Statistics and Data Science for Researchers

Statistics & Data Science
By OgbonLab

Statistics for researchers who refuse to p-hack.

From probability axioms to causal inference, Bayesian analysis, and ML for researchers, all in the browser, all reproducible.

13 parts 95 sections Free, browser-native
Start reading → First up: Why probability? Axioms and Kolmogorov

Table of contents

Every section is a working session: text, math, code, interactive widgets. Click any title to jump in.

Part 1: Part 0, Probability from zero

  1. Why probability? Axioms and Kolmogorov
  2. Random variables and distributions
  3. Joint, conditional, marginal
  4. Expectations and moments
  5. The catalog of common distributions
  6. The law of large numbers
  7. The central limit theorem
  8. Transformations of random variables
  9. Moment-generating and characteristic functions
  10. Simulation as intuition

Part 2: Part 1, Estimation

  1. Estimators and their properties
  2. Method of moments
  3. Maximum likelihood
  4. Fisher information and the Cramér-Rao bound
  5. Bias-variance, MSE, and the efficiency frontier
  6. Sampling distributions and the standard error
  7. Bootstrap, jackknife, and resampling first principles
  8. Robust and M-estimators
  9. Consistency, asymptotics, and "large enough"

Part 3: Part 2, Hypothesis testing without p-hacking

  1. The Neyman-Pearson framework, honestly
  2. Type-I, Type-II, power, and effect size
  3. t-tests, χ², F-tests done by hand
  4. What a p-value is, and what it is not
  5. Multiple testing: FWER and FDR
  6. Preregistration and the garden of forking paths
  7. Equivalence testing and TOST
  8. The replication crisis and what to actually do

Part 4: Part 3, Confidence intervals and uncertainty

  1. Exact vs asymptotic CIs
  2. Bootstrap CIs (percentile, BCa, basic)
  3. Profile-likelihood and likelihood-ratio CIs
  4. Prediction intervals vs confidence intervals
  5. Calibration: when 95% really means 95%
  6. Communicating uncertainty without lying

Part 5: Part 4, Linear regression, done seriously

  1. OLS as geometry
  2. Assumptions and what breaks when they fail
  3. Diagnostics: residuals, leverage, influence
  4. Heteroscedasticity, GLS, and weighted regression
  5. Robust regression
  6. Interactions and nonlinear terms
  7. Model selection: AIC, BIC, cross-validation
  8. Causal warnings: regression is not causation

Part 6: Part 5, Generalised linear models

  1. From linear to generalised: link and family
  2. Logistic regression and odds ratios
  3. Poisson and negative-binomial counts
  4. Deviance, residuals, and GLM diagnostics
  5. Mixed-effects and hierarchical models intro
  6. When the GLM is not enough

Part 7: Part 6, Causal inference for researchers

  1. Potential outcomes and the fundamental problem
  2. Randomised controlled trials, designed right
  3. Confounding and the DAG toolkit
  4. Propensity scores, matching, and IPTW
  5. Instrumental variables
  6. Regression discontinuity
  7. Difference-in-differences and synthetic controls
  8. Sensitivity analysis: bounding what unobserved confounding could do

Part 8: Part 7, Bayesian methods

  1. Prior, likelihood, posterior, the mechanics
  2. Conjugate priors and analytic posteriors
  3. Metropolis-Hastings by hand
  4. Gibbs sampling on a 2D example
  5. Hamiltonian Monte Carlo intuition
  6. Posterior-predictive checks
  7. Model comparison: Bayes factors and WAIC

Part 9: Part 8, Resampling and nonparametrics

  1. Bootstrap, deeper: parametric vs nonparametric
  2. Permutation tests and exchangeability
  3. Cross-validation done right
  4. Rank-based methods and U-statistics
  5. Kernel density estimation
  6. Quantile regression and distribution-free CIs

Part 10: Part 9, Machine learning for researchers

  1. The ML mindset: prediction vs explanation
  2. Regularisation: ridge, lasso, elastic net
  3. Trees, random forests, and gradient boosting
  4. Calibration and probability outputs
  5. Fairness audits and equalised odds
  6. Causal forests and double ML
  7. Reporting an ML result so the reader can trust it
  8. When NOT to use ML

Part 11: Part 10, Real-research capstones

  1. Capstone 1, a designed RCT, end to end
  2. Capstone 2, an observational study with confounding
  3. Capstone: Meta-analysis with publication-bias correction
  4. Capstone: Bayesian dose-response with MCMC
  5. Capstone: ML deployment with fairness audit
  6. Capstone: Reproducibility audit and multiverse analysis

Part 12: Part 11, Self-assessment quizzes

  1. Quiz, Part 0: Probability from zero
  2. Quiz, Part 1: Estimation
  3. Quiz, Part 2: Hypothesis testing
  4. Quiz, Part 3: Confidence intervals
  5. Quiz, Part 4: Linear regression
  6. Quiz, Part 5: GLMs
  7. Quiz, Part 6: Causal inference
  8. Quiz, Part 7: Bayesian methods
  9. Quiz, Part 8: Resampling and nonparametrics
  10. Quiz, Part 9: ML for researchers
  11. Quiz, Part 10: Capstones
  12. Final exam, integrated assessment

Part 13: Part 12, Master research-analyst workflow

  1. Master research-analyst workflow card

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