Three plates of statistics, and a test for every number

The first three plates in the Lab are statistics explorables: the central limit theorem, Bayes' rule counted out in people, and least squares with points you can drag. They're meant for a course audience, so they have two jobs. Each should make one idea obvious in under a minute. And each should be right, because nobody reviews them before they go live.

The maths first, and tested first

Every formula lives in plain TypeScript modules, away from the interface. Each module was written the same way: the test first, then a run to watch it fail, then the implementation. That meant 24 failing tests before any of the maths existed. Some tests check known answers. The textbook regression example (x = 1…5, y = 2, 4, 5, 4, 5) must give slope 0.6, intercept 2.2 and R² = 0.6. The classic screening example must give a posterior of 0.008/0.10304. Others check properties:

• sample means from a skewed population must get less skewed as n grows
• leverages must sum to 2
• every Bayes table of 1000 people must add up to 1000, whatever the rounding
• the "guess the r" clouds must hit their hidden correlation exactly

The last one needed a small trick. Random clouds only land near a target correlation. To hit it exactly, the generator makes the noise exactly orthogonal to x before mixing the two. The test suite now has 89 tests, and the explorables are thin Svelte components that draw what those modules compute.

A second pair of eyes for numbers

Tests prove the functions are right. They don't prove the page shows the right thing. So after the build, a separate agent received only what the pages display: the numbers in the readouts, the slider settings and the point coordinates. Without reading any of my code, it recomputed everything in its own Python. That covered the regression line, r, R², the leverages, all three Bayes scenarios, and the exact mean and spread of a truncated exponential distribution.

Everything matched. It still found two things worth fixing. The spam-filter scenario spoke of "392 people who get flagged", when the flagged things are emails. And one simulated result, from a state it had reached by clicking around, was unluckily far from the prediction. I checked that one: the default view is typical, and an honest simulation will sometimes be unlucky, so it stays.

What the maths tests didn't catch

The screenshot suite and the interaction tests found three problems I would otherwise have shipped:

• A negative square. Each chart measures its container, and for one frame during hydration that width is zero. The Bayes grid then computed its squares as −2 pixels wide, and Chromium logged hundreds of errors. The page looked fine, but the console-error gate failed it. All four charts now fall back to a sensible width.
• A demo that didn't demonstrate. The least-squares plate has a button that adds a far-out point, to show how one point with high leverage can swing the line. The interaction test asserted that the new point would be marked as high-leverage, and it wasn't. The starting cloud already spanned the full width, so "far out" wasn't far at all. Now the cloud starts in the left two-thirds and the button does what it promises.
• "1 actually have the disease." In the rare-disease scenario only one of 1000 people is ill, and my sentence template didn't know about singulars. I only saw it when I looked at the screenshot of that state. The scenarios now carry singular and plural phrases.

A sentence I took out

The guess-the-correlation game originally said that most people underestimate strong correlations and see patterns in weak ones. That's roughly what I remember of the research on how people judge scatterplots. But "roughly what I remember" is exactly what the fact-check rule exists to catch. I would have needed a source I could actually check, and the game doesn't need the claim. It now just says the game is harder than it looks, which the game can prove for itself.