📊 Statystyka

Bayesian Inference (2D)New📱Adjust the prior belief and likelihood/sensitivity, then click Add Evidence to watch Bayes'… Birthday Paradox Probability Grid (2D)New📱Adjust the group size and run real Monte Carlo trials to see randomly generated birthdays… Probability Distributions 2D Plotter (2D)New📱An interactive Canvas2D plotter for five named probability distributions - Normal, Binomial,… Linear Regression: OLS Scatter Plot (2D)New📱Interactive 2D least-squares linear regression. Click to add data points, generate random… Principal Component Analysis (2D)New📱Interactive 2D PCA visualizer. Adjust the correlation and spread of a point cloud, or click… Normal Distribution — Bell Curve & Z-Score Explorer (2D)New📱Explore the Gaussian bell curve on an interactive 2D canvas. Drag the mean and standard… Bayesian Updating (2D)New📱Watch a Beta prior curve transform into a posterior curve as simulated coin flips arrive.… Benford's Law Digit Chart (2D)New📱Compare the theoretical Benford leading-digit curve against real frequencies counted from… Regression to the Mean (2D)New📱A 2D scatter-plot companion to the Regression to the Mean simulator: repeated noisy… Galton Board (2D)New📱Drop balls through a 2D side-view Galton board and watch them bounce through a triangular… Hypothesis Testing: t-test & p-value (2D)New📱Interactive 2D hypothesis testing simulator with real t-test, two-sample t-test and… Error Propagation & Uncertainty (2D)New📱A 2D Canvas histogram shows Monte Carlo samples of z = f(x,y) alongside the analytical… 2D Bootstrap Resampling — Confidence IntervalsNew📱A Canvas2D lab that resamples a dataset with replacement thousands of times and lets you… Student's t-Test (2D)New📱A 2D companion to the Student's t-test simulator: run one-sample, two-sample and paired… 2D Random Walk: Gaussian Displacement & MSDNew📱Hundreds of independent 2D random walkers with adjustable step distribution (uniform-angle… Model Selection: AIC vs BIC (2D)New📱Fit least-squares polynomials of degree 1 to 10 to noisy data in a three-panel 2D lab and… Data Triangulation 2D: Combining Independent EstimatesNew📱Interactive 2D research-methodology simulator: three independent methods (survey,… Q-Q Plot 2D: Testing Normality with a Quantile-Quantile ScatterNew📱Draw random samples from normal, skewed, heavy-tailed, uniform or bimodal populations and… Chi-Square Test: Distribution & Category Rose (2D)New📱A 2D-native chi-square goodness-of-fit simulator: a polar rose chart shows observed vs… No-U-Turn Sampler: 2D Contour, Phase-Space & Energy ViewNew📱Watch the No-U-Turn Sampler draw from a curved Bayesian posterior on a pannable, zoomable 2D… Regression Diagnostics: Leverage & Cook's Distance (2D)New📱Drag points on a linked 2D scatter, Cook's-distance bar chart and leverage/residual… Statistical Power & Type I/II Errors (2D)New📱Drag sample size, effect size and significance level — or grab the critical line directly —… Publication Bias & the Funnel Plot (2D)New📱Simulate a pool of independent studies testing the same real effect, filter which ones get… Variational Inference: Watching a Posterior Get ApproximatedNew📱A diagonal Gaussian climbs the ELBO via stochastic gradient ascent with the… Multicollinearity & VIF: Why Correlated Predictors Break RegressionNew📱Drag two predictor variables from independent to nearly collinear and watch an OLS… Computerized Adaptive Testing — Item Response Theory SimulatorNew📱Watch a computerized adaptive test pick the most informative question from a 50-item bank at… Likelihood Surface ExplorerNew📱Draw a random sample and watch its full log-likelihood surface over (μ, σ) render in 3D —… Pearson Correlation & Covariance Ellipse Explorer (2D)New📱Generate a synthetic 2D scatter plot from a chosen population correlation and watch the… One-Way ANOVA 2D: Strip Plot & F-DistributionNew📱Interactive 2D one-way ANOVA simulator: a live jittered strip plot of every sampled point… Statistical SamplingNew📱Repeatedly sample from a population and histogram the means to visualize the Central Limit… Statistical SamplingNew📱Simulate a Galton board where each ball's path through pegs determines its landing bin,… UFO Case ClusteringNew📱Analyze spatial and temporal patterns in UFO reports using the Clark-Evans statistic to… UFO Case ClusteringNew📱Visualize 3D spacetime data of UFO sightings, distinguishing genuine clusters from random noise. Pollution AnalysisNew📱Analyze pollution data using Benford's Law to detect anomalies in numeric records. Pollution AnalysisNew📱Visualize leading digit frequencies of pollution data in a 3D bar chart compared to… Pollution Incident AnalysisNew📱Genuine pollution incident severities follow a power-law distribution, while embellished… Pollution Incident AnalysisNew📱On a 3D log-log surface, genuine data forms a straight ridge, whereas embellished data… Anomaly DetectionNew📱Explore base-rate neglect by comparing intuitive probabilities with Bayes' theorem calculations. Anomaly DetectionNew📱Visualize a population split into genuine anomalies and mundane events, each producing… Pollution and UFO SightingsNew📱Explore how a shared environmental factor can create an illusion of causation between… Pollution and UFO SightingsNew📱Visualize the relationship in three dimensions to see how removing the influence of a hidden… Witness ConsensusNew📱Simulate how multiple