Description

ABOUT THE BOOK

This book is an introductory and has been written in view of the fact that those students who do not have enough background of Statistical Methods, they would certainly be happy  to use these statistical concepts including their role in analysis and drawing inferential conclusions for the data of Applied Sciences. It would also help them in understanding the concepts involved in collection, classification, tabulation, analysis, graphical presentation and interpretation of data. The students would get an exposure to the descriptive statistics (numerical and graphical) random variables, probability, probability distributions, estimation of parameters, concept of sampling distribution, tests of significance, theory of estimation of the parameters, correlation and regression, types of data for probit analysis, non-parametric tests and multivariate statistical techniques.

It has been written primarily on the ICAR course pattern to suit the mediocre students. Eventually, the usual basic material and methods included in this book are the output of the experience achieved by the authors while teaching in Jawaharlal Nehru Krishi Vishwa Vidyalaya, Jabalpur (M.P.) in relation to various courses of Statistics to graduate and post-graduate students. This book can serve as a guide not merely in Agricultural University but also in traditional one as far as the topics, analysis and methods are concerned. The difficult mathematical expressions and derivations have been given in simplified forms. Several illustrative examples along with objective type questions (multiple choice) and chapterwise exercises have also been added to demonstrate the methods in vivid way.

The authors hope that this book  would certainly be more useful to the teachers and the students working in the University.

CONTENTS

S. NO.	TITLE	PAGE
	FOREWORD	4-5
	ACKNOWLEDGMENTS	6
	PREFACE	7-8
	ABOUT THE AUTHORS	18
	ABOUT THE BOOK	19
1	INTRODUCTION	21-30
1.1	Origin, meaning and history of statistics	21
1.2	Definition of statistics	22
1.3	Importance and scope of statistics	23
1.4	Functions of statistics	25
1.5	Uses of statistics in agriculture	26
1.6	Limitations of statistics	27
1.7	Lack of trust in statistics	28
2	COLLECTION, EDITING, CLASSIFICATION AND TABULATION OF DATA	31-49
2.1	Introduction	31
2.2	Types of data	31
2.3	Methods of collection of primary data	32
2.4	Sources of collection of secondary data	35
2.5	Editing of data	35
2.6	Precautions in the use of secondary data	36
2.7	Classification	38
2.8	Definition of classification	39
2.9	Precautions at the time of classifying a numerical data	39
2.10	Basis of classification	40
2.11	Functions of classification	42
2.12	Construction of a discrete frequency distribution	42

 

