An Introduction to Statistics with Python: With Applications in the Life Sciences 2nd

Now in its second edition, this textbook provides an introduction to Python and its use for statistical data analysis. It covers common statistical tests for continuous, discrete and categorical data, as well as linear regression analysis and topics from survival analysis and Bayesian statistics. For this new edition, the introductory chapters on Python, data input and visualization have been reworked and updated. The chapter on experimental design has been expanded, and programs for the determination of confidence intervals commonly used in quality control have been introduced. The book also features a new chapter on finding patterns in data, including time series. A new appendix describes useful programming tools, such as testing tools, code repositories, and GUIs. The provided working code for Python solutions, together with easy-to-follow examples, will reinforce the reader’s immediate understanding of the topic. Accompanying data sets and Python programs are also available online. With recent advances in the Python ecosystem, Python has become a popular language for scientific computing, offering a powerful environment for statistical data analysis. With examples drawn mainly from the life and medical sciences, this book is intended primarily for masters and PhD students. As it provides the required statistics background, the book can also be used by anyone who wants to perform a statistical data analysis. Preface Preface to the First Edition Preface to the Second Edition For Whom This Book Is Acknowledgments Contents Abbreviations Part I Python and Statistics 1 Introduction 1.1 Why Statistics? 1.2 Conventions 1.3 Accompanying Material 2 Python 2.1 Getting Started 2.1.1 Distributions and Packages 2.1.2 Installation of Python 2.1.3 Installation of R and rpy2 2.1.4 Python Resources 2.1.5 A Simple Python Program 2.2 Elements of Scientific Python Programming 2.2.1 Python Datatypes 2.2.2 Indexing and Slicing 2.2.3 Numpy Vectors and Arrays 2.2.4 pandas DataFrames 2.2.5 Functions, Modules, and Packages 2.3 Interactive Programming—IPython/Jupyter 2.3.1 Workflow 2.3.2 Jupyter Interfaces 2.3.3 Personalizing IPython/Jupyter 2.3.4 Sample Interactive Session 2.3.5 Converting Interactive Commands into a Python Program 2.4 Statistics Packages for Python 2.4.1 Seaborn—Data Visualization 2.4.2 Pingouin 2.4.3 Statsmodels—Tools for Statistical Modeling 2.5 Programming Tips 2.5.1 General Programming Tips 2.5.2 Python Tips 2.5.3 IPython/Jupyter Tips 2.6 Exercises 3 Data Input 3.1 Text 3.1.1 Visual Inspection 3.1.2 Reading ASCII-Data 3.1.3 Regular Expressions 3.2 Excel 3.3 Matlab 3.4 Binary Data: NPZ Format 3.5 Other Formats 3.6 Exercises 4 Data Display 4.1 Introductory Example 4.2 Plotting in Python 4.2.1 Functional and Object-Oriented Approaches 4.2.2 Interactive Plots 4.3 Saving a Figure 4.4 Preparing Figures for Presentation 4.4.1 General Considerations 4.4.2 Modifying SVG Figures 4.5 Display of Statistical Data Sets 4.5.1 Plots of Data with One Variable 4.5.2 Plots of Data with Two or More Variables 4.6 Exercises Part II Distributions and Hypothesis Tests 5 Basic Statistical Concepts 5.1 Populations and Samples 5.2 Data Types 5.2.1 Categorical 5.2.2 Numerical 5.2.3 Data with One, Two, or More Variables 5.3 Probability Distributions 5.3.1 Definitions 5.3.2 Discrete Distributions 5.3.3 Continuous Distributions 5.3.4 Expected Value and Variance 5.4 Degrees of Freedom 5.5 Study Design 5.5.1 Terminology 5.5.2 Overview 5.5.3 Types of Studies 5.5.4 Design of Experiments 5.5.5 Recommendations for Researchers 5.5.6 Personal Advice 5.5.7 Good Study Design: Clinical Investigation Plan 6 Distributions of One Variable 6.1 Characterizing a Distribution 6.1.1 Distribution Center 6.1.2 Quantifying Variability 6.1.3 Parameters Describing the Form of a Distribution 6.1.4 Important Methods of Probability Density Functions 6.2 Discrete Distributions 6.2.1 Bernoulli Distribution 6.2.2 Binomial Distribution 6.2.3 Poisson Distribution 6.2.4 Hypergeometric Distribution 6.3 Normal Distribution 6.3.1 Examples of Normal Distributions 6.3.2 Central Limit Theorem 6.3.3 Distributions and Hypothesis Tests 6.4 Continuous Distributions Derived from the Normal Distribution 6.4.1 T-Distribution 6.4.2 Chi-Square Distribution 6.4.3 F-Distribution 6.5 Other Continuous Distributions 6.5.1 Lognormal Distribution 6.5.2 Weibull Distribution 6.5.3 Exponential Distribution 6.5.4 Uniform Distribution 6.6 Confidence Intervals of Selected Statistical Parameters 6.7 Exercises 7 Hypothesis