Conceptual DemosStatLens

Interactive demonstrations of key statistical concepts.

• Sampling Distributions

  Pick a population shape, set sample size, draw samples. Watch the sampling distribution of x̄ build up — CLT in action.

• Sampling Bias Lab

  The Gettysburg Address activity: pick "representative" words by eye (biased high) vs. random samples. Why random sampling matters.

• CI Coverage

  Draw many CIs from a known population. See what "95% confidence" really means — about 95% capture the true parameter.

• Why the Percentile CI Works

  Build the true sampling distribution, then bootstrap from one frozen sample. The bootstrap distribution has roughly the same shape and spread, shifted to sit at x̄ — watch the percentile interval capture μ close to whenever x̄ was a typical draw.

• What is a Randomization Test?

  Walk through the IMS Ch. 11 card-shuffle activity step by step on the real randomization tool. See the data, shuffle, build a null distribution, draw conclusions.

• Decision Errors

  Run many studies with or without a real effect. Watch detections, missed effects (Type II), and false alarms (Type I) accumulate.

• Power Lab

  Empirical power converging to theory, and the "dance of the p-values" — how sample size and effect size drive your chance of detecting an effect.