statistical methods agricultural workers

378 Pages·2012·5.93 MB·English

STATISTICAL METHODS
FOR
AGRICULTURAL WORKERS

ST ATISTICAL METHODS
FOR
AGRICULTURAL WORKERS
BY
V. G. PANSE, B.Se., Ph.D. (Lond.), F.N.I.
Statistical Adviser
Indian Council of Agricultural Research, New Delhi
AND
\
P. V. SUKHATME, Ph.D., D.Se. (Lond.), F.N.1.
Chief, Statistics Branch
Food and Agriculture Organization of the United Nations, Rome
Published by
INDIAN COUNCIL OF AGRICULTURAL RESEARCH
NEW DELHI
Published 1954
Reprinted 1957
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PREFACE
THIS book had its origin in the proposal to revise and reprint
the' Handbook of Stati~tics for Use in Plant Breeding and
Agricultural Problems' by F. J. F. Shaw published by the Indian
(then Imperial) Council of Agricultural Research in 1936 but
which has been out of print for some years. The present authors
were invited by the Council to revise and bring it up to date
in order that it should meet the normal requirements of the
present-day agricultural research workers. In the course of
the revision It became clear that not only would there have
to be a change in the order and manner of the presentation of the
subject-matter but also a considerable expansion in the scope of
the material included in the book, even whde keeping within the
limits set out by the objective of the book, namely, to provide
an elementary text-book for' the use of agricultural research
workers whose mathematical attainments are modest. As it turned
out finally the revision amounted to an almost complete rewriting
of the book and addition of several new chapters.
The book now consists of sixteen chapters divided into two
parts, the first with six chapters dealing with statistical methods
and the second with the design of experiments. The elaboration
of the second part is in keeping with the greater emphasis now
rightly laid on the proper planning of experiments in order that
they may supply efficiently and economically the information
sought. The subject-matter has been illustrated throughout with
appropriate examples and the appendices would provide material
helpful in practical work. With the new arrangement the book
commences with a chapter on frequency distribution, graphic
representation, averages and measures of <iispersion, etc., which
were dealt with in the second .and third. chapters of the previous
publication. The material relating to nonna! c~;ve and probability
integral is presented in the. second chapter ill'"a 'more concise and
systematic manner than was done in the fourth and fifth
chapters of the original. A note on binomial distribution is also
included in this chapter on account of its utility in dealing with
frequency data, proportions, etc. The third chapter introduces
vi
the idea of sampling and sampling errors and is practically new.
Opportunity is taken for an early introduction of the analysis of
variance by explaining the technique in an elementary form in
the fourth chapter. The fifth chapter is devoted to methods of
handling frequency data. Besides giving the various uses of the ;Y2
test, the more important methods· of estimating linkage including
the one based on maximum likelihood are discussed. In presenting
methods dealing with the relations between two variables consi
derable changes have been made and the technique of regression
has been given due prominence. It is presented in the sixth
chapter. The topics of partial and multiple regression and corre
lation and intrac1ass correlation which were not treated in the
previous publication are incorporated in the same chapter.
The remaining chapters of the book deal with design of
experiments. Apart from randomized block and latin square
designs and some ideas relating to soil heterogeneity and ana
lysis of covariance, the entire· material in this part is new.
Chapter VII introduces the principles of replication, randomization
.and local control underlying the design of experiments as well as
the idea of efficiency of an experiment. Randomized block and
latin square designs are discussed in the eighth chapter with the
addition of. material on size and shape of blocks, number of
replications, the process of randomization, etc. Three new
chapters, IX to XI, have been added in order to deal with
factorial experimentation, confounding and split-plot and strip
plot designs. Analysis of covariance and methods of dealing with
incomplete data are presented in Chapter XII. Chapter XIIl
should be of special interest to plant breeders as it discusses the
designs and analysis of replicated progeny row and compact
family block trials and introduces incomplete block designs.
The important problem of the analysis of groups of experiments
has. been discussed in Chapter XIV. A special chapter has been
devoted to the consideration of practical aspects of field experi
mentation in order to emphasize their importance in the efficient
prosecution of experimental studies. The last chapter, XVI, deals
with the problem of conducting experiments on farmers' own
land, which is assuming a rapidly growing importance and in
which interesting developments are expected.
VII
In view of the restriction on the scope of the book mentioned
earlier and in due regard to its size it was not considered desirable
to attempt a more exhaustive treatment of the subject-matter or
to include more explanatory material concerning the principles
discussed. For the benefit of the more enterprising student, who
wishes to pursue the study of the subject in greater detail, references
to further sources of information concerning various aspects of
statistical methods and design of experiments have been given.
It is to be hoped that in its present form the book will meet the
day to day needs of the agricultural and other biological research
workers and form a suitable text for teaching the subject to the
students of these sciences.
The authors wish to record their keen appreciation of the
careful and painstaking work done by Mr. S. D. Bokil, who was
associated throughout with the project of preparing the present
text. Their thanks are also due to Mr. V. N. Amble for hIs
help in preparing the drafts of certain new sections and in
making a critical scrutiny of several chapters of the manuscript
and to Messrs. K. S. Krishnan and K. S. Avadhani for checking
the numerical calculations. Lastly, they wish to make a special
mention of the help they received from Dr. P. N. Saxena in
reading the proofs.
The authors are indebted to Professor Sir Ronald A. Fisher,
Cambridge, and to Messrs. Oliver and Boyd Ltd., Edinburgh,
for their permission to reprint Tables I and III from their book
'Statistical Methods for Research Workers '.
V. G. PANSE.
New Delhi, January 1954. P. V. SUKHATME.

