Statistical Inference

Notes & simulations

Interactive simulations for statistics, econometrics, and causal inference. The idea is to see how things like sampling distributions, p-values, and OLS actually work, not just read about them.

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Probability & Uncertainty

• Foundations — Distributions, Sampling & Confidence Intervals
• Variance, SD & Standard Error — Population vs Sample, SD vs SE & Why n − 1
• The Sampling Distribution — Data vs Sampling Distribution & When to Assume Normality

The Central Limit Theorem

• CLT Simulator — Interactive CLT Simulator
• LLN vs CLT — Why Averages Stabilize Before They Become Normal

Inference

• p-values & Confidence Intervals — What They Actually Mean
• The Bootstrap — Resampling-Based Inference
• Power, Alpha, Beta & MDE — Hypothesis Testing & Experiment Design
• Monte Carlo Experiments — How We Understand Estimators
• Multiple Testing — False Discoveries & the Replication Crisis

Regression

• Regression & the CEF — OLS and the Conditional Expectation Function
• Residuals & Controls — Diagnostics, Partialling Out & Omitted Variable Bias
• Frisch-Waugh-Lovell — Partialling Out & OVB

Standard Errors & Diagnostics

• Heteroskedasticity — Constant vs Non-Constant Variance & Robust SEs
• Clustered SEs — When Observations Aren’t Independent
• Measurement Error — Why Noisy Regressors Bias You Toward Zero
• Bias-Variance Tradeoff — Underfitting, Overfitting & MSE Decomposition
• When Inference Breaks Down — Why Variation Is the Fuel of Inference

Causal Thinking

• From Correlation to Causation — Why Correlation Isn’t Enough & When It Becomes Causal

Bayesian Thinking

• Bayesian Updating — One Gentle Introduction