Conceptual DemosStatLens

Interactive demonstrations of key statistical concepts.

• Galton Board

  Drop balls through a field of pegs and watch the binomial distribution pile up underneath, with the exact probabilities and the normal approximation drawn over it.

• Law of Large Numbers

  Toss a coin or roll a die over and over. The running proportion (or average) settles toward what the model predicts — while the running total wanders further from zero.

• 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.

• Sampling Designs

  Simple random, stratified, cluster and convenience sampling compared on the same population — what each costs, and how much each one's estimates vary.

• CI Coverage

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

• Why ± 2 SE Works

  The capture argument with no numbers on it: the axis is marked in standard errors either side of the parameter, you drag one sample's statistic, and the interval reaches the parameter exactly when the statistic landed inside the shaded band. Has a printable instructor guide.

• What Estimating the SE Costs

  The sequel: where the multiplier comes from, and what you pay for not knowing the standard error. Lay the candidate margins against one ruler of true standard errors and watch the usable one fall short — for a mean (σ → s), where t* repairs it exactly, and for a proportion (p → p̂), where nothing does, which is why the course simulates. Has a printable instructor guide.

• Confidence Intervals by Repeated Sampling

  Draw sample after sample from a population you choose. The middle 95% of the sample means gives the margin of error — carry it over to one sample and that is a confidence interval.

• 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.