• Descriptive
    • Moments
    • Concentration
    • Central Tendency
    • Variability
    • Stem-and-Leaf Plot
    • Histogram & Frequency Table
    • Data Quality Forensics
    • Conditional EDA
    • Quantiles
    • Kernel Density Estimation
    • Normal QQ Plot
    • Bootstrap Plot

    • Multivariate Descriptive Statistics
  • Distributions
    • Binomial Probabilities
    • Geometric Probabilities
    • Negative Binomial Probabilities
    • Hypergeometric Probabilities
    • Multinomial Probabilities
    • Dirichlet
    • Poisson Probabilities

    • Exponential
    • Gamma
    • Erlang
    • Weibull
    • Rayleigh
    • Maxwell-Boltzmann
    • Lognormal
    • Pareto
    • Inverse Gamma
    • Inverse Chi-Square

    • Beta
    • Power
    • Beta Prime (Inv. Beta)
    • Triangular

    • Normal (area)
    • Logistic
    • Laplace
    • Cauchy (standard)
    • Cauchy (location-scale)
    • Gumbel
    • Fréchet
    • Generalized Extreme Value

    • Normal RNG
    • ML Fitting
    • Tukey Lambda PPCC
    • Box-Cox Normality Plot
    • Noncentral t
    • Noncentral F
    • Sample Correlation r

    • Empirical Tests
  • Hypotheses
    • Theoretical Aspects of Hypothesis Testing
    • Bayesian Inference
    • Minimum Sample Size

    • Empirical Tests
    • Multivariate (pair-wise) Testing
  • Models
    • Manual Model Building
    • Guided Model Building
  • Time Series
    • Time Series Plot
    • Decomposition
    • Exponential Smoothing

    • Blocked Bootstrap Plot
    • Mean Plot
    • (P)ACF
    • VRM
    • Standard Deviation-Mean Plot
    • Spectral Analysis
    • ARIMA

    • Cross Correlation Function
    • Granger Causality
  1. Preface
  • Preface
  • Getting Started
    • 1  Introduction
    • 2  Why Do We Need Innovative Technology?
    • 3  Basic Definitions
    • 4  The Big Picture: Why We Analyze Data
  • Introduction to Probability
    • 5  Definitions of Probability
    • 6  Jeffreys’ axiom system
    • 7  Bayes’ Theorem
    • 8  Sensitivity and Specificity
    • 9  Naive Bayes Classifier
    • 10  Law of Large Numbers

    • 11  Problems
  • Probability Distributions
    • 12  Bernoulli Distribution
    • 13  Binomial Distribution
    • 14  Geometric Distribution
    • 15  Negative Binomial Distribution
    • 16  Hypergeometric Distribution
    • 17  Multinomial Distribution
    • 18  Poisson Distribution

    • 19  Uniform Distribution (Rectangular Distribution)
    • 20  Normal Distribution (Gaussian Distribution)
    • 21  Gaussian Naive Bayes Classifier
    • 22  Chi Distribution
    • 23  Chi-squared Distribution (1 parameter)
    • 24  Chi-squared Distribution (2 parameters)
    • 25  Student t-Distribution
    • 26  Fisher F-Distribution
    • 27  Exponential Distribution
    • 28  Lognormal Distribution
    • 29  Gamma Distribution
    • 30  Beta Distribution
    • 31  Weibull Distribution
    • 32  Pareto Distribution
    • 33  Inverse Gamma Distribution
    • 34  Rayleigh Distribution
    • 35  Erlang Distribution
    • 36  Logistic Distribution
    • 37  Laplace Distribution
    • 38  Gumbel Distribution
    • 39  Cauchy Distribution
    • 40  Triangular Distribution
    • 41  Power Distribution
    • 42  Beta Prime Distribution
    • 43  Sample Correlation Distribution
    • 44  Dirichlet Distribution
    • 45  Generalized Extreme Value (GEV) Distribution
    • 46  Frechet Distribution
    • 47  Noncentral t Distribution
    • 48  Noncentral F Distribution
    • 49  Inverse Chi-Squared Distribution
    • 50  Maxwell-Boltzmann Distribution
    • 51  Distribution Relationship Map

