This book covers all the topics taught at the postgraduate level in the life sciences discipline. Part I covers the basics of biostatistics. Part II covers advanced topics that are needed to be applied by researchers. The main objective of this book is to explain the complicated concepts of biostatistics in an easy to understand manner using illustrations and numerical examples. The book will be a useful source for postgraduates and researchers in agricultural, biological, medical, earth, social, psychological and pharmaceutical sciences.
Preface * Acknowledgements * Abbreviations Part I: BASIC Chapter 1 Introduction: Statistics and Biostatistics * Types of Data * Variables and their Types * History and Applications * History * Applications Chapter 2 Data Handling I: Graphical Methods: Classification and Tabulation * Classification * Frequency Tables * Graphical Methods * Graphical Methods for Qualitative Data * Graphical Methods for Quantitative Data Chapter 3 Data Handling II: Descriptive Statistics: Measures of Location or Measures of Central Tendency * Measures of Dispersion * Measures of Skewness and Kurtosis * Moments * Sheppard Correction for Moments * Measures of Skewness and Kurtosis * Absolute Measures of Dispersion Chapter 4 Concepts of Probability: Uncertainty and Random Experiments * Sample Space and Events * Definition of Sample Space * Definition of Events * Types of Events (Definitions) * Definitions of Probability * Classical Definition * Statistical Definition * Axiomatic Definition of Probability * Additive Rule of Probability * Multiplicative Rule * Conditional Probability * Independent Events * The Bayes Rule or Bayes Theorem Chapter 5 Random Variables and their Characteristics: Definition and Types of Random Variables * Definition of Random Variable * Types of Random Variables * Functions for Probability Distribution of a Random Variable * Probability Mass Function (pmf) * Probability Density Function (pdf) * Probability Distribution of Random Variable * Cumulative Distribution Function (cdf) * Joint pmf, Joint pdf, Marginal and Conditional pdf and Independent Random Variables *Joint pmf and Joint pdf * Marginal and Conditional Distributions * Independent Random Variables * Expected Values of Random Variables and their Rules * Rules for the Expected Values * Expected Values of Function of Random Variables * Generating Functions * Probability Generating Function * Moment Generating Function * Characteristic Function * Raw and Central Moments * Raw Moments * Central Moments * Coefficients of Skewness and Kurtosis Chapter 6 Distributions: Discrete and Continuous Distributions * Binomial Distribution * Properties of Binomial Distribution * Poisson Distribution * Properties of Poisson Distribution * Hypergeometric Distribution * Properties of Hypergeometric Distribution * Geometric Distribution * Properties of Geometric Distribution * Negative Binomial Distribution * Properties of Negative Binomial Distribution * Normal Distribution * Properties of Normal Distribution * Uniform and Rectangular Distributions * Properties of Rectangular Distribution * Bivariate Normal Distribution * Chi-square Distribution * Properties of Chi-square Distribution * Student's t-Distribution * Properties of t-Distribution * F-Distribution * Properties of F-Distribution Chapter 7 Biostatistical Inference: Inference * Examples of Use of Inductive Inference * General Concepts * Estimation * Point and Interval Estimation * Criteria for a Good Estimator * Methods of Estimation * Testing of Hypothesis * Two Types of Errors * Procedure of Testing of Hypothesis Chapter 8 Tests of Significance: One Sample Problems for Testing Mean * Two Sample Problems for Testing Means * One Sample Problems for Testing Variance * Two Sample Problems for Testing Variances * Comparing Several Variances: Bartlett's Test * Comparison of Several Means Chapter 9 Bivariate and Multivariate Data: Measuring and Testing Relationship: Simple or Pearson's Product Moment Correlation Coefficient * Simple Linear Regression * Tests of Correlation * Tests of Regression Coefficient * Testing Homogeneity of Correlation and Regression Coefficients * Intraclass and Spearman's Rank Correlation Chapter 10 Analysis of Categorical Data: Independence and Association: Two Categories: Estimation and Tests of Proportions * Testing Independence and Homogeneity in 2 x 2 and