21 6 0.000 1.000
treatment5 - treatment7 -15.25 8.21 6 -1.857 0.113
treatment5 - treatment8 5.00 8.21 6 0.609 0.565
treatment5 - treatment9 1.00 7.34 6 0.136 0.896
treatment5 - treatment10 1.00 8.21 6 0.122 0.907
treatment5 - treatment11 -8.25 8.21 6 -1.005 0.354
treatment5 - treatment12 -1.25 8.21 6 -0.152 0.884
treatment6 - treatment7 -15.25 8.21 6 -1.857 0.113
treatment6 - treatment8 5.00 7.34 6 0.681 0.521
treatment6 - treatment9 1.00 8.21 6 0.122 0.907
treatment6 - treatment10 1.00 7.34 6 0.136 0.896
treatment6 - treatment11 -8.25 8.21 6 -1.005 0.354
treatment6 - treatment12 -1.25 8.21 6 -0.152 0.884
treatment7 - treatment8 20.25 8.21 6 2.466 0.049 *
treatment7 - treatment9 16.25 8.21 6 1.979 0.095
treatment7 - treatment10 16.25 8.21 6 1.979 0.095
treatment7 - treatment11 7.00 7.34 6 0.953 0.377
treatment7 - treatment12 14.00 7.34 6 1.906 0.105
treatment8 - treatment9 -4.00 8.21 6 -0.487 0.643
treatment8 - treatment10 -4.00 7.34 6 -0.545 0.606
treatment8 - treatment11 -13.25 8.21 6 -1.614 0.158
treatment8 - treatment12 -6.25 8.21 6 -0.761 0.475
treatment9 - treatment10 -0.00 8.21 6 -0.000 1.000
treatment9 - treatment11 -9.25 8.21 6 -1.126 0.303
treatment9 - treatment12 -2.25 8.21 6 -0.274 0.793
treatment10 - treatment11 -9.25 8.21 6 -1.126 0.303
treatment10 - treatment12 -2.25 8.21 6 -0.274 0.793
treatment11 - treatment12 7.00 7.34 6 0.953 0.377
Treatment Groups
================
Method : lsd
Treatment Adjusted Means SE df lower.CL upper.CL Group
8 73.25 5.61 6 59.52 86.98 1
9 77.25 5.61 6 63.52 90.98 12
10 77.25 5.61 6 63.52 90.98 12
5 78.25 5.61 6 64.52 91.98 12
6 78.25 5.61 6 64.52 91.98 12
2 79.00 3.00 6 71.66 86.34 12
12 79.50 5.61 6 65.77 93.23 12
3 82.00 3.00 6 74.66 89.34 12
4 83.33 3.00 6 76.00 90.67 12
1 84.67 3.00 6 77.33 92.00 12
11 86.50 5.61 6 72.77 100.23 12
7 93.50 5.61 6 79.77 107.23 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 1718 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 1717 286
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
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 Means
===============
Treatment Block Means SE r Min Max Adjusted Means
1 256.00 3.06 3 250.00 260.00 256.00
10 3 450.00 <NA> 1 450.00 450.00 437.67
11 1 300.00 <NA> 1 300.00 300.00 299.42
12 1 289.00 <NA> 1 289.00 289.00 288.42
2 228.00 6.11 3 220.00 240.00 228.00
3 247.67 10.17 3 237.00 268.00 247.67
4 264.00 18.68 3 227.00 287.00 264.00
5 2 281.00 <NA> 1 281.00 281.00 293.92
6 3 395.00 <NA> 1 395.00 395.00 382.67
7 1 347.00 <NA> 1 347.00 347.00 346.42
8 3 226.00 <NA> 1 226.00 226.00 213.67
9 2 311.00 <NA> 1 311.00 311.00 323.92
Comparisons
===========
Method : lsd
contrast estimate SE df t.ratio p.value sig
treatment1 - treatment2 28.00 13.81 6 2.027 0.089
treatment1 - treatment3 8.33 13.81 6 0.603 0.568
treatment1 - treatment4 -8.00 13.81 6 -0.579 0.584
treatment1 - treatment5 -37.92 20.72 6 -1.830 0.117
treatment1 - treatment6 -126.67 20.72 6 -6.113 0.001 ***
treatment1 - treatment7 -90.42 20.72 6 -4.363 0.005 **
treatment1 - treatment8 42.33 20.72 6 2.043 0.087
treatment1 - treatment9 -67.92 20.72 6 -3.278 0.017 *
treatment1 - treatment10 -181.67 20.72 6 -8.767 0.000 ***
treatment1 - treatment11 -43.42 20.72 6 -2.095 0.081
treatment1 - treatment12 -32.42 20.72 6 -1.564 0.169
treatment2 - treatment3 -19.67 13.81 6 -1.424 0.204
treatment2 - treatment4 -36.00 13.81 6 -2.606 0.040 *
treatment2 - treatment5 -65.92 20.72 6 -3.181 0.019 *
treatment2 - treatment6 -154.67 20.72 6 -7.464 0.000 ***
