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.
Count & Chance
Interactive statistics experiments
Move the assumptions, rerun the sample, and see why a statistical summary can change before trusting its conclusion.
All examples use synthetic data generated in your browser. They are teaching models, not findings about real people or events.
Interactive synthetic lab
runs in this browser
View the values behind this chart
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SEEDRepeatable seedsSame seed, same synthetic draw
Visible assumptionsParameters stay beside the result
Chart plus valuesEvery graphic has a text or table view
Source-backed definitionsPrimary references, original examples
The experiment shelf
Twelve ways to test your intuition
Every lab isolates one idea. Adjust a control, inspect the raw values, then follow the linked guide for the derivation and limits.
LAB 02Sampling
One value, two centers
Move one synthetic observation and compare how the mean, median, and middle 80% respond.
LAB 03Uncertainty
What 95% covers
Generate many intervals from one fixed synthetic population and count how often the method captures its known mean.
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 06Relationships
What correlation leaves out
Compare positive, negative, near-zero unstructured, and near-zero curved synthetic relationships to see what a linear summary cannot preserve.
LAB 07Communication
Points are not percent
Set a baseline and a new rate, then compare percentage points, relative change, and absolute counts side by side.
LAB 08Relationships
Why extremes drift inward
Create two noisy synthetic measurements, select the most extreme first results, and compare the same selected group on retest.
LAB 09Sampling
When more answers miss the target
Repeat a probability sample and a tilted voluntary sample, then separate shrinking random variation from persistent selection bias.
LAB 10Uncertainty
Why fair sequences form streaks
Generate binary sequences, count their runs, and compare independent trials with a mechanism that alternates too often.
LAB 11Communication
The same values on two axes
Place five synthetic rates on a full and focused scale, then measure how axis limits change visible distance without changing the data.
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.
Start with a misconception
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.
Read the guideuncertainty 8 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.
Read the guiderelationships 8 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.
Read the guideA 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