D. VENKATESAN
D. VENKATESAN
D. VENKATESAN Department of Statistics Annamalai University Annamalai Nagar - 608 002, Tamil Nadu, India
The Book is an introductory text, presenting some of the basic concepts and techniques of Statistical inference. It has been written primarily to suit the students and research workers in the area of agricultural science. An understanding of the logic and theory of statistics is essential for the students of agriculture who are expected to know the techniques of analysing data and drawing useful conclusions. It has been the intention of the authors to keep the book at a readability level appropriate for students who do not have a mathematical background. This book can serve as comprehensive reference source of statistical techniques helpful to agricultural research workers in the interpretation of data.
Preface
1. Introduction
1.1 Definition of Statistics
1.2 Statistics as Numerical Data
1.3 Function of Statistics
1.4 Divisions of Statistics
1.5 Importance and Scope of Statistics
1.6 Collection of Data
1.7 The Preliminaries in Collecting Data
1.8 Methods of Collecting Primary Data
1.9 Sources of Secondary Data
1.10 Unpublished Source
1.11 Limitations of Statistics
2. Classification, Tabulation and Graphical Representation
2.1 Quantitative Classification
2.2 Variable
2.3 Array
2.4 Frequency Distribution
2.5 Cumulative Frequency Distribution
2.6 Diagrammatic and Graphical Representation
3. Measures of Central Tendency
3.1 Introduction
3.2 Definition of Measures of Central Tendency
3.3 Objectives of a Statistical Average
3.4 Various Measures of Central Tendency
3.5 Requisites of a Satisfactory Measure of Central Tendency
3.6 Comparison of Mean, Median and Mode
3.7 Empirical Relationship among Mean, Median and Mode
4. Measures of Dispersion
4.1 Introduction and Measuring
4.2 The Characteristics for an Ideal Measure of Dispersion
4.3 Absolute and Relative Measures of Dispersion
4.4 Various Measures of Dispersion
4.5 Skewness
4.6 Kurtosis
5. Probability
5.1 Random Experiment
5.2 Sample Space
5.3 Event
5.4 Mathematical or Classical Definition of Probability
5.5 Statistical Definition of Probability
5.6 Conditional Probability
5.7 Bayes’ Probabilities
6. Probability Distributions
6.1 Random Variable (R.V)
6.2 Distribution Function
6.3 Moments
6.4 Moment Generating Function (M.G.F)
6.5 Cumulants
6.6 Binomial Distribution
6.7 Bernoulli’S Theorem
6.8 Relation between the Probabilities of X and (X+1) Successes in Binomial Distribution
6.9 Poisson Distribution
6.10 For Poisson Variate X, Relationship Between the Probabilities, P(X=x) And P(X = x+1)
6.11 Normal Distribution
7. Sampling and Sampling Distribution
7.1 Meaning of Sampling
7.2 Census Method
7.3 Sample Method
7.4 Merits of the Sample Method
7.5 Methods of Sampling
7.6 Sampling and Non-sampling Errors
7.7 Classification of Data
7.8 Sampling and Its Uses
7.9 Definitions
7.10 Sampling Methods
7.11 Unrestricted Random Sampling
7.12 Estimation of Population Parameters
7.13 Properties of Estimates
7.14 Restricted Sampling
7.15 Systematic Sampling
7.16 Methods of Selection
7.17 Cluster Sampling
7.18 Multistage Sampling
7.19 Sampling Distribution
7.20 Student’s t-Distribution
7.21 Chi-Square Distribution
7.22 Fisher's z-Distribution
8. Tests of Significance Testing Hypothesis about Population Mean
8.1 Statistical Hypotheses
8.2 Statistical Test
8.3 Decision Errors
8.4 Critical Region
8.5 Level of Significance
8.6 One and Two-Tailed Tests
8.7 Degrees of Freedom
8.8 Test Statistic
8.9 Steps in Testing of Hypothesis
8.10 Comparing Two Population Means Independent Samples with Equal Variances
8.11 Comparison of Two Population Means Independent Samples with Unequal Variances
8.12 Comparison of Two Population Means Correlated Samples
8.13 Testing the Significance of an Observed Correlation Coefficient
8.14 Comparison of Two Population Variances
9. Chi-Square and Association of Attributes
9.1 Expected Frequencies
9.2 Testing of Independence of Attributes in Contingency Table
9.3 Association of Attributes
9.4 Difference between Correlation and Association
9.5 Notation and Terminology
9.6 Consistency of Data
9.7 Association and Disassociation
9.8 Methods of Studying Association
9.9 Association of Three Attributes
9.10 Partial Association
10. Correlation and Regression
10.1 Introduction
10.2 Meaning of Correlation
10.3 Linear and Non-linear Correlation
10.4 Simple, Multiple and Partial Correlation
10.5 Correlation and Causation
10.6 Usefulness of Correlation
10.7 Methods of Studying Correlation
10.8 Coefficient of Determination
10.9 Coefficieint of Non-determination
10.10 Coefficient of Alienation
10.11 Probable Error
10.12 Regression Analaysis
11. Analysis of Variance
11.1 Introduction
11.2 One-way Classification
11.3 Two – way Classification
12. Design of Experiments
12.1 Introduction
12.2 Basic Concepts
12.3 Basic Principles of Experimental Designs
12.4 Size and Shape of Experimental Units
12.5 Completely Randomized Design
12.6 Randomized Block Design
12.7 Latin Square Design
13. Multiple Comparison Tests
13.1 Scheffe’s Method for Comparing All Contrasts
13.2 Tukey’s Test
13.3 The Fisher Least Significant Difference (LSD) Method
13.4 Duncan’s Multiple Range Test (DMRT)
13.5 The Newman – Keuls Test
14. Factorial Experiments
14.1 Advantages and Disadvantages of Factorial Experiments
14.2 Basic Concepts
14.3 Computation of Main Effects and Interactions
14.4 Layout Factorial Experiments
14.5 Analysis and Interpretation Factorial Experiments
14.6 Confounding in Factorial Experiments
15. Split Plot Design
15.1 Advantages and Disadvantages of Split Plot Design
15.2 Layout and Analysis
15.3 Some Variations in the Split Design
15.4 Split-Split Plot Design
References
Start Pages
Introduction
Classification, Tabulation and Graphical Representation
Measures of Central Tendency
Measures of Dispersion
Probability
Probability Distributions
Sampling and Sampling Distribution
Tests of Significance Testing Hypothesis about Population Mean
Chi-Square and Association of Attributes
Correlation and Regression
Analysis of Variance
Design of Experiments
Multiple Comparison Tests
Factorial Experiments
Split Plot Design
End Pages