treatment2 - treatment7 -118.42 20.72 6 -5.715 0.001 **
treatment2 - treatment8 14.33 20.72 6 0.692 0.515
treatment2 - treatment9 -95.92 20.72 6 -4.629 0.004 **
treatment2 - treatment10 -209.67 20.72 6 -10.118 0.000 ***
treatment2 - treatment11 -71.42 20.72 6 -3.447 0.014 *
treatment2 - treatment12 -60.42 20.72 6 -2.916 0.027 *
treatment3 - treatment4 -16.33 13.81 6 -1.182 0.282
treatment3 - treatment5 -46.25 20.72 6 -2.232 0.067
treatment3 - treatment6 -135.00 20.72 6 -6.515 0.001 ***
treatment3 - treatment7 -98.75 20.72 6 -4.766 0.003 **
treatment3 - treatment8 34.00 20.72 6 1.641 0.152
treatment3 - treatment9 -76.25 20.72 6 -3.680 0.010 *
treatment3 - treatment10 -190.00 20.72 6 -9.169 0.000 ***
treatment3 - treatment11 -51.75 20.72 6 -2.497 0.047 *
treatment3 - treatment12 -40.75 20.72 6 -1.967 0.097
treatment4 - treatment5 -29.92 20.72 6 -1.444 0.199
treatment4 - treatment6 -118.67 20.72 6 -5.727 0.001 **
treatment4 - treatment7 -82.42 20.72 6 -3.977 0.007 **
treatment4 - treatment8 50.33 20.72 6 2.429 0.051
treatment4 - treatment9 -59.92 20.72 6 -2.892 0.028 *
treatment4 - treatment10 -173.67 20.72 6 -8.381 0.000 ***
treatment4 - treatment11 -35.42 20.72 6 -1.709 0.138
treatment4 - treatment12 -24.42 20.72 6 -1.178 0.283
treatment5 - treatment6 -88.75 26.75 6 -3.318 0.016 *
treatment5 - treatment7 -52.50 26.75 6 -1.963 0.097
treatment5 - treatment8 80.25 26.75 6 3.000 0.024 *
treatment5 - treatment9 -30.00 23.93 6 -1.254 0.257
treatment5 - treatment10 -143.75 26.75 6 -5.374 0.002 **
treatment5 - treatment11 -5.50 26.75 6 -0.206 0.844
treatment5 - treatment12 5.50 26.75 6 0.206 0.844
treatment6 - treatment7 36.25 26.75 6 1.355 0.224
treatment6 - treatment8 169.00 23.93 6 7.063 0.000 ***
treatment6 - treatment9 58.75 26.75 6 2.196 0.070
treatment6 - treatment10 -55.00 23.93 6 -2.299 0.061
treatment6 - treatment11 83.25 26.75 6 3.112 0.021 *
treatment6 - treatment12 94.25 26.75 6 3.523 0.012 *
treatment7 - treatment8 132.75 26.75 6 4.962 0.003 **
treatment7 - treatment9 22.50 26.75 6 0.841 0.433
treatment7 - treatment10 -91.25 26.75 6 -3.411 0.014 *
treatment7 - treatment11 47.00 23.93 6 1.964 0.097
treatment7 - treatment12 58.00 23.93 6 2.424 0.052
treatment8 - treatment9 -110.25 26.75 6 -4.121 0.006 **
treatment8 - treatment10 -224.00 23.93 6 -9.362 0.000 ***
treatment8 - treatment11 -85.75 26.75 6 -3.205 0.018 *
treatment8 - treatment12 -74.75 26.75 6 -2.794 0.031 *
treatment9 - treatment10 -113.75 26.75 6 -4.252 0.005 **
treatment9 - treatment11 24.50 26.75 6 0.916 0.395
treatment9 - treatment12 35.50 26.75 6 1.327 0.233
treatment10 - treatment11 138.25 26.75 6 5.168 0.002 **
treatment10 - treatment12 149.25 26.75 6 5.579 0.001 **
treatment11 - treatment12 11.00 23.93 6 0.460 0.662
Treatment Groups
================
Method : lsd
Treatment Adjusted Means SE df lower.CL upper.CL Group
8 213.67 18.27 6 168.95 258.38 12
2 228.00 9.77 6 204.10 251.90 1
3 247.67 9.77 6 223.76 271.57 123
1 256.00 9.77 6 232.10 279.90 1234
4 264.00 9.77 6 240.10 287.90 234
12 288.42 18.27 6 243.70 333.13 345
5 293.92 18.27 6 249.20 338.63 345
11 299.42 18.27 6 254.70 344.13 45
9 323.92 18.27 6 279.20 368.63 56
7 346.42 18.27 6 301.70 391.13 56
6 382.67 18.27 6 337.95 427.38 67
10 437.67 18.27 6 392.95 482.38 7In 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.
If truncate.means = TRUE, then any negative adjusted
means will be truncated to zero with a warning.
7.2 print.augmentedRCBD()
The results of analysis in an object of class
augmentedRCBD can be printed to the console as follows.
