Biostatistics - An Introduction

481 Pages·2013·8.451 MB·English

by  P Mariappan

Biostatistics
An Introduction
Dr P. Mariappan
Department of Mathematics
Bishop Heber College
Tiruchirappalli, Tamil Nadu
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ISBN 9788131775141
eISBN 9789332514157

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I am dedicating this text to my beloved brother Lr P. Ravichandran,
Mrs R. Indira alias Chandra,
Ms R. Atchathaa and
Master R. Aniruth Kumar
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CONTENTS
Foreword xii
Preface xiii
Acknowledgements xiv
About the Author xv
1 Introduction to Statistics and Its Biological
Applications 1
1.1 Introduction 1
1.1.1 Sampling Methods 2
1.2 Is Statistics a Science? 2
1.3 Application of Statistics in Biology 2
1.3.1 Phases of the Statistical Decision-Making Process 3
1.4 Responsibility of the Decision Maker 4
1.5 Functions and Limitations of Statistics 4
1.5.1 Functions of Statistics 4
1.5.2 Limitations of Statistics 5
1.6 Distrust of Statistics 6
1.7 Nature of Statistical Law 6
1.7.1 Law of Statistical Regularity 6
1.7.2 Law of Inertia of Large Numbers 7
Exercises 7
Answer the Questions 7
2 Data Structures, Data Sources and Data Collection 9
2.1 Introduction 9
2.2 Data Structures 9
2.2.1 Univariate Data 10
2.2.2 Bivariate Data 10
2.2.3 Multivariate Data 10
2.3 Data Sources 11
2.3.1 Primary Sources 11
2.3.2 Secondary Sources 11
2.3.3 Internal Source 11
2.3.4 External Source 11
2.3.5 Advantages and Disadvantages of Primary Data
Over the Secondary Data 11
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vi Contents
2.4 Data Collection 12
2.4.1 Survey Design 13
2.4.2 Pilot Survey of the Questionnaire 14
2.4.3 Editing Primary Data 15
2.4.4 Possible Errors in Secondary Data 15
2.4.5 Points to Be Considered While Using Secondary Data 15
2.4.6 Census and Sampling Methods 16
Exercises 21
Answer the Questions 21
3 Data Presentation 23
3.1 Introduction 23
3.2 Classification of Data 23
3.2.1 Types of Classification 23
3.3 Data Presentation 24
3.3.1 Textual Form 24
3.3.2 Tabular Form 25
3.3.3 Graphical Form 25
3.4 Types of Variables and Data 25
3.5 Levels of Measurement 26
3.5.1 Ratio Scale 26
3.5.2 Interval Scale 26
3.5.3 Ordinal Scale 27
3.5.4 Nominal Scale 27
3.6 Frequency 27
3.6.1 Frequency Distributions 27
3.7 Types of Class Interval 28
3.7.1 Exclusive Method 29
3.7.2 Inclusive Method 29
3.7.3 Open-end Method 30
3.8 Tally Mark 30
3.9 Construction of a Discrete Frequency Distribution 30
3.10 Construction of a Continuous Frequency Distribution 31
3.11 Cumulative and Relative Frequencies 32
3.11.1 Cumulative Frequency 33
3.11.2 Relative Frequency 33
3.12 Diagrammatic Representation of Data 34
3.12.1 Advantages and Disadvantages of Diagrammatic
Representation 34
3.12.2 Types of Diagrams 35
Exercises 47
Answer the Questions 49
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Contents vii
4 Measures of Central Tendency 51
4.1 Introduction 51
4.2 Measures of Central Tendency 51
4.2.1 Properties of Best Average 52
4.3 Arithmetic Mean 52
4.3.1 Discrete Data 52
4.3.2 Discrete Data with Frequency 52
4.3.3 Continuous Data with Frequency 53
4.4 Mathematical Properties of Arithmetic Mean 54
4.4.1 Disadvantages of Arithmetic Mean Related to Other Averages 54
4.5 Median 63
4.5.1 Discrete Data 63
4.5.2 Discrete Data with Frequency 63
4.5.3 Continuous Data with Frequency 64
4.5.4 Graphical Method to Find the Median 71
4.6 Quartiles, Deciles and Percentiles 73
4.7 Mode 78
4.7.1 Discrete Data 78
4.7.2 Discrete Data with Frequency 79
