Learning Track: A Recap of Undergraduate Statistics

Claudius Gräbner-Radkowitsch

Learning Track: A Recap of Undergraduate Statistics

A curated sequence of pages covering the statistical fundamentals every empirical researcher needs: from conceptual foundations and data types through descriptive statistics, probability theory, and sampling.

Author

Claudius Gräbner-Radkowitsch

Published

June 15, 2026

Modified

June 15, 2026

1 Who this track is for

This track is for students and researchers who want a solid conceptual and practical grounding in the statistical fundamentals that underpin empirical work in the social sciences and management. It is particularly useful as a self-contained recap for students entering a methods course who need to refresh core ideas, or for anyone whose statistics education was primarily procedural and who wants to build deeper understanding.

No prior experience with R is assumed for the first two pages. Pages three and beyond involve R code alongside explanations — you do not need to follow along in R, but doing so will deepen your understanding.

By the end of the track, you will be able to describe and summarize data using appropriate statistical measures, interpret probability distributions and use them for inference, and understand the logic connecting sample statistics to population parameters.

2 Core sequence

Work through these pages in order. Each page builds on the previous one.

Conceptual Foundations of Statistics What statistics is, why intuition is insufficient for interpreting data, and how probability theory provides the reference points we need. Start here.
Data Fundamentals: Types, Scales, and Notation The building blocks of data: categorical vs. numerical variables, the four scales of measurement, and standard statistical notation. Essential vocabulary for everything that follows.
Descriptive Statistics in R Measures of centrality, dispersion, and association — computed in R. Includes correlation matrices, simple linear regression as a descriptive tool, and Anscombe’s quartet as a lesson in why visualization matters.
Essentials of Probability Theory for Statistics Random variables, probability distributions, the normal distribution, expected values, and the bridge between descriptive statistics and probability. The conceptual foundation for inferential statistics.
Sampling and Statistical Inference How we move from sample statistics to conclusions about populations: sampling variability, Monte Carlo simulation, sampling distributions, standard error, the Central Limit Theorem, and the Law of Large Numbers.
Hypothesis Testing and Confidence Intervals Applying sampling theory to evaluate claims (hypothesis testing, p-values) and construct ranges of plausible values (confidence intervals). Includes the connection between the two and a guide to common misconceptions.

3 Supplementary reference

Common Probability Distributions A reference companion to page 4: binomial, Poisson, uniform, exponential, beta, and gamma distributions, with guidance on when to use each and how to work with them in R. Not part of the main sequence but useful alongside or after page 4.

4 All statistics resources

Title	Description
Common Probability Distributions: A Reference Overview	An overview of probability distributions beyond the normal: binomial, Poisson, uniform, exponential, beta, and gamma — with guidance on when to use each and how to work with them in R.
Conceptual Foundations of Statistics	A first orientation to statistical thinking: what statistics is, why intuition alone is insufficient for interpreting data, and how probability theory provides the reference points we need to evaluate observations.
Data Fundamentals: Types, Scales, and Notation	An introduction to the building blocks of data: types of variables (categorical vs. numerical), scales of measurement (nominal, ordinal, interval, ratio), and the statistical notation used to describe them.
Descriptive Statistics in R	A guided introduction to descriptive statistics in R, covering measures of centrality, dispersion, and association — including correlation matrices, simple linear regression, and Anscombe’s quartet as a lesson in why visualization matters.
Hypothesis Testing and Confidence Intervals	Applying sampling theory to make inferences: how to evaluate claims using data (hypothesis testing and p-values) and how to construct ranges of plausible values for population parameters (confidence intervals).
Essentials of Probability Theory for Statistics	A conceptual and practical introduction to probability theory: random experiments, events, conditional probability, random variables, the normal distribution, expected values, and the bridge to descriptive statistics.
Sampling and Statistical Inference	How we move from sample statistics to conclusions about populations: sampling variability, Monte Carlo simulation, sampling distributions, standard error, the Central Limit Theorem, and the Law of Large Numbers.
Exercise: Causal Reasoning and the Gender Wage Gap	Practice DAG-based causal reasoning using a three-model regression progression on the gender wage gap — identify confounders and mediators, interpret coefficient changes, and specify a DAG in dagitty.
Exercise: Predicting Firm Exit with Logistic Regression	Practice logistic regression end-to-end: fit a model for binary firm exit, extend it with additional predictors, interpret odds ratios, compute scenario-based predicted probabilities, and communicate findings with inline R code.
Experiments in R	How to analyze experimental data in R: t-tests for simple comparisons, one-way and two-way ANOVA for multi-group designs, effect sizes, post-hoc tests, and power analysis.
Hypothesis Testing and Confidence Intervals: Practice Exercises	Conceptual and computational exercises to test and reinforce your understanding of hypothesis testing, p-values, confidence intervals, and the connections between them.
Linear Regression in R	Practical implementation of simple and multiple linear regression in R: fitting models with lm(), interpreting coefficients, computing R², understanding omitted variable bias, applying log and quadratic transformations, and reading diagnostic plots.
Logarithms: A Gentle Introduction	A practical introduction to logarithms for data science: what they are, the natural logarithm, the relationship with exponential functions, and when and why to use log transformations in statistical analysis.
Logistic Regression for Binary Outcomes in R	Understand why OLS fails for binary outcomes, fit logistic regression with glm(), and translate log-odds into predicted probabilities and average marginal effects.
Categorical Variables and Interaction Terms in Regression	Extend linear regression to handle categorical predictors with multiple levels and interaction terms, using a real earnings dataset to explore how the age–earnings profile differs by gender.
Panel Data and Fixed Effects in R	Understand the logic of panel data, learn to distinguish within- from between-unit variation, estimate fixed effects models with fixest, and connect the FE identification argument to causal reasoning.
Causal Reasoning with DAGs	Learn to use Directed Acyclic Graphs (DAGs) to distinguish causal from associational claims, identify confounders, mediators, and colliders, and determine what to control for in a regression model.
Regression Residuals and Model Diagnostics	Understand the distinction between residuals and error terms, learn the key assumptions of linear regression, and apply visual and quantitative diagnostic tests to evaluate model quality.
Human Development and Social Indicators	How the Human Development Index and its gender-sensitive relatives are constructed, what the choice of geometric aggregation encodes, and why directly measured education, health, and infrastructure indicators are often more informative than any composite.
Income, Output, and Complexity Indicators	What GDP and GNI per capita actually measure, why the real/nominal and PPP adjustments matter, and how the Economic Complexity Index captures productive capabilities that income measures miss.
Measuring Inequality and Poverty	How the Lorenz curve, the Gini coefficient, top shares, and the Palma ratio describe a distribution, how absolute poverty lines and the Multidimensional Poverty Index identify deprivation, and why these measures disagree.

Citation

BibTeX citation:

@inreference{graebner2026-statistics-recap,
  author = {Gräbner-Radkowitsch, Claudius},
  editor = {Gräbner-Radkowitsch, Claudius},
  title = {Learning {Track:} {A} {Recap} of {Undergraduate}
    {Statistics}},
  booktitle = {Method and Inquiry},
  date = {2026-06-15},
  url = {https://euf-methodology-hub.netlify.app/tracks/statistics-recap},
  langid = {en}
}

For attribution, please cite this work as:

Gräbner-Radkowitsch, Claudius. 2026. “Learning Track: A Recap of Undergraduate Statistics.” In Method and Inquiry, edited by Claudius Gräbner-Radkowitsch. June 15. https://euf-methodology-hub.netlify.app/tracks/statistics-recap.