Statistical Analysis of Agricultural Experiments Part I Single Factor Experiments

414 Pages·2016·12.23 MB·English

Statistical Analysis of Agricultural Experiments
Part - I : Single Factor Experiments
V K Gupta
Rajender Parsad
Lal Mohan Bhar
Baidya Nath Mandal
ICAR-Indian Agricultural Statistics Research Institute
Library Avenue, Pusa, New Delhi - 110012
www.iasri.res.in
ISO 9001:2008 Certified
Lasertypeset & Printed by:
M/s Royal Offset Printers, A-89/1, Naraina Industrial Area, Phase-I, New Delhi-110028
Preface
Design of Experiments is an integral component of every scientific endeavour,
particularly the agricultural sciences where the designing of an experiment
is an inevitable component of research. This is due to the fact that advancement
of any scientific discipline happens through new knowledge and technology
developments and indeed, a scientifically designed experiment is a valuable tool
in this process. The doyen of agricultural sciences Professor M.S. Swaminathan
rightly said, “It is the effective use of the tools of statistical design of experiments
that paved the way for the green revolution.”
A carefully designed experiment is able to answer all the queries of a researcher
with accuracy and reliability with efficient use of available resources of the
experimenters. Thus, for successful experimentation, it is highly desirable that
scientists and researchers of scientific disciplines, including agricultural sciences,
understand the basic principles of designing an experiment and analysis of resultant
data from the completed experiment. It may be emphasized that a researcher should
always consult a statistician before, during and after experimentation, if he is not
convinced enough about using a design for his experiment or an analysis technique
for this data. In any designed experiments, there are certain factors which are
beyond the control of the experimenter. In order to reduce the influence of these
factors, the experiment has to be suitably planned and executed scientifically with
immense care. In this regard, interactions with a statistician before the experiment
begins is expected to be highly beneficial to the experimenter because he can devise
a suitable design keeping in view the questions the experimenter has in mind, the
factors he wants to consider and the amount of available resources he can afford.
Though, a number of statistical books on designing and analysis of experiments
are available, most of these books are intended for statisticians because the subject
is treated through rigorous algebraic theories. Researchers of applied scientific
disciplines are often not interested in the mathematical derivation of the statistical
formulae. They would rather be happy with basic ideas behind using a design for
a particular experimental situation and subsequently analysis steps with necessary
precautions while doing the analysis.
The authors have conducted a number of training programmes on designing and
analysis of experiments for the research scientists of Indian National Agricultural
Research and Education System. Through the interaction with the trainee scientists,
the authors felt that there is a strong need for preparing a book on design and
analysis of experiments covering basic concepts, enough examples of situations for
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use of various designs, and easy to follow analysis steps. This book is an attempt
in that direction. In this book, the subject of design and analysis of experiments
has been treated in simple language giving basic concepts of various designs and
essential steps of analysis of data from designed experiments. Moreover, examples
of analysis of data have been provided for each of the designs covered in the book.
The additional strength of the book is that for each of the designs covered in this
book, SAS and R codes for analysis have been provided for performing the analysis.
It is hoped that this will enable the readers to directly analyze their data from their
experiments.
Since the topic of design and analysis of experiments is vast, the book has been
divided into two parts; first part covering fundamentals of design and analysis of
experiments related to, by and large, single factor experiments and the second part
focusing mostly on multifactor experiments and advanced topics. The composition
of the first part of the book is as follows. It starts with an introductory Chapter
on design of experiments which gives an introduction to the terminologies and
basic concepts of experimental designs along with a brief history of the subject.
No claim is being made for this Chapter to be completely exhaustive. In Chapter
2, introduction is made to some most commonly used designs namely completely
randomized designs, randomized complete block designs and Latin square designs.
Chapter 3 discusses contrast analysis, a very useful tool for answering many
questions of the experimenters through designed experiments. Chapter 4 deals
with analysis of covariance, a useful technique for controlling variability when one
or more covariates linearly related to response variable are available. Chapters 5, 6
and 7 are devoted to study of various important classes of block designs. The topics
such as outliers in experimental designs, groups of experiments are studied in the
subsequent Chapters. One Chapter has been devoted to multivariate analysis of
variance for simultaneously analyzing multiple response variables. The book has
four Annexures. Annexure I gives introduction to SAS and Annexure II introduces
the reader to the R software, currently trending open source statistical software.
Annexure III is devoted to multiple comparisons while Annexure IV describes web
resource “Design Resources Server.” The readers would find Annexure I and II very
useful in having a good understanding of the codes that have been used throughout
the book. Annexure III and IV will help in a better understanding of the contents
of the book. Part I of the book ends with a bibliography on the topics covered in
this book. Although an attempt has been made to give an elaborate bibliography, no
claim is made to this being exhaustive.
Help has been received from many places and persons in preparing the
manuscript of this book. The ideas received from our teachers Dr. Arun Nigam
and Dr. Aloke Dey have been very helpful in giving a shape to this book. In fact
the authors are indebted to both Dr. Nigam and Dr. Dey for introducing us to this
very important area of research in Statistics which is intertwined with agricultural
sciences and helps improving the quality of agricultural research by making use
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of appropriate and sophisticated designs of experiments and analysis of data. We
convey our gratitude towards Dr. Bikas Sinha and Dr. Rahul Mukerjee who have
always motivated us in this endeavour. They have always been a deep source of
inspiration for us.
A special mention may be made about the invaluable help and support received
from Mrs. Jyoti Gangwani, a technical officer working in the National Professor
scheme who has very meticulously checked the results of all the experimental
designs given in this book by reanalyzing the data from every single designed
experiment reported in this book. She has also helped with the editing of the
manuscript and then reading very carefully the galley proofs. Her contribution in
the development of the manuscript of this book has been monumental in many
ways. The authors would like to thank her whole heartedly for being always present
with a helping hand, whenever asked for.
The authors are thankful to the Director, IASRI for his encouragement
throughout the preparation of this manuscript. Thanks are also due to Director,
IASRI for providing all facilities required for handling the project of writing this
book.
The authors, in particular the first author, would like to place on record the
strength received from the Education Division of the ICAR for providing the
financial support in the National Professor Scheme for undertaking this assignment
of writing this book and getting this published. The authors are beholden to the
Deputy Director General (Education), ICAR for his constant encouragement
throughout the preparation of this manuscript. The funds received from the
Division of Education, ICAR, for publication of scientific manuscripts is highly
appreciated and immensely acknowledged.
The authors fervently expect that the book would be enormously useful to the
agricultural scientists in planning and designing their experiments and analyzing
the data generated from their experiments. The authors would look forward
to getting suggestions from all around to help improve the contents of the next
edition of the book so that the readers can benefit from the contents. The errors and
omissions are likely to be present in this book. The authors would exceedingly feel
grateful if these are brought to their notice.
V K Gupta
Rajender Parsad
Lal Mohan Bhar
Baidya Nath Mandal
Place: New Delhi
Date: February, 2016
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