📊 Statistics

Bootstrap Resampling DistributionNewInteractive 3D simulation of the bootstrap: repeatedly resamples an original dataset with… Design of Experiments: Full Factorial vs One-Factor-at-a-TimeNewInteractive 3D simulation of a 2^3 full factorial design of experiments: a glowing cube… Multiple Comparisons: p-Hacking vs BonferroniNewRun many independent hypothesis tests on pure random noise with no real underlying effect… Survival Analysis: Kaplan-Meier Estimator with Censored DataNewGenerate a cohort of subjects with random time-to-event and dropout censoring, then watch… Factor Analysis SimulatorNewInteractive factor analysis: six correlated test scores generated from two hidden latent… Confidence Intervals, the Z-Test, and What "Coverage" Really MeansNewWhat a 95% confidence interval actually promises, how the Z-test uses the same machinery to… Bayesian Statistics: Live Beta-Binomial Posterior UpdatingNewFlip a simulated coin and watch a Beta prior turn into a posterior in real time via Bayes'… A/B Test Lab: Peeking, SRM & BanditsNewWatch two live variants collect visitors while a p-value trace, a sample-ratio-mismatch… Advanced Statistics - Comprehensive GuideNewThis simulation introduces users to advanced statistical methods, including regression… Research Methods & Experimental DesignNewThis simulation demonstrates the core principles of experimental design and research… Error Propagation & UncertaintyNewBuild a formula for z = f(x,y) and watch Monte Carlo confirm the analytical error… Bayesian Inference — Prior, Likelihood & PosteriorNewAdd observations and watch a Beta-Binomial posterior update live — pick a scenario, adjust… Birthday Paradox — Probability SimulationJust 23 people give a 50% chance of a shared birthday — run Monte Carlo trials and watch… Student's t-TestRun one-sample, two-sample or paired t-tests and watch the t-distribution, p-value shading… Benford's LawCount leading digits in Fibonacci numbers, populations or your own data and see how closely… Regression to the MeanPick extreme performers from a correlated pair of scores and watch their follow-up drift… Ball Cascade Patterns in a Peg BoardObserve how balls fall through a peg board, illustrating the principles of probability and… Linear Regression — OLS Least SquaresDrag data points and let ordinary least squares refit the line, with residuals, slope,… Bayesian UpdatingFlip a coin and watch a Beta-Binomial posterior update live, converging on the true bias p… Hypothesis Testing — t-test & p-valueDraw samples, run a t-test and see how effect size, sample size and alpha move the p-value,… PCA — Principal Component AnalysisRotate a cloud of correlated points onto its principal components, watching eigenvectors… Bootstrap Resampling — Confidence IntervalsResample one dataset thousands of times with replacement to build a sampling distribution… Normal Distribution & Central Limit Theorem — Interactive SimulatorAdjust μ and σ to reshape the PDF and CDF, then watch the Central Limit Theorem pull sample… Probability Distributions ExplorerAdjust parameters live across Normal, Binomial, Poisson, Exponential and Uniform… Random WalkGaussian, Lévy flight and lattice walkers diffuse from the origin — watch the √t…