Methodology

One question per experiment

Each lab begins with a misconception that can be tested by changing a small number of assumptions. The model is deliberately narrower than a real study. That constraint helps a reader see the mechanism, but it also means the result must not be exported into a real-world conclusion without a suitable design and data.

Parameter ranges are bounded to values that keep the display interpretable and computation responsive. A control changes the model described on the page; it does not query an external database or reveal a hidden real-world estimate.

Deterministic random draws

Random-looking examples use a text seed. The seed is hashed into a 32-bit state and passed to a deterministic pseudorandom generator. Equal seeds produce equal streams in supported browsers. Normal draws use the Box-Muller transform. Right-skewed examples exponentiate normal draws to form a log-normal teaching population.

The generator is suitable for reproducible illustrations. It is not a cryptographic generator, a security test, or a claim that statistical randomness can be proved from a visual pattern. Selecting New draw changes the seed; moving a parameter keeps the current seed so the effect of that parameter is easier to compare.

Calculations

Core summaries use the open-source simple-statistics project where an established implementation fits the task. Site-specific functions compose those primitives for repeated sample means, Tukey IQR fences, known-sigma z intervals, natural-frequency Bayes counts, weighted group rates, percentage changes, correlation examples, paired regression-to-the-mean simulations, biased response mixtures, binary run lengths, axis-scale comparisons, and families of null-hypothesis tests.

Unit tests check deterministic output and mathematical invariants. Examples include: histogram counts must add to the source count; a higher base rate must increase the expected true share among otherwise identical alerts; aggregate rates must equal success totals divided by case totals; selected retest means should move inward in the fixed regression model; a representative response mixture must recover the population target; run counts must match the displayed sequence; axis scaling must leave data values unchanged; and a Bonferroni threshold must equal the family alpha divided by the test count.

What the charts show

Charts are generated in the browser from the same result object used to create the metrics and value table. This avoids presenting a decorative picture unrelated to the stated calculation. Color is never the only carrier of meaning: labels, counts, position, captions, and tables provide additional cues.

Some figures show only a subset of repeated values so individual marks remain legible. The caption states when this happens. Aggregate counts still use the full simulation.

Editorial workflow

1. Define the question, assumptions, and prohibited interpretations.
2. Implement the pure calculation and deterministic generator.
3. Add tests for fixed examples, edge conditions, and reproducibility.
4. Write an original guide around a synthetic scenario.
5. Check statistical definitions against primary teaching or standards sources.
6. Review mobile, keyboard, reduced-motion, and no-JavaScript behavior.
7. Run content, link, build-output, and production-configuration checks.

Limits

A correct simulation can still answer the wrong question. The labs do not repair biased samples, define causal estimands, validate measurement, or choose a decision threshold. They are designed to make those missing choices harder to overlook. Readers applying statistics to consequential work should use methods and review appropriate to their field.