• 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. 2  Why Do We Need Innovative Technology?
  • 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

  • 2.1 The Core Problem: Reproducibility and Teaching
  • 2.2 Why Innovation Is Needed Now
  • 2.3 What “Innovative Technology” Means in This Handbook
  • 2.4 Advantages Over Traditional Compendia
  • 2.5 Historical Note: From Compendia to Web-Native Reproducibility
  1. Getting Started
  2. 2  Why Do We Need Innovative Technology?

2  Why Do We Need Innovative Technology?

2.1 The Core Problem: Reproducibility and Teaching

The problem of irreproducible research has been discussed for decades de Leeuw (2001), Peng, Dominici, and Zeger (2006), Schwab, Karrenbach, and Claerbout (2000), Green (2003), Gentleman (2005), Koenker and Zeileis (2007), Donoho and Huo (2005). Claerbout’s principle captures the core issue de Leeuw (2001):

An article about computational science in a scientific publication is not the scholarship itself, it is merely advertising of the scholarship. The actual scholarship is the complete software development environment and that complete set of instructions that generated the figures.

Jan de Leeuw’s comments sharpen the point:

First, there is no reason to single out figures. The same principle applies to tables, standard errors, and so on.
Second, the same principle applies to teaching: students should be able to reproduce and study our computations on their own machines.
Third, it is often unclear what a “software environment” is, and restrictive tooling can create unnecessary barriers.

These issues are not only scientific; they are educational. If students cannot reproduce or interact with an analysis, the learning experience becomes fragile and incomplete.

2.2 Why Innovation Is Needed Now

Reproducibility is not just a methodological requirement; it is an access problem. Modern education and research require tools that are:

  • low-friction: no complex installation or configuration to get started,
  • transparent: inputs, parameters, and code are visible or recoverable,
  • reusable: analyses can be adapted and rerun on new data,
  • scalable: the same content works in a classroom, in self-study, and in open web contexts.

Traditional workflows can achieve reproducibility, but they often impose high technical barriers. Innovative technology is needed to make reproducible computation the default, not a special effort.

2.3 What “Innovative Technology” Means in This Handbook

This handbook implements a web-native model of reproducible computing:

  • Quarto produces executable documents where results are linked to code.
  • Shiny apps provide interactive computation that can be reused instantly.
  • Archived links and embedded inputs make it possible to trace outputs back to exact parameters.

In other words, the handbook is not just a text; it is a computational system.

2.4 Advantages Over Traditional Compendia

Traditional compendia are valuable, but they require downloading, installing, and running the material locally. The handbook’s approach offers:

  • zero-install access (browser-based),
  • immediate reuse through clickable, parameterized computations,
  • easier dissemination via stable URLs,
  • better pedagogical integration: methods and tools are co-located.

This makes the material more accessible to students and more reliable for educators.

2.5 Historical Note: From Compendia to Web-Native Reproducibility

Several solutions were proposed early on (Gentleman (2005), Donoho and Huo (2005), Leisch (2003)). The R package Sweave Leisch (2003) and the concept of the Compendium were foundational: text, code, and data bundled together for reproducibility. This approach influenced the early design of the R Framework and the Compendium Platform that shaped this handbook.

However, the modern web allows a more direct implementation: instead of bundling everything into an archive, computations can be made reproducible in place, through web-native documents and interactive tools.

de Leeuw, Jan. 2001. “Reproducible Research: The Bottom Line.” In Department of Statistics Papers, 2001031101. Department of Statistics, UCLA. http://repositories.cdlib.org/uclastat/papers/2001031101.
Donoho, D. L., and X. Huo. 2005. “BeamLab and Reproducible Research.” International Journal of Wavelets, Multiresolution and Information Processing 2 (4): 391–414.
Gentleman, R. 2005. “Applying Reproducible Research in Scientific Discovery.” In. BioSilico. https://web.archive.org/web/20090530044050if_/http://gentleman.fhcrc.org:80/Fld-talks/RGRepRes.pdf.
Green, P. J. 2003. “Diversities of Gifts, but the Same Spirit.” The Statistician, 423–38.
Koenker, R., and A. Zeileis. 2007. “Reproducible Econometric Research (a Critical Review of the State of the Art).” In Research Report Series. 60. Department of Statistics; Mathematics Wirtschaftsuniversität Wien.
Leisch, F. 2003. “Sweave and Beyond: Computations on Text Documents.” In Proceedings of the 3rd International Workshop on Distributed Statistical Computing. Vienna, Austria.
Peng, R. D., F. Dominici, and S. L. Zeger. 2006. “Reproducible Epidemiologic Research.” American Journal of Epidemiology.
Schwab, M., N. Karrenbach, and J. Claerbout. 2000. “Making Scientific Computations Reproducible.” Computing in Science & Engineering 2 (6): 61–67.
1  Introduction
3  Basic Definitions

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

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