# Print results for variable y1
print(out1)
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
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 Means
===============
Treatment Block Means SE r Min Max Adjusted Means
1 84.67 3.84 3 79.00 92.00 84.67
10 3 74.00 <NA> 1 74.00 74.00 77.25
11 1 89.00 <NA> 1 89.00 89.00 86.50
12 1 82.00 <NA> 1 82.00 82.00 79.50
2 79.00 1.15 3 77.00 81.00 79.00
3 82.00 2.65 3 78.00 87.00 82.00
4 83.33 3.93 3 78.00 91.00 83.33
5 2 79.00 <NA> 1 79.00 79.00 78.25
6 3 75.00 <NA> 1 75.00 75.00 78.25
7 1 96.00 <NA> 1 96.00 96.00 93.50
8 3 70.00 <NA> 1 70.00 70.00 73.25
9 2 78.00 <NA> 1 78.00 78.00 77.25
Comparisons
===========
Method : lsd
contrast estimate SE df t.ratio p.value sig
treatment1 - treatment2 5.67 4.24 6 1.336 0.230
treatment1 - treatment3 2.67 4.24 6 0.629 0.553
treatment1 - treatment4 1.33 4.24 6 0.314 0.764
treatment1 - treatment5 6.42 6.36 6 1.009 0.352
treatment1 - treatment6 6.42 6.36 6 1.009 0.352
treatment1 - treatment7 -8.83 6.36 6 -1.389 0.214
treatment1 - treatment8 11.42 6.36 6 1.795 0.123
treatment1 - treatment9 7.42 6.36 6 1.166 0.288
treatment1 - treatment10 7.42 6.36 6 1.166 0.288
treatment1 - treatment11 -1.83 6.36 6 -0.288 0.783
treatment1 - treatment12 5.17 6.36 6 0.812 0.448
treatment2 - treatment3 -3.00 4.24 6 -0.707 0.506
treatment2 - treatment4 -4.33 4.24 6 -1.022 0.346
treatment2 - treatment5 0.75 6.36 6 0.118 0.910
treatment2 - treatment6 0.75 6.36 6 0.118 0.910
treatment2 - treatment7 -14.50 6.36 6 -2.280 0.063
treatment2 - treatment8 5.75 6.36 6 0.904 0.401
treatment2 - treatment9 1.75 6.36 6 0.275 0.792
treatment2 - treatment10 1.75 6.36 6 0.275 0.792
treatment2 - treatment11 -7.50 6.36 6 -1.179 0.283
treatment2 - treatment12 -0.50 6.36 6 -0.079 0.940
treatment3 - treatment4 -1.33 4.24 6 -0.314 0.764
treatment3 - treatment5 3.75 6.36 6 0.590 0.577
treatment3 - treatment6 3.75 6.36 6 0.590 0.577
treatment3 - treatment7 -11.50 6.36 6 -1.808 0.121
treatment3 - treatment8 8.75 6.36 6 1.376 0.218
treatment3 - treatment9 4.75 6.36 6 0.747 0.483
treatment3 - treatment10 4.75 6.36 6 0.747 0.483
treatment3 - treatment11 -4.50 6.36 6 -0.707 0.506
treatment3 - treatment12 2.50 6.36 6 0.393 0.708
treatment4 - treatment5 5.08 6.36 6 0.799 0.455
treatment4 - treatment6 5.08 6.36 6 0.799 0.455
treatment4 - treatment7 -10.17 6.36 6 -1.598 0.161
treatment4 - treatment8 10.08 6.36 6 1.585 0.164
treatment4 - treatment9 6.08 6.36 6 0.956 0.376
treatment4 - treatment10 6.08 6.36 6 0.956 0.376
treatment4 - treatment11 -3.17 6.36 6 -0.498 0.636
treatment4 - treatment12 3.83 6.36 6 0.603 0.569
treatment5 - treatment6 0.00 8.21 6 0.000 1.000
treatment5 - treatment7 -15.25 8.21 6 -1.857 0.113
treatment5 - treatment8 5.00 8.21 6 0.609 0.565
treatment5 - treatment9 1.00 7.34 6 0.136 0.896
treatment5 - treatment10 1.00 8.21 6 0.122 0.907
treatment5 - treatment11 -8.25 8.21 6 -1.005 0.354
treatment5 - treatment12 -1.25 8.21 6 -0.152 0.884
treatment6 - treatment7 -15.25 8.21 6 -1.857 0.113
treatment6 - treatment8 5.00 7.34 6 0.681 0.521
treatment6 - treatment9 1.00 8.21 6 0.122 0.907
treatment6 - treatment10 1.00 7.34 6 0.136 0.896
treatment6 - treatment11 -8.25 8.21 6 -1.005 0.354
treatment6 - treatment12 -1.25 8.21 6 -0.152 0.884
treatment7 - treatment8 20.25 8.21 6 2.466 0.049 *
treatment7 - treatment9 16.25 8.21 6 1.979 0.095
treatment7 - treatment10 16.25 8.21 6 1.979 0.095
treatment7 - treatment11 7.00 7.34 6 0.953 0.377
treatment7 - treatment12 14.00 7.34 6 1.906 0.105
treatment8 - treatment9 -4.00 8.21 6 -0.487 0.643
treatment8 - treatment10 -4.00 7.34 6 -0.545 0.606
treatment8 - treatment11 -13.25 8.21 6 -1.614 0.158
treatment8 - treatment12 -6.25 8.21 6 -0.761 0.475
treatment9 - treatment10 -0.00 8.21 6 -0.000 1.000
treatment9 - treatment11 -9.25 8.21 6 -1.126 0.303
treatment9 - treatment12 -2.25 8.21 6 -0.274 0.793
