Describe before you summarize
What does one headline number leave out?
3 lessonsChoose and describe a summary without hiding its denominator, distribution, or scale.
Count & Chance
Statistics you can inspect, rerun, and challenge
Work from a claim to its data, calculation, and limits. Twelve interactive labs are paired with source-backed guides, learning routes, self-checks, and downloadable case files.
All examples use synthetic data generated in your browser. They are teaching models, not findings about real people or events.
- 12
- interactive labs
- 12
- source-backed guides
- 4
- learning routes
- 3
- downloadable cases
Interactive synthetic labruns in this browser
View the values behind this chart
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SEEDStart with a question
Four routes through the full collection
Each route connects three readings to three rerunnable labs, a concrete practice task, and checked answers.
Samples, bias, and uncertainty
When does more data fail to mean better evidence?
3 lessonsDistinguish selection quality, random error, standard error, and interval coverage.
Compare like with like
Which hidden structure can reverse or weaken a comparison?
3 lessonsAudit comparisons for nonlinearity, unequal mixtures, and selection on extreme measurements.
Evaluate a statistical claim
What context must travel with a striking result?
3 lessonsAsk for the prior rate, graphical baseline, effect size, denominator, and full analysis family.
Selected experiments
Test an intuition before reading the answer
Every lab exposes its controls, seed, raw values, CSV, assumptions, and failure conditions. These four span sampling, uncertainty, comparison, and multiplicity.
LAB 01Sampling
Why averages settle down
Draw repeated samples from a right-skewed synthetic population and watch the distribution of their means change with sample size.
LAB 04Uncertainty
When accurate alerts mislead
Change prevalence, sensitivity, and specificity, then inspect every expected true and false alert in a synthetic population.
LAB 05Relationships
When every group wins but the total loses
Adjust the mix of two synthetic groups and see how different weights can reverse an aggregate comparison.
LAB 12Uncertainty
Twenty chances for one false alarm
Generate complete families of valid null p-values and compare an unadjusted threshold with Bonferroni family-wise control.
Applied casebook
Make a decision from the rows, not the headline
Three complete synthetic case files include the data dictionary, calculation table, audit tasks, checked answer, and a downloadable CSV.
- Quality alerts under a rare base rate
- A rollout result that reverses after standardization
- A large voluntary survey that misses its population
CASE 02 / ROLLOUTB wins in both groups, A wins in total
| Option | New | Returning | Raw total |
|---|---|---|---|
| A | 60% | 90% | 84% |
| B | 65% | 95% | 71% |
Why? The options received different proportions of new and returning visitors. A 50/50 standardization gives A 75% and B 80%.
Read the derivation
Guides that show their working
sampling 8 min
Why Sample Means Become Bell-Shaped
A skewed population can produce nearly normal averages. The change belongs to repeated sampling, not to the original observations.
uncertainty 10 min
When a 99% Accurate Alert Is Only Half Right
Even a strong detector can produce a surprising share of false alerts when the event it seeks is rare. The missing ingredient is the base rate.
relationships 10 min
When Every Group Improves but the Total Gets Worse
A combined rate can reverse the comparison inside every subgroup when the groups appear in different proportions.
A small model, honestly labeled
What happens inside a lab?
Inputs are clamped to documented ranges, a seeded generator creates the sample, and a pure statistics function produces both the chart and its accessible value table.
01Choose assumptions02Generate synthetic values03Compute the summary04Check where it fails
Read the methodology