4.7.3 Continuous Data with Frequency 79
4.7.4 Graphical Method to Evaluate the Mode 89
4.8 Comparison of Mean, Median and Mode 89
4.9 Weighted Arithmetic Mean 92
4.9.1 Advantages of the Weighted Mean 93
4.10 Geometric Mean 93
4.11 Harmonic Mean 94
Exercises 95
Answer the Questions 103
5 Dispersion 105
5.1 Introduction 105
5.2 Range 105
5.2.1 Merits 105
5.2.2 Demerits 106
5.3 Quartile Deviation 106
5.3.1 Merits 107
5.3.2 Demerits 107
5.4 Coefficient of Quartile Dispersion 107
5.5 Mean Deviation 110
5.5.1 Discrete Series 110
5.5.2 Distribution with Frequency 111
5.6 Standard Deviation 113
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viii Contents
5.7 Relative Measures of Dispersion 115
5.7.1 Coefficient of Variation 115
5.7.2 Coefficient of Quartile Deviation 115
Exercises 123
Answer the Questions 133
6 Skewness, Moments and Kurtosis 134
6.1 Introduction 134
6.2 Dispersion and Skewness 134
6.3 Moments 137
6.4 Kurtosis 138
Exercises 142
Answer the Questions 147
7 Correlation and Regression Analysis 148
7.1 Introduction 148
7.2 Correlation 148
7.2.1 Simple Correlation/Correlation 149
7.2.2 Rank Correlation 149
7.2.3 Group Correlation 149
7.2.4 Assumptions for Karl Pearson’s Coefficient of Correlation 149
7.2.5 Limitations of Correlation 149
7.2.6 Properties of Correlation 150
7.2.7 Scatter Diagram 150
7.3 Karl Pearson’s Coefficient of Correlation 150
7.4 Coefficient of Correlation for a Grouped Data 156
7.5 Probable Error of the Coefficient of Correlation 159
7.6 Rank Correlation 161
7.7 Regression Equations 166
7.7.1 Regression 166
7.7.2 Regression Equation Y depends on X 166
Exercises 177
Answer the Questions 181
8 Probability 183
8.1 Introduction 183
8.2 Definition for Certain Key Terms 183
8.3 Meaning of Probability 184
8.3.1 Addition Rules for Probability 189
8.3.2 Addition Theorem on Probability 190
8.3.3 Multiplication Rule on Probability When Events
Are Independent 192
8.3.4 Compound Probability or Conditional Probability 193
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Contents ix
8.4 Baye’s Theorem 199
Exercises 205
Answer the Questions 207
9 Random Variables and Expectation 210
9.1 Introduction 210
9.2 Random Variable 210
9.2.1 Discrete Random Variable 210
9.2.2 Continuous Random Variable 211
9.3 Probability Distribution 211
9.3.1 Discrete Probability Distribution 211
9.3.2 Characteristics of a Discrete Probability Distribution 212
9.3.3 Probability Function 212
9.4 Mathematical Expectation 214
9.5 Mean of a Random Variable 214
9.6 Standard Results 214
9.7 Variance of a Random Variable 215
Exercises 217
Answer the Questions 218
10 Discrete Probability Distribution [Binomial
and Poisson Distributions] 220
10.1 Introduction 220
10.2 Binomial Distribution 220
10.2.1 Characteristics of a Bernoulli Process 221
10.2.2 Definition of Binomial Distribution 221
10.2.3 Conditions of Binomial Distribution 221
10.2.4 Properties of Binomial Distributions 221
10.2.5 Mean of Binomial Distribution 222
10.2.6 Variance of Binomial Distribution 222
10.3 Poisson Distribution 228
10.3.1 Definition of Poisson Distribution 228
10.3.2 Properties of Poisson Distribution 228
10.3.3 Mean of the Poisson Distribution 229
10.3.4 Variance of the Poisson Distribution 229
Exercises 234
Answer the Questions 236
11 Continuous Probability Distribution 237
11.1 Introduction 237
11.2 Definition of Normal Distribution 237
11.3 Standard Normal Distribution 239
11.4 Properties of Normal Distribution 240
Exercises 251
Answer the Questions 254
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