• 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. Getting Started
  2. 3  Basic Definitions
  • 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

  • 3.1 Reproducibility (Computational)
  • 3.2 Replicability (Independent Confirmation)
  • 3.3 Literate Programming
  • 3.4 Reproducible Computing
  • 3.5 Research Compendia (Modern View)
  • 3.6 How This Handbook Implements Reproducibility
  • 3.7 Minimal Reproducibility Checklist
  • 3.8 Historical Note: The R Framework and Compendium Platform
  1. Getting Started
  2. 3  Basic Definitions

3  Basic Definitions

3.1 Reproducibility (Computational)

Reproducibility means that someone else can take the same data, the same code, and the same computational environment and obtain the same results. In this handbook, reproducibility is a practical goal: you should be able to rerun a method, verify its output, and reuse it for your own data with minimal friction.

3.2 Replicability (Independent Confirmation)

Replicability means that independent researchers can confirm a finding using new data (and often different code). Replicability is a scientific standard, while reproducibility is a computational standard. Both matter, but they are distinct.

3.3 Literate Programming

Literate programming is a style of writing where code and explanation are interwoven. The document is produced by executing the code, so the narrative and the results remain consistent by construction.

3.4 Reproducible Computing

Reproducible computing is the practical application of reproducibility in statistical work: data, code, and results are connected in a way that can be rerun, verified, and adapted by the reader.

3.5 Research Compendia (Modern View)

A research compendium is an organized package of text, code, data, and environment details that enables reproduction and reuse. In modern practice, this includes:

  • the analysis script or notebook,
  • the data or data source,
  • the computational environment (e.g., package versions),
  • the resulting outputs (figures, tables, reports).

This handbook itself is a web-native compendium: it combines explanatory text, code-backed results, and interactive computational tools in a single, navigable system.

3.6 How This Handbook Implements Reproducibility

This handbook is built around a reproducible workflow:

  • Quarto generates executable documents in which results are tied to code.
  • Shiny apps expose methods as interactive computations that can be reproduced and adapted by the reader.
  • Links and embedded inputs make it easy to jump from the explanation to a working computational implementation.

The intent is not only to explain methods but to make them directly usable and recomputable.

3.7 Minimal Reproducibility Checklist

For any method or analysis, ask:

  1. Can I access the data (or an equivalent example)?
  2. Can I see or run the code?
  3. Is the computational environment specified or reproducible (e.g., R/package versions, renv lockfile, or container)?
  4. Are the results traceable back to the exact inputs and code used (e.g., a Shiny URL with embedded inputs or an archived computation)?

If the answer is “yes” to all four, the analysis is reproducible.

3.8 Historical Note: The R Framework and Compendium Platform

The original vision of this handbook came from the R Framework and the Compendium Platform, which aimed to make statistical computation reproducible on the web. The R Framework provided modular statistical services, while the Compendium Platform stored computations as archived, citable resources. This early infrastructure influenced the handbook’s emphasis on transparency, reuse, and traceable computation.

While today’s implementation uses more modern tooling (Quarto, Shiny, and web-based deployment), the goal remains the same: make statistical analysis open, reproducible, and immediately usable by the reader.

2  Why Do We Need Innovative Technology?
4  The Big Picture: Why We Analyze Data

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

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