Statistics, by seeing it happen

A ground-up probability & statistics course where almost every idea is demonstrated on real data — not just asserted.

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Three ways to use this

Play with it · interactive explorables — drag a slider, watch the statistics change, live in your browser

🎮

Watch 100 confidence intervals

Drag the sample size and confidence level and watch ~95 of 100 intervals capture the true mean — on real data.

flagship demo, made draggable
Read it as a scroll-story →
🎮

The Central Limit Theorem, by hand

Pick a wildly non-normal population, drag the sample size, and watch the average turn into a bell curve.

the engine of inference
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p-values, errors & power

Slide the true effect size and significance level and see Type I error, Type II error, and power trade off in real time.

hypothesis testing, visualized

New here? · start with this — no statistics yet, just how to drive a notebook

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How these notebooks work (start here)

Never used a notebook? Five minutes here and you'll know how to run a lesson, re-run safely, and read the output. No statistics yet.

data: no data yet — just orientation

Part 1 — Seeing data & the logic of chance · lessons 1–10

1

Describing a real dataset

Center, spread, shape, correlation and z-scores — the first questions to ask of any data.

data: Palmer Penguins
Another dataset →The code behind it →
2

Distributions: shape, skew & outliers

Frequency tables, histograms, skew, the IQR outlier rule, and z-scores — when a single number lies.

data: Old Faithful · Lending Club
Another dataset →The code behind it →
3

Relationships: correlation & the regression line

Scatterplots, the correlation r, the least-squares line, residuals & R² — and why correlation isn't causation.

data: Ames housing
Another dataset →The code behind it →
4

Where data comes from: sampling & study design

Sampling methods, bias, experiments vs. observation, random assignment & confounding — how trustworthy data is made.

data: simulation + a known population
5

Probability & conditional probability

Marginal, joint and conditional probability, independence, and a first taste of Bayes — counted from real survivors.

data: Titanic
Another dataset →The code behind it →
6

Counting: permutations & combinations

Permutations, combinations and the choose function — the counting that powers the binomial.

data: dice & cards (simulation)
7

Random variables, expectation & variance

Turn outcomes into numbers: probability distributions, expected value, variance, and the law of large numbers.

data: dice simulation · US Births 2014
Another dataset →The code behind it →
8

Binomial & Poisson — counting events

Two workhorse models for counts: successes out of n (binomial) and rare events per interval (Poisson).

data: US Births 2014 · USGS earthquakes
Another dataset →The code behind it →
9

The normal distribution & the empirical rule

The bell curve, the 68–95–99.7 rule, and turning z-scores into probabilities — checked on real heights.

data: Galton family heights
Another dataset →The code behind it →
10

Sampling distributions & the Central Limit Theorem

The engine of the whole course: averages of samples become normal — even when the data is wildly skewed.

data: Lending Club · simulation
Another dataset →The code behind it →

Part 2 — Drawing conclusions from data · lessons 11–20, the inference half

11

Estimation & standard error

Point estimates, bias vs. precision, and the standard error — how far a sample statistic typically lands from the truth, and the √n law that shrinks it.

data: Ames housing
Another dataset →The code behind it →
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What a 95% confidence interval really means

The flagship simulation: build 100 confidence intervals from real data and watch ~95 capture the true mean.

data: Ames, Iowa housing
Another dataset →The code behind it →
13

Hypothesis testing: p-values, errors & power

Null vs. alternative, the p-value, significance, Type I/II errors, and the power of a test — built by simulating the null world.

data: simulation on a known population
Another dataset →The code behind it →
14

Inference for proportions (one & two)

Confidence intervals and tests for one proportion and for the difference of two — counted from real births.

data: US Births 2014
Another dataset →The code behind it →
15

t-tests: one-sample, two-sample & paired

Comparing means with the t-distribution: against a target, between two groups, and within matched pairs.

data: ToothGrowth · Swim (paired)
Another dataset →The code behind it →
16

Comparing many groups: ANOVA

One-way ANOVA and the F-test — is at least one group mean different, without inflating error by testing every pair?

data: Palmer Penguins
Another dataset →The code behind it →
17

Chi-square: goodness-of-fit & independence

Testing counts: does a distribution match what we expected, and are two categorical variables associated?

data: Titanic
Another dataset →The code behind it →
18

Correlation & regression: inference

Is the slope real, or just luck? A confidence interval and test for a regression slope, with residual diagnostics.

data: Ames housing
Another dataset →The code behind it →
19

Multiple regression (intro)

Several predictors at once: adjusted ('holding others constant') effects, and how to read a regression table.

data: Ames housing
Another dataset →The code behind it →
20

The bootstrap & permutation tests

Inference by resampling: a bootstrap confidence interval and a permutation test — honest answers when the textbook formula runs out.

data: Old Faithful · ToothGrowth
Another dataset →The code behind it →