2.13	Construction of a continuous frequency distribution	43
2.14	Tabulation- meaning and importance	44
2.15	Types of tables	45
2.16	Constituents of a table	46
2.17	Requisites of a good table	46
2.18	Functions of tabulation	46
3	FREQUENCY DISTRIBUTIONS AND DESCRIPTIVE STATISTICS WITH DIAGRAMS & GRAPHS	50-93
3.1	Introduction	50
3.2	Grouped frequency distribution	51
3.3	Continuous frequency distribution	52
3.4	Relative frequency distribution	53
3.5	Cumulative frequency distribution	53
3.6	Frequency density	54
3.7	Relative frequency density	55
3.8	Variables and variate	55
3.9	Descriptive statistics with diagrams and graphs	57
3.10	Diagrams and graphs	57
3.11	Types of diagrams	58
3.12	Exploratory data analysis(EDA)	73
3.13	Graphs of frequency distributions	76
3.14	Advantages of diagrams and graphs	89
4	DESCRIPTIVE STATISTICS: MEASURES OF CENTRAL TENDENCY	94-153
4.1	Meaning of measures of central tendency	94
4.2	Characteristics for an ideal measure of central tendency	94
4.3	Arithmetic mean	94
4.4	Properties of arithmetic mean	102
4.5	Merits and demerits of arithmetic mean	110
4.6	Weighted arithmetic mean	111
4.7	Median	114
4.8	Merits and demerits of median	120
4.9	Uses of median	120
4.10	Mode	120
4.11	Merits and demerits of mode	128
4.12	Uses of mode	128
4.13	Geometric mean	128
4.14	Merits and demerits of geometric mean	132
4.15	Uses of geometric mean	132
4.16	Harmonic mean	132
4.17	Merits and demerits of harmonic mean	134
4.18	Selection of an average	134
4.19	Partition values	135
4.20	Graphical estimation of the partition values	141
4.21	Graphical estimation of mode	143
5	DESCRIPTIVE STATISTICS: MEASURES OF DISPERSION	154-185
5.1	Meaning of dispersion	154
5.2	Characteristics for an ideal  measure of dispersion	154
5.3	Measures of dispersion	155
5.4	Root mean square deviation	157
5.5	Relation between σ and s	157
5.6	Simplified formula of variance	158
5.7	Effect of change of origin and scale on variance and standard deviation	158
5.8	Variance and standard deviation of the combined distribution	160
5.9	Co-efficient of dispersion	161
5.10	Co-efficient of variation	162
5.11	Sheppard’s correction for variance	162
6	DESCRIPTIVE STATISTICS: MOMENTS AND MEASURES OF SKEWNESS & KURTOSIS	186-201
6.1	Introduction	186
6.2	Central moments expressed in terms of moment about an arbitrary origin	186
6.3	Moments about an arbitrary origin expressed in terms of central moments	187
6.4	Skewness	188
6.5	Measures of skewness	189
6.6	Kurtosis	191
7	PROBABILITY, RANDOM VARIABLE AND ITS MATHEMATICAL EXPECTATION	202-244
7.1	Introduction	202
7.2	Random experiment	202
7.3	Sample space	203
7.4	Trial and events	204
7.5	Exhaustive events	204
7.6	Favourable events	205
7.7	Mutually exclusive events	205
7.8	Equally likely events	205
7.9	Independent  events	205
7.10	Mathematical or classical definition of probability	206
7.11	Limitations of mathematical or classical definition	206
7.12	Statistical or empirical definition of probability	206
7.13	Additive law of probability	206
7.14	Multiplicative law of probability	207
7.15	Random variable	208
7.16	Mathematical expectation	208
7.17	Additive law of expectation	208
7.18	Multiplicative law of expectation	209
7.19	Covariance	211
8	BASIC DISCRETE PROBABILITY DISTRIBUTIONS	245-307
8.1	Introduction	245
8.2	Bernoulli distribution	245
8.3	Mean and variance of Bernoulli distribution	246
8.4	Binomial distribution	246
8.5	Mean and variance of binomial distribution	247
8.6	Recurrence relation for the probabilities of binomial distribution	248
8.7	Recurrence relation for the moments of binomial distribution	249
8.8	Additive property of binomial distribution	250
8.9	Truncated binomial distribution at the point zero	250
8.10	Examples of binomial distribution	251
8.11	Moment generating function of binomial distribution	252
8.12	Probability generating function of binomial distribution	253
8.13	Poisson distribution	266
8.14	Mean and variance of Poisson distribution	267
8.15	Recurrence relation for the probabilities of Poisson distribution	268
8.16	Recurrence relation for the moments of Poisson distribution	269
8.17	Additive property of independent poisson variates	270
8.18	Truncated poisson distribution at the point zero	270
8.19	Moment generating function of Poisson distribution	271
8.20	Probability generating function of Poisson distribution	271
8.21	Negative binomial distribution	284
8.22	Moment generating function of negative binomial distribution	285
8.23	Probability generating function of negative binomial distribution	286
8.24	Recurrence relation for the fitting of negative binomial distribution	287
8.25	Truncated negative binomial distribution	288
8.26	Geometric distribution	288
8.27	Moment generating function of geometric distribution	289
8.28	Probability generating function of geometric distribution	289
8.29	Truncated geometric distribution at the point zero	290
8.30	Probability generating function of truncated geometric distribution	290
8.31	Recurrence relation for the fitting of geometric distribution	291
8.32	Power series distribution	293
8.33	Moment generating function of P.S.D	294
9	BASIC CONTINUOUS PROBABILITY DISTRIBUTIONS	308-333
9.1	Normal distribution	308
9.2	Chief characteristics of normal distribution and normal probability curve	309
9.3	Median of normal distribution	310
9.4	Mode of normal distribution	310
9.5	Applications of normal distribution	311
9.6	Gamma distribution	322
9.7	Moment generating function of gamma distribution	323
9.8	Additive property of gamma distribution	324
9.9	Beta distribution of first kind	324
9.10	Moments of beta distribution of first kind	324
9.11	Beta distribution of second kind	325
9.12	Moments of beta distribution of second kind	325
9.13	Exponential distribution	326
9.14	Moment generating function of exponential distribution.	326
10	CONCEPT OF SAMPLING DISTRIBUTION AND TESTS OF SIGNIFICANCE	334-375
10.1	Large sample theory	324
10.2	Concept of sampling distribution	324
10.3	Chi-square variate	335
10.4	moment generating function  of χ2 distribution	337
10.5	Additive property of χ2 variates	337
10.6	Distribution of ( , S2) in sampling from normal population	337
10.7	Student’s t definition	339
10.8	F- distribution (definition)	340
10.9	Fisher’s ‘t’ definition	340
10.10	Sampling distribution	341
10.11	Statistic and parameter	341
10.12	Standard error	342
10.13	Chi- square distribution	342
10.14	Student t-distribution	343
10.15	F-distribution	344
10.16	Tests of significannce	345
10.17	Test of significance for large samples	346
10.18	Conditions for the validity of χ2 – test	348
10.19	Yates’s correction for continuity of χ2	350
10.20	Test of significance for small samples	350
10.21	F- test	352
11	THEORY OF ESTIMATION AND CONFIDENCE INTERVALS	376-398
11.1	Introduction	376
11.2	Characteristics of estimator	376
11.3	Fisher-Neyman criterion for the existence of sufficient statistic	378
11.4	Factorization theorem (only statement)	379
11.5	Method of estimation	379
11.6	Confidence interval	388
11.7	Construction of a confidence interval	388
12	CORRELATION AND REGRESSION	399-447
12.1	Introduction	399
12.2	Scatter diagram	399
12.3	Karl Pearson co-efficient of correlation	400
12.4	Properties of correlation coefficient	402
12.5	Show that the correlation coefficient lies in -1 to +1	402
12.6	Rank correlation	403
12.7	Regression	405
12.8	Lines of regression	405
12.9	Properties of regression coefficient	407
12.10	Angle between two lines of regression	408
12.11	Multiple and  partial correlation	410
12.12	Yule’s notation	410
12.13	Derivation of the equation of the plane of regression	411
12.14	Multiple correlation coefficient	412
12.15	Partial correlation coefficient	414
13	POLYNOMIAL REGRESSION MODELS AND THEIR FITTING	448-476
13.1	Introduction	448
13.2	Fitting of other curves	449
13.3	Fitting a straight line through matrix approach	452
13.4	Polynomial regression models and their fitting	459
13.5	Linear regression	460
13.6	Different forms of Sxy, Sxx and Syy	461
13.7	Confidence interval for the parameter β1 in the regression models	464
13.8	Confidence interval for the parameter β0 in the regression models	464
13.9	Relationship between t and F statistic  terms of regression	465
13.10	Percentage variation explained	466
13.11	Fitting a straight line in matrix form	466
13.12	The analysis of variance in matrix form of linear regression model	467
13.13	Adjusted R2 statistic	469
14	PROBIT ANALYSIS	477-492
14.1	Introduction	477
14.2	The probit transformation	478
14.3	Practical applications of probit analysis	479
14.4	Fitting a provisional probit regression line	480
14.5	Fitting a  probit regression line  by the method of maximum likelihood	485
15	NON-PARAMETRIC STATISTICAL METHODS	493-514
15.1	Introduction	493
15.2	Sign test	494
15.3	Wilcoxon signed rank test	495
15.4	Mann- Whitney U test	495
15.5	Kruskal- Wallis test	496
15.6	Run test for randomness	497
15.7	Friedman two way ANOVA by ranks	497
15.8	Median test	498
15.9	Kendall’s coefficient of concordance	498
15.10	Wald- Wolfowitz run test for small samples	500
15.11	Kolmogorox- Smirnov test of goodness of fit	502
15.12	Chi- square test of independence (contingency table)	502
16	MULTI-VARIATE STATISTICAL ANALYSIS	515-559
16.1	Introduction	515
16.2	Normal distribution	516
16.3	Bi-variate normal distribution	516
16.4	Multi-variate normal distribution	517
16.5	Multi-variate analytical tools	518
16.6	Hotelling T2: Test of hypothesis about the mean value	519
16.7	Comparing mean vectors from two population	523
16.8	Classification and discrimination	525
16.9	Discriminant analysis	526
16.10	D2 statistic	532
16.11	Cluster analysis	535
16.12	Principal component analysis (PCA)	540
16.13	Canonical correlation	546
16.14	Factor analysis	549
	GLOSSARY	560-567
	REFERENCES	568

