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Sampling & Inference

Sampling distributions, the Central Limit Theorem, standard error and confidence intervals: how a sample lets you say something about a population.

14 articles

Illustration: A correlogram: bars outside the band show memory in the series at that lag

Sep 28, 20267 min read

Autocorrelation Explained: When Data Points Aren't Independent

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Illustration: Drop each observation once, re-estimate, and use the spread of the estimates

Sep 23, 20268 min read

The Jackknife: Estimating Bias and Standard Error by Leaving One Out

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Illustration: 2,000 resamples of one 25-value sample, with the middle 95% of resampled means highlighted

Sep 21, 20267 min read

Bootstrap Sampling: Confidence Intervals Without a Formula

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Sep 18, 20267 min read

The Finite Population Correction: Sampling Without Replacement From a Small Population

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Illustration: A slightly biased but far more precise estimator can beat an unbiased one on MSE

Sep 14, 20268 min read

Unbiased Estimators and Mean Squared Error: What Makes an Estimate Good?

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Illustration: Quadruple the sample size and the sampling distribution is half as wide

Sep 1, 20267 min read

Standard Error: What It Measures and Why It Matters

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Illustration: The likelihood of 7 heads in 10 flips peaks at p = 0.7 — the maximum-likelihood estimate

Aug 28, 20267 min read

Maximum Likelihood Estimation: The Method Behind the Formulas

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Illustration: The simple Wald interval spills below zero; the Wilson interval stays inside the possible range

Aug 26, 20267 min read

The Wilson Score Interval: A Better Confidence Interval for Proportions

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Illustration: A Beta posterior after 11 successes in 20 trials, with the central 95% of belief shaded

Aug 24, 20268 min read

Bayesian Credible Intervals: A Worked Example, Computed From Scratch

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Illustration: Extreme first scores are followed, on average, by less extreme second scores

Aug 18, 20267 min read

Regression to the Mean: Why Extreme Results Tend to Moderate

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Illustration: Only the loudest corner of the population answered — the sample no longer represents everyone

Aug 12, 20268 min read

Types of Bias in Research: Selection, Response, and Measurement Bias

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Illustration: Four ways to draw a sample from the same population — each with different trade-offs

Aug 10, 20268 min read

Sampling Methods: Random, Stratified, Cluster, and Systematic Sampling

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Illustration: 19 of 20 intervals capture the true mean; the 1 that miss are in red

Aug 8, 20268 min read

Confidence Intervals: What They Mean and How to Build One

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Illustration: Skewed population on the left; the means of samples of 30 are already bell-shaped on the right

Aug 3, 20269 min read

The Central Limit Theorem, Explained With Worked Examples

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