treatment10 - treatment11 -9.25 8.21 6 -1.126 0.303
treatment10 - treatment12 -2.25 8.21 6 -0.274 0.793
treatment11 - treatment12 7.00 7.34 6 0.953 0.377
Treatment Groups
================
Method : lsd
Treatment Adjusted Means SE df lower.CL upper.CL Group
8 73.25 5.61 6 59.52 86.98 1
9 77.25 5.61 6 63.52 90.98 12
10 77.25 5.61 6 63.52 90.98 12
5 78.25 5.61 6 64.52 91.98 12
6 78.25 5.61 6 64.52 91.98 12
2 79.00 3.00 6 71.66 86.34 12
12 79.50 5.61 6 65.77 93.23 12
3 82.00 3.00 6 74.66 89.34 12
4 83.33 3.00 6 76.00 90.67 12
1 84.67 3.00 6 77.33 92.00 12
11 86.50 5.61 6 72.77 100.23 12
7 93.50 5.61 6 79.77 107.23 2
# Print results for variable y2
print(out2)
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 1718 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 1717 286
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
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 Means
===============
Treatment Block Means SE r Min Max Adjusted Means
1 256.00 3.06 3 250.00 260.00 256.00
10 3 450.00 <NA> 1 450.00 450.00 437.67
11 1 300.00 <NA> 1 300.00 300.00 299.42
12 1 289.00 <NA> 1 289.00 289.00 288.42
2 228.00 6.11 3 220.00 240.00 228.00
3 247.67 10.17 3 237.00 268.00 247.67
4 264.00 18.68 3 227.00 287.00 264.00
5 2 281.00 <NA> 1 281.00 281.00 293.92
6 3 395.00 <NA> 1 395.00 395.00 382.67
7 1 347.00 <NA> 1 347.00 347.00 346.42
8 3 226.00 <NA> 1 226.00 226.00 213.67
9 2 311.00 <NA> 1 311.00 311.00 323.92
Comparisons
===========
Method : lsd
contrast estimate SE df t.ratio p.value sig
treatment1 - treatment2 28.00 13.81 6 2.027 0.089
treatment1 - treatment3 8.33 13.81 6 0.603 0.568
treatment1 - treatment4 -8.00 13.81 6 -0.579 0.584
treatment1 - treatment5 -37.92 20.72 6 -1.830 0.117
treatment1 - treatment6 -126.67 20.72 6 -6.113 0.001 ***
treatment1 - treatment7 -90.42 20.72 6 -4.363 0.005 **
treatment1 - treatment8 42.33 20.72 6 2.043 0.087
treatment1 - treatment9 -67.92 20.72 6 -3.278 0.017 *
treatment1 - treatment10 -181.67 20.72 6 -8.767 0.000 ***
treatment1 - treatment11 -43.42 20.72 6 -2.095 0.081
treatment1 - treatment12 -32.42 20.72 6 -1.564 0.169
treatment2 - treatment3 -19.67 13.81 6 -1.424 0.204
treatment2 - treatment4 -36.00 13.81 6 -2.606 0.040 *
treatment2 - treatment5 -65.92 20.72 6 -3.181 0.019 *
treatment2 - treatment6 -154.67 20.72 6 -7.464 0.000 ***
treatment2 - treatment7 -118.42 20.72 6 -5.715 0.001 **
treatment2 - treatment8 14.33 20.72 6 0.692 0.515
treatment2 - treatment9 -95.92 20.72 6 -4.629 0.004 **
treatment2 - treatment10 -209.67 20.72 6 -10.118 0.000 ***
treatment2 - treatment11 -71.42 20.72 6 -3.447 0.014 *
treatment2 - treatment12 -60.42 20.72 6 -2.916 0.027 *
treatment3 - treatment4 -16.33 13.81 6 -1.182 0.282
treatment3 - treatment5 -46.25 20.72 6 -2.232 0.067
treatment3 - treatment6 -135.00 20.72 6 -6.515 0.001 ***
treatment3 - treatment7 -98.75 20.72 6 -4.766 0.003 **
treatment3 - treatment8 34.00 20.72 6 1.641 0.152
treatment3 - treatment9 -76.25 20.72 6 -3.680 0.010 *
treatment3 - treatment10 -190.00 20.72 6 -9.169 0.000 ***
treatment3 - treatment11 -51.75 20.72 6 -2.497 0.047 *
treatment3 - treatment12 -40.75 20.72 6 -1.967 0.097
treatment4 - treatment5 -29.92 20.72 6 -1.444 0.199
treatment4 - treatment6 -118.67 20.72 6 -5.727 0.001 **
treatment4 - treatment7 -82.42 20.72 6 -3.977 0.007 **
treatment4 - treatment8 50.33 20.72 6 2.429 0.051
treatment4 - treatment9 -59.92 20.72 6 -2.892 0.028 *
treatment4 - treatment10 -173.67 20.72 6 -8.381 0.000 ***
treatment4 - treatment11 -35.42 20.72 6 -1.709 0.138
treatment4 - treatment12 -24.42 20.72 6 -1.178 0.283
treatment5 - treatment6 -88.75 26.75 6 -3.318 0.016 *
treatment5 - treatment7 -52.50 26.75 6 -1.963 0.097
treatment5 - treatment8 80.25 26.75 6 3.000 0.024 *
treatment5 - treatment9 -30.00 23.93 6 -1.254 0.257
treatment5 - treatment10 -143.75 26.75 6 -5.374 0.002 **