    • 52  Problems
  • Descriptive Statistics & Exploratory Data Analysis
    • 53  Types of Data
    • 54  Datasheets

    • 55  Frequency Plot (Bar Plot)
    • 56  Frequency Table
    • 57  Contingency Table
    • 58  Binomial Classification Metrics
    • 59  Confusion Matrix
    • 60  ROC Analysis

    • 61  Stem-and-Leaf Plot
    • 62  Histogram
    • 63  Data Quality Forensics
    • 64  Quantiles
    • 65  Central Tendency
    • 66  Variability
    • 67  Skewness & Kurtosis
    • 68  Concentration
    • 69  Notched Boxplot
    • 70  Scatterplot
    • 71  Pearson Correlation
    • 72  Rank Correlation
    • 73  Partial Pearson Correlation
    • 74  Simple Linear Regression
    • 75  Moments
    • 76  Quantile-Quantile Plot (QQ Plot)
    • 77  Normal Probability Plot
    • 78  Probability Plot Correlation Coefficient Plot (PPCC Plot)
    • 79  Box-Cox Normality Plot
    • 80  Kernel Density Estimation
    • 81  Bivariate Kernel Density Plot
    • 82  Conditional EDA: Panel Diagnostics
    • 83  Bootstrap Plot (Central Tendency)
    • 84  Survey Scores Rank Order Comparison
    • 85  Cronbach Alpha

    • 86  Equi-distant Time Series
    • 87  Time Series Plot (Run Sequence Plot)
    • 88  Mean Plot
    • 89  Blocked Bootstrap Plot (Central Tendency)
    • 90  Standard Deviation-Mean Plot
    • 91  Variance Reduction Matrix
    • 92  (Partial) Autocorrelation Function
    • 93  Periodogram & Cumulative Periodogram

    • 94  Problems
  • Hypothesis Testing
    • 95  Normal Distributions revisited
    • 96  The Population
    • 97  The Sample
    • 98  The One-Sided Hypothesis Test
    • 99  The Two-Sided Hypothesis Test
    • 100  When to use a one-sided or two-sided test?
    • 101  What if \(\sigma\) is unknown?
    • 102  The Central Limit Theorem (revisited)
    • 103  Statistical Test of the Population Mean with known Variance
    • 104  Statistical Test of the Population Mean with unknown Variance
    • 105  Statistical Test of the Variance
    • 106  Statistical Test of the Population Proportion
    • 107  Statistical Test of the Standard Deviation \(\sigma\)
    • 108  Statistical Test of the difference between Means -- Independent/Unpaired Samples
    • 109  Statistical Test of the difference between Means -- Dependent/Paired Samples
    • 110  Statistical Test of the difference between Variances -- Independent/Unpaired Samples

    • 111  Hypothesis Testing for Research Purposes
    • 112  Decision Thresholds, Alpha, and Confidence Levels
    • 113  Bayesian Inference for Decision-Making
    • 114  One Sample t-Test
    • 115  Skewness & Kurtosis Tests
    • 116  Paired Two Sample t-Test
    • 117  Wilcoxon Signed-Rank Test
    • 118  Unpaired Two Sample t-Test
    • 119  Unpaired Two Sample Welch Test
    • 120  Two One-Sided Tests (TOST) for Equivalence
    • 121  Mann-Whitney U test (Wilcoxon Rank-Sum Test)
    • 122  Bayesian Two Sample Test
    • 123  Median Test based on Notched Boxplots
    • 124  Chi-Squared Tests for Count Data
    • 125  Kolmogorov-Smirnov Test
    • 126  One Way Analysis of Variance (1-way ANOVA)
    • 127  Kruskal-Wallis Test
    • 128  Two Way Analysis of Variance (2-way ANOVA)
    • 129  Repeated Measures ANOVA
    • 130  Friedman Test
    • 131  Testing Correlations
    • 132  A Note on Causality

    • 133  Problems
  • Regression Models
    • 134  Simple Linear Regression Model (SLRM)
    • 135  Multiple Linear Regression Model (MLRM)
    • 136  Logistic Regression
    • 137  Generalized Linear Models
    • 138  Multinomial and Ordinal Logistic Regression
    • 139  Cox Proportional Hazards Regression
    • 140  Conditional Inference Trees
    • 141  Leaf Diagnostics for Conditional Inference Trees
    • 142  Conditional Random Forests
    • 143  Hypothesis Testing with Linear Regression Models (from a Practical Point of View)