witnesses' testimonies combine to increase confidence in an event's… Witness ConsensusNew📱Visualize combined witness testimonies as stacked bars forming a tower, with the height of… Pearson Correlation Coefficient ExplorerNew📱Generate a synthetic 3D scatter plot from a chosen population correlation and watch the… Regression Diagnostics: Leverage & Cook's DistanceNew📱Drag points on a live OLS regression scatter and watch leverage, standardized residuals and… One-Way ANOVA: Between vs Within-Group VarianceNew📱Draw random samples for three or more groups in 3D and watch between-group and within-group… Variational Inference: Watching a Posterior Get ApproximatedNew📱A diagonal Gaussian climbs the ELBO via stochastic gradient ascent with the… No-U-Turn Sampler: Adaptive HMC Trajectory DoublingNew📱Watch the No-U-Turn Sampler draw from a curved Bayesian posterior in 3D: a binary tree of… Chi-Square Test: Observed vs Expected FrequenciesNew📱Draw random samples from a fair or deliberately biased categorical generator and watch a… Statistical Power & Type I/II ErrorsNew📱Drag sample size, effect size and significance level to watch two overlapping 3D sampling… Multicollinearity & VIF: Why Correlated Predictors Break RegressionNew📱Drag two predictor variables from independent to nearly collinear and watch an OLS… Data Triangulation: Combining Independent EstimatesNew📱Three independent research methods — a survey, a controlled experiment and a field… Publication Bias & the Funnel PlotNew📱Simulate a pool of independent studies testing the same real effect, filter which ones get… Likelihood Surface ExplorerNew📱Draw a random sample and watch its full log-likelihood surface over (μ, σ) render in 3D —… Model Selection: AIC vs BICNew📱Fit least-squares polynomials of degree 1 to 10 to noisy data and watch AIC and BIC penalize… Q-Q Plot: Testing Normality with Quantile-Quantile DiagnosticsNew📱Draw random samples from normal, skewed, heavy-tailed, uniform or bimodal populations and… Computerized Adaptive Testing — Item Response Theory SimulatorNew📱Watch a computerized adaptive test pick the most informative question from a 50-item bank at… Bootstrap Resampling DistributionNew📱Interactive 3D simulation of the bootstrap: repeatedly resamples an original dataset with… Design of Experiments: Full Factorial vs One-Factor-at-a-TimeNew📱Interactive 3D simulation of a 2^3 full factorial design of experiments: a glowing cube… Multiple Comparisons: p-Hacking vs BonferroniNew📱Run many independent hypothesis tests on pure random noise with no real underlying effect… Survival Analysis: Kaplan-Meier Estimator with Censored DataNew📱Generate a cohort of subjects with random time-to-event and dropout censoring, then watch… Factor Analysis SimulatorNew📱Interactive factor analysis: six correlated test scores generated from two hidden latent… Confidence Intervals, the Z-Test, and What "Coverage" Really MeansNew📱What a 95% confidence interval actually promises, how the Z-test uses the same machinery to… Bayesian Statistics: Live Beta-Binomial Posterior UpdatingNew📱Flip a simulated coin and watch a Beta prior turn into a posterior in real time via Bayes'… A/B Test Lab: Peeking, SRM & BanditsNew📱Watch two live variants collect visitors while a p-value trace, a sample-ratio-mismatch… Advanced Statistics - Comprehensive GuideNew📱This simulation introduces users to advanced statistical methods, including regression… Research Methods & Experimental DesignNew📱This simulation demonstrates the core principles of experimental design and research… Error Propagation & UncertaintyNew📱Build a formula for z = f(x,y) and watch Monte Carlo confirm the analytical error… Bayesian Inference — Prior, Likelihood & PosteriorNew📱Add observations and watch a Beta-Binomial posterior update live — pick a scenario, adjust… Birthday Paradox — Collision Probability📱Just 23 people give a 50% chance of a shared birthday — run Monte Carlo trials and watch… Student's t-Test📱Run one-sample, two-sample or paired t-tests and watch the t-distribution, p-value shading… Benford's Law📱Count leading digits in Fibonacci numbers, populations or your own data and see how closely… Regression to the Mean📱Pick extreme performers from a correlated pair of scores and watch their follow-up drift… Ball Cascade Patterns in a Peg Board📱Observe how balls fall through a peg board, illustrating the principles of probability and… Linear Regression — OLS Least Squares📱Drag data points and let ordinary least squares refit the line, with residuals, slope,… Bayesian Updating📱Flip a coin and watch a Beta-Binomial posterior update live, converging on the true bias p… Hypothesis Testing — t-test & p-value📱Draw samples, run a t-test and see how effect size, sample size and alpha move the p-value,… PCA — Principal Component Analysis📱Rotate a cloud of correlated points onto its principal components, watching eigenvectors… Bootstrap Resampling — Confidence Intervals📱Resample one dataset thousands of times with replacement to build a sampling distribution… Normal Distribution & Central Limit Theorem📱Adjust μ and σ to reshape the PDF and CDF, then watch the Central Limit Theorem pull sample… Probability Distributions Explorer📱Adjust parameters live across Normal, Binomial, Poisson, Exponential and Uniform… Random Walk📱Gaussian, Lévy flight and lattice walkers diffuse from the origin — watch the √t…