r x c Contingency Table Chapter 11 Electronic Data Handling: Introduction to Computers * Man-Machine Communication: Binary Code and High Level Languages * Working on DOS, Windows, MS Office and Computer Networks Part II: ADVANCED Chapter 12 Types and Architecture of Studies: Planning of Experiments in Lab and in Fields * Design of Experiments (DoE) * Case-control, Cross Sectional, Longitudinal Studies and Clinical Trials * Observational Cohort Studies and Longitudinal Studies * Clinical Trials * Case-control Studies * Cross-sectional Studies * Advantages and Disadvantages of Various Studies Chapter 13 Data Collection: Census and Sampling: Census of Human Population and Animal Population * Random Sampling from Theoretical Distribution and from Finite Population * Selection of Random Sample from a Theoretical Distribution * Random Sampling from a Finite Population * Stratified Random Sampling * Cluster Sampling and Area Sampling * Systematic Sampling * Two-stage and Multistage Sampling * Purposive or Judgement Sampling * Snowball Sampling * Probability Sampling Chapter 14 Analysis of Data: With Violated Assumptions and from Complex Designs: Comparison of Two Means when Variances are Unequal * Comparison of Several Means and Completely Randomised Design * Randomised Block Design * Latin Square Design (LSqD) * Factorial Analysis * 22 Factorial Experiment * p x q Factorial Experiment * Nested Designs * BIBD and PBIBD * Balanced Incomplete Block Design (BIBD) * Partially Balanced Incomplete Block Design (PBIBD) * Multiple Comparisons * Equal Number of Replications or Equal Sample Sizes * Unequal Number of Replications or Unequal Sample Sizes * Multiple Comparison in Two Factor ANOVA Chapter 15 Non-Parametric Methods I: One Sample Tests: Test of Goodness of Fit * Kolmogorov-Smirnov Test * Sign Test * Wilcoxon Signed Rank Test Chapter 16 Non-Parametric Methods II: Two Sample Tests: Sign Test for Two Samples * Median Test * Wald-Wolfowitz Runs Test * Wilcoxon Signed Rank Test * Wilcoxon-Mann-Whitney U-Test * Kolmogorov-Smirnov Two Sample Test Chapter 17 Non-Parametric Methods III: k-Sample Tests: Median Test for k-Samples * Kruskal-Wallis k-Sample Test * Friedman's Test for RBD * Median Test for Two-Way Classification * Olmstead-Tukey Corner (or Quadrant Sum) Test of Association * Coefficient of Concordance and Kendall's Tau Coefficient Chapter 18 Time Series Analysis: Components of Time Series and their Determination * Determination of Components of Time Series * Autocorrelation in Time Series * Stationarity in Time Series, Transformation and Tests of Stationarity * Tests of Stationarity in Time Series * Transformation of Non-Stationary Time Series * Prediction or Forecasting Chapter 19 Bioassay: Types of Biological Assays, Direct Assays * Direct Assays * Dilution Assays * Indirect Assays and Dose Response Relationship * The Dose Response Regression * Methods of Estimation of Potency * Parallel Line Assay * Slope Ratio Assay * Quantal Response Assays * Probit Analysis * Logit Analysis * Estimation of Potency * Computational Procedure by Probit Analysis Chapter 20 Multivariate Analysis I: Hoteling's T2 and Mahalanobis D2 * Discriminant Analysis: Classification in Two or More than Two Populations * MANOVA Chapter 21 Multivariate Analysis II: Principal Component Analysis (PCA) * Factor Analysis * Mathematical Formulation of Factor Analysis Model * Factor Analysis Procedures * Test of Number of Factors * Interpretation of Factors * Factor Rotation * Factor Scores * Cluster Analysis * Distance and Similarity Matrices * Clustering Methods Chapter 22 Bioinformatics and Computational Biology: Concepts of Bioinformatics: A Digital Laboratory * Databases and Tools of Bioinformatics * Sequence Analysis * Protein Sequences * FASTA and BLAST * Application of Hidden Markov Model (HMM) * Microarray Data * Probabilistic Modelling and Clustering of Microarray Data * Statistical Significance of Search (or Alignment) * Cluster Analysis of Microarray Data Chapter 23 Computer Techniques: Programming in FORTRAN and C++ * Programming in FORTRAN * Programming in C and C++ * Use of Statistical Packages * SPSS * BMDP * SAS APPENDICES: Appendix A: Statistical and Mathematical Tables * Appendix B: Mathematical Symbols and Expressions * Appendix C: Basics of Matrix Algebra * Appendix D: Elements of Set Theory References * Subject Index * Author Index