    • 144  Problems
  • Introduction to Time Series Analysis
    • 145  Case: the Market of Health and Personal Care Products
    • 146  Decomposition of Time Series
    • 147  Ad hoc Forecasting of Time Series
  • Box-Jenkins Analysis
    • 148  Introduction to Box-Jenkins Analysis
    • 149  Theoretical Concepts
    • 150  Stationarity
    • 151  Identifying ARMA parameters
    • 152  Estimating ARMA Parameters and Residual Diagnostics
    • 153  Forecasting with ARIMA models
    • 154  Intervention Analysis
    • 155  Cross-Correlation Function
    • 156  Transfer Function Noise Models
    • 157  General-to-Specific Modeling
  • Model Building Strategies
    • 158  Introduction to Model Building Strategies
    • 159  Manual Model Building
    • 160  Model Validation
    • 161  Regularization Methods
    • 162  Hyperparameter Optimization Strategies
    • 163  Guided Model Building in Practice
    • 164  Diagnostics, Revision, and Guided Forecasting
    • 165  Leakage, Target Encoding, and Robust Regression
  • References
  • Appendices
    • Appendices
    • A  Method Selection Guide
    • B  Presentations and Teaching Materials
    • C  R Language Concepts for Statistical Computing
    • D  Matrix Algebra
    • E  Standard Normal Table (Gaussian Table)
    • F  Critical values of Student’s \(t\) distribution with \(\nu\) degrees of freedom
    • G  Upper-tail critical values of the \(\chi^2\)-distribution with \(\nu\) degrees of freedom
    • H  Lower-tail critical values of the \(\chi^2\)-distribution with \(\nu\) degrees of freedom

Table of contents

  • Preface

Statistical Analysis for Small and Big Data

An interactive Compendium based on Reproducible Computing

Start here to understand how to use the handbook effectively and what practical skills you will build across chapters.
Author

Patrick Wessa

Published

24 March, 2026

11th edition © All rights reserved.

This work is provided “as is”, without warranty of any kind, express or implied, including but not limited to warranties of merchantability, fitness for a particular purpose, and noninfringement.

All rights reserved. No part of this publication may be reproduced, distributed, or transmitted in any form or by any means, including photocopying, recording, or other electronic or mechanical methods, without the prior written permission of the publisher, except in the case of brief quotations embodied in critical reviews and certain other noncommercial uses permitted by copyright law.

Preface

Science never solves a problem without creating ten more.

– George Bernard Shaw

This handbook began as teaching material: a structured guide for students to learn statistical analysis through explanation, examples, and practice. Over time it evolved into something more open. While it still serves the classroom, it now aims to be a public, web-native compendium for anyone who wants to learn or apply statistics.

A large part of the content–its ideas, tone, and structure–reflects my own work. But I have chosen to make this a hybrid handbook: one that explicitly allows different LLMs to help improve existing sections and add new material, code, and examples. The result is not a fixed textbook but a living document that can grow and adapt.

I see this as an experiment in collaboration between human and artificial intelligence: a way to build an interactive compendium that is more complete, more practical, and more responsive than a traditional book. The goal is to combine careful human judgment with the speed and breadth of modern AI, while keeping transparency and reproducibility at the core.

What this handbook focuses on:

  • core statistical concepts (descriptive, inferential, modeling, and time series),
  • practical methods with real data examples,
  • reproducible workflows that link explanations to computation,
  • interactive tools (Shiny apps) that allow immediate experimentation.

These topics were chosen because they form the smallest set of ideas and tools that reliably supports real statistical work–from basic exploration to modeling and decision-making.

I would like to express my gratitude to the many people who helped me during the creation of earlier versions of this handbook–everyone who supported, edited, proofread, and tested those drafts. I also thank two dedicated LLMs (Claude and ChatGPT) for their tireless dedication to bug-fixing, typo-hunting, refactoring, and the occasional late-night rescue mission.

24 March, 2026, Patrick Wessa
Getting Started

© 2026 Patrick Wessa. Provided as-is, without warranty.

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