 

ABOUT THE AUTHORS

Dr. H.L. Sharma had been working as Professor and Head in the Department of Mathematics and Statistics, College of Agriculture, Jawaharlal Nehru Krishi Vishwa Vidyalaya,  Jabalpur (M.P.) where he was involved in the activities of teaching, research and extension for the last thirty seven years. He obtained his Ph.D degree from Banaras Hindu University, a well known Traditional Central University. He worked as a Post Doctoral Fellow of Rockefeller Foundation, New York in the University of Pennsylvania, Philadelphia (U.S.A.) during academic year 1990-91.

Dr. Sharma   had also been a recipient of Population Association of America (PAA) Travel Award for presentation of his paper in the International Conference of Population Association of America, Chicago (U.S.A.) in the year 1988.

Recently, he visited Denver, Colorado, (U.S.A.) in regard to the Population Association of America (PAA) meeting in the year 2018 and presented his  paper through a series of posters.

He was a member of Broad Subject Matter Area (BSMA) fifth Dean’s Committee during the revision of post graduate courses in Statistical Sciences.

Dr. Sharma guided a number of M.Sc. (Ag) and M.Sc. (Agricultural Statistics) students for their thesis work in the capacity of Major and Minor advisor.

Dr. Sharma published a number of research papers in the National and International journals of repute.

Dr. Amita Sharma has been working as Assistant Professor in the Department of Plant Breeding and Genetics, College of Agriculture, Balaghat, Jawaharlal  Nehru Krishi  Vishwa Vidyalaya, Jabalpur  (M.P.) where she has been involved in the activities of teaching, research and extension  for more than seven years. She obtained her B.Sc. (Ag.) in 2008 and M.Sc. (Ag.) in 2010 in Plant Breeding and Genetics from JNKVV, Jabalpur and Ph.D. (Ag.) in Genetics and Plant Breeding from Banaras Hindu University, a well known Traditional Central University Varanasi (U.P.) in the year 2014.

She has published more than sixty research and review papers in national and international journals of repute and attended many national and international conferences and trainings.

She has experience of about ten years in rice breeding, mutation breeding and molecular breeding.