Experiment, don't just memorize

Interactive laboratories

The simplest way to understand a mathematical claim is sometimes to try breaking it.

Study design · Week 1

Who enters? Who gets treatment?

Change recruitment and treatment assignment to separate association, causal effects among volunteers, and population generalization.

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Descriptive statistics

Center & spread

See an extreme observation pull the mean away from the median.

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Data visualization

Histogram bin explorer

Change the bins without changing a single observation, and inspect the underlying counts.

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Survey design · Sampling bias

Selection bias simulator

Change survey participation while holding everyone's opinions fixed.

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Probability and sampling

Central limit theorem

Generate sampling distributions from populations that are anything but bell-shaped.

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Probability distributions

Normal distribution

Change an interval and watch its probability grow or shrink.

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Conditional probability

Bayesian base rates

Change test accuracy and condition prevalence to see why false positives can dominate.

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Frequentist inference

Confidence interval coverage

Build fifty intervals repeatedly; see how many contain a fixed true mean.

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Hypothesis testing

Exact binomial test

Change the head count and read an exact two-sided p-value.

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Real historical data · multivariable thinking

Simpson's paradox

Switch between aggregate and stratified published data to discover a reversal.

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Estimation and resampling

Bootstrap sampling

Resample waiting times with replacement and examine the estimated uncertainty of the mean.

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Experiments and design-based inference

Exact randomization test

Enumerate all seventy possible treatment allocations for a tiny randomized experiment.

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Regression diagnostics

What the line missed

Introduce curvature, refit a line, and watch residual structure emerge.

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Prefer writing the statistics yourself?The R Workbench runs genuine R through WebAssembly, captures console output and plots, and includes editable examples for bootstrap, Bayes, regression, and hypothesis tests. Runtime loading is optional and starts only when you click Run.

For instructors: predict → experiment → explain teaching prompts and printable student worksheets are available.

The thirteen guided laboratories run entirely in your browser, with no required account or server-side computation.