treatment5 - treatment11 -5.50 26.75 6 -0.206 0.844
treatment5 - treatment12 5.50 26.75 6 0.206 0.844
treatment6 - treatment7 36.25 26.75 6 1.355 0.224
treatment6 - treatment8 169.00 23.93 6 7.063 0.000 ***
treatment6 - treatment9 58.75 26.75 6 2.196 0.070
treatment6 - treatment10 -55.00 23.93 6 -2.299 0.061
treatment6 - treatment11 83.25 26.75 6 3.112 0.021 *
treatment6 - treatment12 94.25 26.75 6 3.523 0.012 *
treatment7 - treatment8 132.75 26.75 6 4.962 0.003 **
treatment7 - treatment9 22.50 26.75 6 0.841 0.433
treatment7 - treatment10 -91.25 26.75 6 -3.411 0.014 *
treatment7 - treatment11 47.00 23.93 6 1.964 0.097
treatment7 - treatment12 58.00 23.93 6 2.424 0.052
treatment8 - treatment9 -110.25 26.75 6 -4.121 0.006 **
treatment8 - treatment10 -224.00 23.93 6 -9.362 0.000 ***
treatment8 - treatment11 -85.75 26.75 6 -3.205 0.018 *
treatment8 - treatment12 -74.75 26.75 6 -2.794 0.031 *
treatment9 - treatment10 -113.75 26.75 6 -4.252 0.005 **
treatment9 - treatment11 24.50 26.75 6 0.916 0.395
treatment9 - treatment12 35.50 26.75 6 1.327 0.233
treatment10 - treatment11 138.25 26.75 6 5.168 0.002 **
treatment10 - treatment12 149.25 26.75 6 5.579 0.001 **
treatment11 - treatment12 11.00 23.93 6 0.460 0.662
Treatment Groups
================
Method : lsd
Treatment Adjusted Means SE df lower.CL upper.CL Group
8 213.67 18.27 6 168.95 258.38 12
2 228.00 9.77 6 204.10 251.90 1
3 247.67 9.77 6 223.76 271.57 123
1 256.00 9.77 6 232.10 279.90 1234
4 264.00 9.77 6 240.10 287.90 234
12 288.42 18.27 6 243.70 333.13 345
5 293.92 18.27 6 249.20 338.63 345
11 299.42 18.27 6 254.70 344.13 45
9 323.92 18.27 6 279.20 368.63 56
7 346.42 18.27 6 301.70 391.13 56
6 382.67 18.27 6 337.95 427.38 67
10 437.67 18.27 6 392.95 482.38 77.3 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] 0.59139757.4 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:
[1m
[22mRemoved 2 rows containing missing values or values outside the scale range
(`geom_bar()`).
plot(freq1)
# Frequency distribution for variable y2
freq2 <- freqdist.augmentedRCBD(out2, xlab = "Trait 2")Warning:
[1m
[22mRemoved 2 rows containing missing values or values outside the scale range
(`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:
[1m
[22mRemoved 2 rows containing missing values or values outside the scale range
(`geom_bar()`).
plot(freq1)
# Frequency distribution for variable y2
freq2 <- freqdist.augmentedRCBD(out2, xlab = "Trait 2", check.col = colset)Warning:
[1m
[22mRemoved 2 rows containing missing values or values outside the scale range
(`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:
[1m
[22mRemoved 2 rows containing missing values or values outside the scale range
(`geom_bar()`).
plot(freq1)
# Frequency distribution for variable y2
freq2 <- freqdist.augmentedRCBD(out2, xlab = "Trait 2",
highlight.check = FALSE)Warning:
[1m
[22mRemoved 2 rows containing missing values or values outside the scale range
(`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 analysis needs to be performed only if the sum of squares of
“Treatment: Test” are significant.
# Genetic variability statistics for variable y1
gva.augmentedRCBD(out1)Warning in gva.augmentedRCBD(out1): P-value for "Treatment: Test" is > 0.05.
Genetic variability analysis may not be appropriate for this trait.$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"Negative estimates of variance components if computed are not abnormal. For information on how to deal with these, refer Robinson et al. (1955) and Dudley and Moll (1969).
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.docx"),
file.type = "word")
# MS word report for variable y2
report.augmentedRCBD(aug = out2,
target = file.path(tempdir(),
"augmentedRCBD output.docx"),
file.type = "word")
Fig. 6: MS Word report generated with
report.agumentedRCBD function.
