Biostatistics - An Introduction

Cover
Contents
Foreword
Preface
Acknowledgements
About the Author
Chapter 1: Introduction to Statistics and its Biological Applications
	1.1 Introduction
		1.1.1 Sampling Methods
	1.2 Is Statistics a Science?
	1.3 Application of Statistics in Biology
		1.3.1 P hases of the Statistical Decision-Making Process
	1.4 Responsibility of the Decision Maker
	1.5 Functions and Limitations of Statistics
		1.5.1 Functions of Statistics
		1.5.2 Limitations of Statistics
	1.6 Distrust of Statistics
	1.7 Nature of Statistical Law
		1.7.1 Law of Statistical Regularity
		1.7.2 Law of Inertia of Large numbers
	Exercises
	Answer the Questions
Chapter 2:
Data Structures, Data Sources and Data Collection
	2.1 Introduction
	2.2 Data Structures
		2.2.1 Univariate Data
		2.2.2 Bivariate Data
		2.2.3 Multivariate Data
	2.3 Data Sources
		2.3.1 Primary Sources
		2.3.2 Secondary Sources
		2.3.3 Internal Source
		2.3.4 External Source
		2.3.5 Advantages and Disadvantages of Primary Data Over the Secondary Data
	2.4 Data Collection
		2.4.1 Survey Design
		2.4.2 Pilot Survey of the Questionnaire
		2.4.3 Editing Primary Data
		2.4.4 Possible Errors in Secondary Data
		2.4.5 Points to Be Considered While Using Secondary Data
		2.4.6 Census and Sampling Methods
	Exercises
	Answer the Questions
Chapter 3: Data Presentation
	3.1 Introduction
	3.2 Classification of Data
		3.2.1 Types of Classification
	3.3 Data Presentation
		3.3.1 Textual Form
		3.3.2 Tabular Form
		3.3.3 Graphical Form
	3.4 Types of Variables and Data
	3.5 Levels of Measurement
		3.5.1 Ratio Scale
		3.5.2 Interval Scale
		3.5.3 Ordinal Scale
		3.5.4 Nominal Scale
	3.6 Frequency
		3.6.1 Frequency Distributions
	3.7 Types of Class Interval
		3.7.1 Exclusive Method
		3.7.2 Inclusive Method
		3.7.3 Open-end Method
	3.8 Tally Mark
	3.9 Construction of a Discrete Frequency Distribution
	3.10 Construction of a Continuous Frequency Distribution
	3.11 Cumulative and Relative Frequencies
		3.11.1 Cumulative Frequency
		3.11.2 Relative Frequency
	3.12 Diagrammatic Representation of Data
		3.12.1 A dvantages and Disadvantages of Diagrammatic Representation
		3.12.2 T ypes of Diagrams
	Exercises
	Answer the Questions
Chapter 4: Measures of Central Tendency
	4.1 Introduction
	4.2 Measures of Central Tendency
		4.2.1 Properties of Best Average
	4.3 Arithmetic Mean
		4.3.1 Discrete Data
		4.3.2 Discrete Data with Frequency
		4.3.3 Continuous Data with Frequency
	4.4 Mathematical Properties of Arithmetic Mean
		4.4.1 Disadvantages of Arithmetic Mean Related to Other Averages
	4.5 Median
		4.5.1 Discrete Data
		4.5.2 Discrete Data with Frequency
		4.5.3 Continuous Data with Frequency
		4.5.4 Graphical Method to Find the Median
	4.6 Quartiles, Deciles and Percentiles
	4.7 Mode
		4.7.1 Discrete Data
		4.7.2 Discrete Data with Frequency
		4.7.3 Continuous Data with Frequency
		4.7.4 Graphical Method to Evaluate the Mode
	4.8 Comparison of Mean, Median and Mode
	4.9 Weighted Arithmetic Mean
		4.9.1 Advantages of the Weighted Mean
	4.10 Geometric Mean
	4.11 Harmonic Mean
	Exercises
	Answer the Questions
Chapter 5: Dispersion
	5.1 Introduction
	5.2 Range
		5.2.1 Merits
		5.2.2 Demerits
	5.3 Quartile Deviation
		5.3.1 Merits
		5.3.2 Demerits
	5.4 Coefficient of Quartile Dispersion
	5.5 Mean Deviation
		5.5.1 Discrete Series
		5.5.2 Distribution with Frequency
	5.6 Standard Deviation
	5.7 Relative Measures of Dispersion
		5.7.1 Coefficient of Variation
		5.7.2 Coefficient of Quartile Deviation
	Exercises
	Answer the Questions
Chapter 6: Skewness, Moments and Kurtosis
	6.1 Introduction
	6.2 Dispersion and Skewness
	6.3 Moments
	6.4 Kurtosis
	Exercises
	Answer the Questions
Chapter 7:
Correlation and Regression Analysis
	7.1 Introduction
	7.2 Correlation
		7.2.1 Simple Correlation/Correlation
		7.2.2 Rank Correlation
		7.2.3 Group Correlation
		7.2.4 Assumptions for Karl Pearson’s Coefficient of Correlation
		7.2.5 Limitations of Correlation
		7.2.6 Properties of Correlation
		7.2.7 Scatter Diagram
	7.3 Karl Pearson’s Coefficient of Correlation
	7.4 Coefficient of Correlation for a Grouped Data
	7.5 Probable Error of the Coefficient of Correlation
	7.6 Rank Correlation
	7.7 Regression Equations
		7.7.1 Regression
		7.7.2 Regression Equation Y depends on X
	Exercises
	Answer the Questions
Chapter 8: Probability
	8.1 Introduction
	8.2 Definition for Certain Key Terms