CONTENTS
PAGE
v
PREFACE
PART 1. STATISTICAL METHODS
CHAPTER
I. FREQUENCY DISTRIBUTIONS
la.l Introduction. 1
Ib.l Frequency Distribution . 2
Ib.2 Graphic Representation 9
Ib.3 Frequency Curve and its Characteristics 10
Ie .1 Measures of Central Value or Location 10
le.2 Measures of Dispersion 12
le.3 The Coefficient of Variation 14
Id.l Methods of Computation . 15
II. THE NORMAL AND BINOMIAL DISTRIBUTIONS
2a. 1 The Probability Integral 22
2a.2 The Normal Curve . 25
2a.3 Use of the Normal Probability Integral 27
2b. 1 Binomial Distribution . 32
III SAMPLING METHOD AND STANDARD ERRORS
3a. 1 Introduction. 36
3b. 1 Random Sampling . 36
3b.2 Use of Random Numbers 38
3b. 3 Expectation of Sample Estimates 40
3b.4 Requisites of Randomization . 40
3c. 1 Distribution of Sample Means 42
3e.2 Confidence Limits 44
PAGE
3d I Standard Error of Sum and Difference
of Means 4S
3d.2 Standard Error of Linear Function of
Independent Variates. 47
3d.3 Sample Estimate of Variance 48
3d.4 Standard Error of Estimate of Propor-
tion . 48
IV. TESTS OF SIGNIFICANCE OF MEANS AND THEIR DIF
FERENCES
4a.l Significance of Means in Large Samples SI
4a.2 Significance of Difference of Means in
Large Samples S4
4b.l Small Samples: 't' Test S7
4b.2 't' Test in Paired Samples 62
4c.l Analysis of Variance 63
4c.2 The 'F' Test 66
4d.l' Fisher and Behren's 'd' Test 67
V. THE X2 TEST AND ESTIMATION OF LINKAGE
Sa.l Introduction 70
Sa.2 Testing the Significance of Proportion 70
Sb.l The X2 Test of Goodness of Fit 72
Sb.2 Test of Independence: 2 x 2 Table 7S
Sb.3 Test of Independence: 2 X r Table 79
Sb.4 Testing Heterogeneity 81
Sb.S Test of Independence: r X c Table 83
Sc.l Use of X2 Test in Genetic Experiments 83
Sc.2 Size of Experiments . 8S
Sc.3 The Partition of X2 86
Sc.4 Detection of Linkage 88