Tests 7.1 Typical Analysis Procedure 7.1.1 Data Screening and Outliers 7.1.2 Normality Check 7.1.3 Transformation 7.2 Hypothesis Tests and Power Analyses 7.2.1 An Example 7.2.2 Generalization and Applications 7.2.3 The Interpretation of the P-Value 7.2.4 Types of Errors 7.2.5 Sample Size 7.3 Sensitivity and Specificity 7.3.1 Related Calculations 7.3.2 Example: Mammogram 7.4 Receiver-Operating-Characteristic (ROC) Curve 7.5 Exercises 8 Tests of Means of Numerical Data 8.1 Distribution of a Sample Mean 8.1.1 One Sample T-Test for a Mean Value 8.1.2 Wilcoxon Signed Rank Sum Test 8.2 Comparison of Two Groups 8.2.1 Paired T-Test 8.2.2 T-Test Between Independent Groups 8.2.3 T-Tests with Pingouin 8.2.4 Non-parametric Comparison of Two Groups: Mann-Whitney Test 8.3 Comparison of Multiple Groups 8.3.1 Analysis of Variance (ANOVA) 8.3.2 Multiple Comparisons 8.3.3 Kruskal–Wallis Test 8.3.4 Two-Way ANOVA 8.3.5 Three-Way ANOVA 8.3.6 Friedman Test 8.4 Summary: Selecting the Right Test for Comparing Groups 8.5 Exercises 9 Tests on Categorical Data 9.1 Proportions and Confidence Intervals 9.1.1 Explanation 9.1.2 Example 9.2 Tests Using Frequency Tables 9.2.1 One-Way Chi-Square Test 9.2.2 Chi-Square Contingency Test 9.2.3 Fisher's Exact Test 9.2.4 McNemar's Test 9.2.5 Cochran's Q Test 9.3 Exercises 10 Analysis of Survival Times 10.1 Survival Distributions 10.2 Survival Probabilities 10.2.1 Censorship 10.2.2 Kaplan–Meier Survival Curve 10.3 Comparing Survival Curves in Two Groups Part III Statistical Modeling 11 Finding Patterns in Signals 11.1 Cross Correlation 11.2 Correlation Coefficient 11.2.1 Covariance 11.2.2 Pearson Correlation Coefficient 11.2.3 Rank Correlation 11.3 Coefficient of Determination 11.3.1 General Linear Regression Model 11.3.2 Interpretation 11.4 Scatterplot Matrix 11.5 Correlation Matrix 11.6 Autocorrelation 11.7 Time-Series Analysis 11.7.1 Data Decomposition 11.7.2 Analysis of Residuals 11.7.3 ARMA models 11.7.4 Integrated ARMA (or ARIMA) Models 11.7.5 Examples of Simple ARIMA Models 12 Linear Regression Models 12.1 Simple Fits 12.2 Design Matrix and Formulas 12.2.1 Example 1: Simple Linear Regression 12.2.2 Example 2: Quadratic Fit 12.2.3 Multilinear Regression 12.2.4 Patsy—The Formula Language 12.2.5 Design Matrix 12.3 Linear Regression Analysis with Python 12.3.1 Example 1: Line Fit with Confidence Intervals 12.3.2 Example 2: Noisy Quadratic Polynomial 12.4 Model Results of Linear Regression Models 12.4.1 Example: Tobacco and Alcohol in the UK 12.4.2 Model Characteristics 12.4.3 Model Coefficients and Their Interpretation 12.4.4 Analysis of Residuals 12.4.5 Comparison to Model With Outlier 12.4.6 Regression Using Sklearn 12.4.7 Conclusion 12.5 Assumptions and Interpretations of Linear Regression 12.5.1 Assumptions 12.5.2 Interpreting Multilinear Regression Models 12.6 Bootstrapping 12.7 Exercises 13 Generalized Linear Models 13.1 Comparing and Modeling Ranked Data 13.2 Elements of GLMs 13.2.1 Exponential Family of Distributions 13.2.2 Linear Predictor and Link Function 13.3 GLM 1: Logistic Regression 13.4 GLM 2: Ordinal Logistic Regression 13.4.1 Model 13.4.2 Optimization 13.4.3 Performance 13.5 Exercises 14 Bayesian Statistics 14.1 Bayesian Versus Frequentist Interpretation 14.1.1 Bayes' Theorem 14.1.2 Bayesian Example 14.2 The Bayesian Approach in the Age of Computers 14.3 Example: Markov-Chain-Monte-Carlo Simulation 14.4 Summing Up Appendix A Useful Programming Tools A.1 Debugger A.2 Test Tools A.3 Code Versioning with git A.3.1 Overview A.3.2 Installation and Interfaces A.3.3 Examples A.4 Graphical User Interfaces (GUIs) A.4.1 PySimpleGUI—Examples A.4.2 PyQtGraph A.4.3 Tips for User Interface A.5 Exercises Appendix B Solutions Appendix C Equations for Confidence Intervals Appendix D Web Ressources Appendix Glossary Appendix Bibliography Index the material is concerned, specifically the rights of translation, reprinting, reuse of 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I Python and Statistics -- 1 Introduction -- 2 Python -- 3 Data Input -- 4 Data Display -- II Distributions and Hypothesis Tests -- 5 Basic Statistical Concepts -- 6 Distributions of One Variable -- 7 Hypothesis Tests -- 8 Tests of Means of Numerical Data -- 9 Tests on Categorical Data -- 10 Analysis of Survival Times -- III Statistical Modelling -- 11 Finding Patterns in Signals -- 12 Linear Regression Models -- 13 Generalized Linear Models -- 14 Bayesian Statistics -- Appendices -- A Useful Programming Tools -- B Solutions -- C Equations for Confidence Intervals -- D Web Ressources -- Glossary -- Bibliography -- Index