	8.3 Meaning of Probability
		8.3.1 Addition Rules for Probability
		8.3.2 Addition Theorem on Probability
		8.3.3 Multiplication Rule on Probability When Events Are Independent
	8.4 Baye’s Theorem
	Exercises
	Answer the Questions
Chapter 9:
Random Variables and Expectation
	9.1 Introduction
	9.2 Random Variable
		9.2.1 Discrete Random Variable
		9.2.2 Continuous Random Variable
	9.3 Probability Distribution
		9.3.1 Discrete Probability Distribution
		9.3.2 Characteristics of a Discrete Probability Distribution
		9.3.3 Probability Function
	9.4 Mathematical Expectation
	9.5 Mean of a Random Variable
	9.6 Standard Results
	9.7 Variance of a Random Variable
	Exercises
	Answer the Questions
Chapter 10:
Discrete Probability Distribution [Binomial and Poisson Distributions]
	10.1 Introduction
	10.2 Binomial Distribution
		10.2.1 Characteristics of a Bernoulli Process
		10.2.2 Definition of Binomial Distribution
		10.2.3 Conditions of Binomial Distribution
		10.2.4 Properties of Binomial Distributions
		10.2.5 Mean of Binomial Distribution
		10.2.6 Variance of Binomial Distribution
	10.3 Poisson Distribution
		10.3.1 Definition of Poisson Distribution
		10.3.2 Properties of Poisson Distribution
		10.3.3 Mean of the Poisson Distribution
		10.3.4 Variance of the Poisson Distribution
	Exercises
	Answer the Questions
Chapter 11:
Continuous Probability Distribution [Normal Distribution]
	11.1 Introduction
	11.2 Definition of Normal Distribution
	11.3 Standard Normal Distribution
	11.4 Properties of Normal Distribution
	Exercises
	Answer the Questions
Chapter 12:
Theory of Sampling
	12.1 Introduction
	12.2 Why Sample?
	12.3 How to Choose It?
	12.4 Sample Design
	12.5 Key Words and Notations
	12.6 Advantages and Disadvantages of Sampling
	12.7 Non Random Errors/Non Sampling Errors
	12.8 Random Errors/Sampling Errors
	12.9 Types of Sample
		12.9.1 Probability Sample
		12.9.2 Non-probability Sample
	12.10 Random Sampling
		12.10.1 Systematic Sampling
		12.10.2 Stratified Sampling
		12.10.3 Multi-stage Sampling
	12.11 Non-Random Sampling Methods
		12.11.1 Convenience Sampling
		12.11.2 Purposive Sampling
		12.11.3 Quota Sampling
		12.11.4 Cluster Sampling
		12.11.5 Sequential Sampling
	12.12 Sampling Distributions
	12.13 Need for Sampling Distribution
	12.14 Standard Error for Different Situations
		12.14.1 When the Population Size Infinite
		12.14.2 When the Population Size is Finite
		12.14.3 Sampling Distribution Based on Sample Means
	12.15 Point and Internal Estimation
		12.15.1 Point Estimate
		12.15.2 Properties of Good Point Estimators
	12.16 Interval Estimate
	12.17 Confidence Interval Estimation for Large Samples
	12.18 Confidence Intervals for Difference between Means
	12.19 Estimating a Population Proportion
	12.20 Estimating the interval based on difference between two proportions
	12.21 Confidence Interval Estimation for Small Sample
	12.22 Determining the Sample Size
	Exercises
	Answer the Questions
Chapter 13:
Hypothesis Testing/Parametric Tests/Distribution Tests/Tests of Significance
	13.1 Introduction
	13.2 Null Hypothesis [H0]
	13.3 Alternative Hypothesis [H1]
	13.4 Type I and Type II Errors
	13.5 Meaning of Parametric and Non-Parametric Test
		13.5.1 Parametric Test
		13.5.2 Non-parametric Test
	13.6 Selection of Appropriate Test – Statistic
	13.7 Methodology of Statistical Testing
	13.8 Test for a Specified Mean – Large Sample
	13.9 Test for Equality of Two Populations – Large Sample
	13.10 Test for Population Proportion – Large Sample
	13.11 Test for Equality of Two Proportions – Large Samples
	13.12 Test for Equality of Two Standard Deviations – Large Samples
	13.13 Student’s t-distribution
	13.14 Properties of t-distribution
	13.15 Test for Specified Mean [Small Sample]
	13.16 Test for Equality of Two Population Means – Small Samples [s1 and s2 are not known]
	13.17 Paired t-test for Difference of Mean
	13.18 Chi-square Distribution
		13.18.1 Chi-square Test
		13.18.2 Test for Goodness of Fit
		13.18.3 Tests for Independence of Attributes
		13.18.4 Whenever the Expected Frequencies of the Cell Entries are Less than 5
		13.18.5 Test for a Specified Population Variance
	13.19 Snedecor’s F-distribution
		13.19.1 Test for Difference of Two Population’s Variance
	13.20 Analysis of Variance [ANOVA]
		13.20.1 One Way Classification
		13.20.2 Two Way Classification
	Exercises
	Answer the Questions
Appendix A
Appendix B
Index