Alternatively, the analysis results can also be exported to a MS Excel file as follows.
# MS excel report for variable y1
report.augmentedRCBD(aug = out1,
target = file.path(tempdir(),
"augmentedRCBD output.xlsx"),
file.type = "excel")
# MS excel report for variable y2
report.augmentedRCBD(aug = out2,
target = file.path(tempdir(),
"augmentedRCBD output.xlsx"),
file.type = "excel")
Fig. 6: MS Excel 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.
Fig. 8. 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"
ANOVA, Treatment Adjusted
=========================
Mean.Sq
Source Df y1 y2
Block (ignoring Treatments) 2 180.04 * 3509.67 **
Treatment (eliminating Blocks) 11 25.92 ⁿˢ 5360.49 **
Treatment: Check 3 17.64 ⁿˢ 716.75 ⁿˢ
Treatment: Test and Test vs. Check 8 29.02 ⁿˢ 7101.89 **
Residuals 6 26.97 286.25
ⁿˢ P > 0.05; * P <= 0.05; ** P <= 0.01
ANOVA, Block Adjusted
=====================
Mean.Sq
Source Df y1 y2
Treatment (ignoring Blocks) 11 52.33 ⁿˢ 5882.50 **
Treatment: Check 3 17.64 ⁿˢ 716.75 ⁿˢ
Treatment: Test vs. Check 1 16.87 ⁿˢ 27694.41 **
Treatment: Test 7 72.27 ⁿˢ 4980.41 **
Block (eliminating Treatments) 2 34.75 ⁿˢ 638.58 ⁿˢ
Residuals 6 26.97 286.25
ⁿˢ P > 0.05; * P <= 0.05; ** P <= 0.01
Coefficient of Variation
========================
Trait CV
y1 6.37
y2 6.06
Overall Adjusted Mean
=====================
Trait Overall.adjusted.mean
y1 81.06
y2 298.48
Standard Errors
===============
Comparison y1 y2
A Test Treatment and a Control Treatment 6.70 21.84
Control Treatment Means 4.24 13.81
Two Test Treatments (Different Blocks) 8.21 26.75
Two Test Treatments (Same Block) 7.34 23.93
Critical Difference
===================
alpha = 0.05
Comparison y1 y2
A Test Treatment and a Control Treatment 16.41 53.45
Control Treatment Means 10.38 33.80
Two Test Treatments (Different Blocks) 20.09 65.46
Two Test Treatments (Same Block) 17.97 58.55
Descriptive Statistics
======================
Trait Count Mean Std.Error Std.Deviation Min Max Skewness Skewness_sig
y1 12 81.06 1.55 5.36 73.25 93.50 0.93 ⁿˢ
y2 12 298.48 18.92 65.55 213.67 437.67 0.74 ⁿˢ
Kurtosis Kurtosis_sig
3.52 ⁿˢ
2.79 ⁿˢ
ⁿˢ P > 0.05; * P <= 0.05; ** P <= 0.01
Genetic Variability Analysis
============================
k = 2.063
Trait Mean PV GV EV GCV GCV.category PCV PCV.category ECV
y1 † 81.06 72.27 45.30 26.97 8.30 Low 10.49 Medium 6.41
y2 298.48 4980.41 4694.16 286.25 22.95 High 23.64 High 5.67
hBS hBS.category GA GAM GAM.category
62.68 High 10.99 13.56 Medium
94.25 High 137.22 45.97 HighWarning:
† P-value for "Treatment: Test" is > 0.05. Genetic variability analysis may not be appropriate for this trait.Warning:
‡ Negative GV detected.
GCV, GCV category, hBS, hBS category, GA, GAM and
GAM category could not be computed.
Warning Messages
================
[Frequency Distribution]
<y1>
Removed 2 rows containing missing values or values outside the scale range
(`geom_bar()`).
<y2>
Removed 2 rows containing missing values or values outside the scale range
(`geom_bar()`).
[GVA]
<y1>
P-value for "Treatment: Test" is > 0.05. Genetic variability analysis may not be appropriate for this trait.
Treatment Means
===============
Treatment Block y1 y2
1 84.67 256.00
10 3 77.25 437.67
11 1 86.50 299.42
12 1 79.50 288.42
2 79.00 228.00
3 82.00 247.67
4 83.33 264.00
5 2 78.25 293.92
6 3 78.25 382.67
7 1 93.50 346.42
8 3 73.25 213.67
9 2 77.25 323.928.2 print.augmentedRCBD.bulk()
The results of analysis in an object of class
augmentedRCBD.bulk can be printed to the console as
follows.
# Print results
print(bout)
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"
ANOVA, Treatment Adjusted
=========================
Mean.Sq
Source Df y1 y2
Block (ignoring Treatments) 2 180.04 * 3509.67 **
Treatment (eliminating Blocks) 11 25.92 ⁿˢ 5360.49 **
Treatment: Check 3 17.64 ⁿˢ 716.75 ⁿˢ
Treatment: Test and Test vs. Check 8 29.02 ⁿˢ 7101.89 **
Residuals 6 26.97 286.25
ⁿˢ P > 0.05; * P <= 0.05; ** P <= 0.01
ANOVA, Block Adjusted
=====================
Mean.Sq
Source Df y1 y2
Treatment (ignoring Blocks) 11 52.33 ⁿˢ 5882.50 **
Treatment: Check 3 17.64 ⁿˢ 716.75 ⁿˢ
Treatment: Test vs. Check 1 16.87 ⁿˢ 27694.41 **
Treatment: Test 7 72.27 ⁿˢ 4980.41 **
Block (eliminating Treatments) 2 34.75 ⁿˢ 638.58 ⁿˢ
Residuals 6 26.97 286.25
ⁿˢ P > 0.05; * P <= 0.05; ** P <= 0.01
Coefficient of Variation
========================
Trait CV
y1 6.37
y2 6.06
Overall Adjusted Mean
=====================
Trait Overall.adjusted.mean
y1 81.06
y2 298.48
Standard Errors
===============
Comparison y1 y2
A Test Treatment and a Control Treatment 6.70 21.84
Control Treatment Means 4.24 13.81
Two Test Treatments (Different Blocks) 8.21 26.75
Two Test Treatments (Same Block) 7.34 23.93
Critical Difference
===================
alpha = 0.05
Comparison y1 y2
A Test Treatment and a Control Treatment 16.41 53.45
Control Treatment Means 10.38 33.80
Two Test Treatments (Different Blocks) 20.09 65.46
Two Test Treatments (Same Block) 17.97 58.55
Descriptive Statistics
======================
Trait Count Mean Std.Error Std.Deviation Min Max Skewness Skewness_sig
y1 12 81.06 1.55 5.36 73.25 93.50 0.93 ⁿˢ
y2 12 298.48 18.92 65.55 213.67 437.67 0.74 ⁿˢ
Kurtosis Kurtosis_sig
3.52 ⁿˢ
2.79 ⁿˢ
ⁿˢ P > 0.05; * P <= 0.05; ** P <= 0.01
Genetic Variability Analysis
============================
k = 2.063
Trait Mean PV GV EV GCV GCV.category PCV PCV.category ECV
y1 † 81.06 72.27 45.30 26.97 8.30 Low 10.49 Medium 6.41
y2 298.48 4980.41 4694.16 286.25 22.95 High 23.64 High 5.67
hBS hBS.category GA GAM GAM.category
62.68 High 10.99 13.56 Medium
94.25 High 137.22 45.97 HighWarning:
† P-value for "Treatment: Test" is > 0.05. Genetic variability analysis may not be appropriate for this trait.Warning:
‡ Negative GV detected.
GCV, GCV category, hBS, hBS category, GA, GAM and
GAM category could not be computed.
Warning Messages
================
[Frequency Distribution]
<y1>
Removed 2 rows containing missing values or values outside the scale range
(`geom_bar()`).
<y2>
Removed 2 rows containing missing values or values outside the scale range
(`geom_bar()`).
[GVA]
<y1>
P-value for "Treatment: Test" is > 0.05. Genetic variability analysis may not be appropriate for this trait.
Treatment Means
===============
Treatment Block y1 y2
1 84.67 256.00
10 3 77.25 437.67
11 1 86.50 299.42
12 1 79.50 288.42
2 79.00 228.00
3 82.00 247.67
4 83.33 264.00
5 2 78.25 293.92
6 3 78.25 382.67
7 1 93.50 346.42
8 3 73.25 213.67
9 2 77.25 323.928.3 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"),
file.type = "word")
Fig. 9: MS Word report generated with
report.agumentedRCBD.bulk function.
Alternatively, the analysis results can also be exported to a MS Excel file as follows.
# MS excel report
report.augmentedRCBD.bulk(aug.bulk = bout,
target = file.path(tempdir(),
"augmentedRCBD bulk output.xlsx"),
file.type = "excel")
Fig. 10: MS Excel 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. ().
augmentedRCBD: Analysis of Augmented Randomised Complete Block
Designs. R package version 0.1.7.9000,
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},
note = {R package version 0.1.7.9000 https://aravind-j.github.io/augmentedRCBD/ 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
R version 4.4.1 (2024-06-14)
Platform: aarch64-apple-darwin20
Running under: macOS Sonoma 14.5
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRlapack.dylib; LAPACK version 3.12.0
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
time zone: UTC
tzcode source: internal
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] diagram_1.6.5 shape_1.4.6.1 augmentedRCBD_0.1.7.9000
loaded via a namespace (and not attached):
[1] tidyselect_1.2.1 farver_2.1.2 dplyr_1.1.4
[4] bitops_1.0-8 fastmap_1.2.0 RCurl_1.98-1.16
[7] TH.data_1.1-2 fontquiver_0.2.1 mathjaxr_1.6-0
[10] promises_1.3.0 XML_3.99-0.17 digest_0.6.36
[13] estimability_1.5.1 mime_0.12 lifecycle_1.0.4
[16] multcompView_0.1-10 gfonts_0.2.0 survival_3.6-4
[19] magrittr_2.0.3 compiler_4.4.1 rlang_1.1.4
[22] sass_0.4.9 tools_4.4.1 utf8_1.2.4
[25] yaml_2.3.10 data.table_1.15.4 knitr_1.48
[28] labeling_0.4.3 askpass_1.2.0 htmlwidgets_1.6.4
[31] curl_5.2.1 plyr_1.8.9 xml2_1.3.6
[34] multcomp_1.4-26 numform_0.7.0 httpcode_0.3.0
[37] withr_3.0.1 desc_1.4.3 grid_4.4.1
[40] fansi_1.0.6 gdtools_0.3.7 xtable_1.8-4
[43] colorspace_2.1-1 ggplot2_3.5.1 emmeans_1.10.3
[46] scales_1.3.0 MASS_7.3-60.2 crul_1.5.0
[49] cli_3.6.3 mvtnorm_1.2-5 rmarkdown_2.27
[52] crayon_1.5.3 ragg_1.3.2 generics_0.1.3
[55] httr_1.4.7 reshape2_1.4.4 cachem_1.1.0
[58] stringr_1.5.1 splines_4.4.1 vctrs_0.6.5
[61] Matrix_1.7-0 sandwich_3.1-0 jsonlite_1.8.8
[64] fontBitstreamVera_0.1.1 systemfonts_1.1.0 jquerylib_0.1.4
[67] glue_1.7.0 pkgdown_2.1.0 codetools_0.2-20
[70] stringi_1.8.4 flextable_0.9.6 gtable_0.3.5
[73] later_1.3.2 munsell_0.5.1 tibble_3.2.1
[76] pillar_1.9.0 htmltools_0.5.8.1 openssl_2.2.0
[79] R6_2.5.1 textshaping_0.4.0 Rdpack_2.6
[82] evaluate_0.24.0 shiny_1.9.1 lattice_0.22-6
[85] highr_0.11 rbibutils_2.2.16 moments_0.14.1
[88] openxlsx_4.2.6.1 fontLiberation_0.1.0 httpuv_1.6.15
[91] bslib_0.8.0 Rcpp_1.0.13 zip_2.3.1
[94] uuid_1.2-1 officer_0.6.6 xfun_0.46
[97] fs_1.6.4 zoo_1.8-12 pkgconfig_2.0.3 References
Anscombe, F. J., and Glynn, W. J. (1983). Distribution of the kurtosis
statistic
b
for normal samples. Biometrika 70, 227–234. doi:10.1093/biomet/70.1.227.
Burton, G. W. (1951). Quantitative inheritance in pearl millet
(Pennisetum glaucum). Agronomy Journal
43, 409–417. doi:10.2134/agronj1951.00021962004300090001x.
Burton, G. W. (1952). Qualitative inheritance in grasses.
Vol. 1. in Proceedings of the 6th
International Grassland Congress,
Pennsylvania State College,
17–23.
D’Agostino, R. B. (1970). Transformation to normality of the null
distribution of
g.
Biometrika 57, 679–681. doi:10.1093/biomet/57.3.679.
Dudley, J. W., and Moll, R. H. (1969). Interpretation and use of
estimates of heritability and genetic variances in plant breeding.
Crop Science 9, 257–262. doi:10.2135/cropsci1969.0011183X000900030001x.
Federer, W. T. (1956b). Augmented (or Hoonuiaku)
Designs. New York: Cornell University Available at: https://ecommons.cornell.edu/handle/1813/32841.
Federer, W. T. (1956a). Augmented (or Hoonuiaku) designs.
The Hawaiian Planters’ Record LV(2), 191–208.
Federer, W. T. (1961). Augmented designs with one-way elimination of
heterogeneity. Biometrics 17, 447–473. doi:10.2307/2527837.
Federer, W. T., and Searle, S. R. (1976). Model
Considerations and Variance
Component Estimation in Augmented
Completely Randomized and
Randomized Complete Blocks
Designs-Preliminary Version. New
York: Cornell University Available at: https://hdl.handle.net/1813/32691.
Johnson, H. W., Robinson, H. F., and Comstock, R. E. (1955). Estimates
of genetic and environmental variability in soybeans. Agronomy
journal 47, 314–318. doi:10.2134/agronj1955.00021962004700070009x.
Lush, J. L. (1940). Intra-sire correlations or regressions of offspring
on dam as a method of estimating heritability of characteristics.
Proceedings of the American Society of Animal Nutrition 1940,
293–301. doi:10.2527/jas1940.19401293x.
Robinson, H. F. (1966). Quantitative genetics in relation to breeding on
centennial of Mendelism. Indian Journal of Genetics and
Plant Breeding, 171.
Robinson, H. F., Comstock, R. E., and Harvey, P. H. (1955). Genetic
variances in open pollinated varieties of corn. Genetics 40,
45–60. doi:10.1093/genetics/40.1.45.
Sivasubramaniam, S., and Madhavamenon, P. (1973). Genotypic and
phenotypic variability in rice. The Madras Agricultural Journal
60, 1093–1096.
Tippmann, S. (2015). Programming tools: Adventures with
R. Nature News 517, 109. doi:10.1038/517109a.