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Statistics

Hypothesis testing, PCA, bootstrap resampling, normal distribution and other foundational tools of statistical inference — all interactive.

📊 15 simulations 🆕 Category added 2026-05-16

🧪 Simulations (15)

🎲 Random Walk 📊 Probability Distributions Explorer 🎂 Birthday Paradox — Probability Simulation ⚖️ Bayesian Inference — Prior, Likelihood & Posterior 📈 Linear Regression — OLS Least Squares 📊 Hypothesis Testing — t-test & p-value 🔢 PCA — Principal Component Analysis 🔁 Bootstrap Resampling — Confidence Intervals 📊 Normal Distribution & Central Limit Theorem — Interactive Simulator 📊 Bayesian Updating 🔢 Benford's Law 📉 Regression to the Mean 📊 Student's t-Test 🎯 Galton Board 📏 Error Propagation & Uncertainty

❓ Frequently asked questions

What is a p-value?

The p-value is the probability of observing data at least as extreme as what was measured, assuming the null hypothesis is true. A p-value below 0.05 traditionally suggests rejecting the null. But it does NOT measure the probability the null is correct — a common misinterpretation.

What is PCA?

Principal Component Analysis finds linear combinations of variables (components) that capture the most variance. The first component points along the direction of greatest spread; subsequent components are orthogonal. Used for dimensionality reduction, visualisation and feature engineering.

What is the central limit theorem?

CLT states that the sum (or average) of many independent random variables tends toward a normal distribution, regardless of the individual distributions. This is why the bell curve appears everywhere: heights, measurement errors, lab assays.

What is bootstrap resampling?

Bootstrapping draws random samples (with replacement) from your data to estimate the sampling distribution of a statistic. Useful when analytic confidence intervals are intractable — works for medians, ratios, correlations. The basic procedure: resample → compute → repeat 10 000 times.

When should I use a t-test vs a non-parametric test?

Use a t-test when data are approximately normal or n is large (CLT applies). Use Wilcoxon / Mann-Whitney when data are non-normal, ordinal, or have heavy outliers. The interactive simulations let you compare both on synthetic data.

Every Statistics simulation here runs free in your browser, letting you experiment with each interactive Statistics model — probability distributions, hypothesis testing, regression analysis, central limit theorem and sampling variability — without installing anything. Adjust parameters, observe real-time results and learn Statistics online at your own pace, whether you are a student, educator or curious researcher. Statistics underpins virtually every field of modern inquiry: clinical trials use it to establish whether new treatments genuinely outperform placebos, pollsters rely on sampling theory to estimate election outcomes from a few thousand respondents, and quality engineers apply control charts to keep manufacturing processes within tolerance. Exploring these 15 simulations hands-on builds the intuition that formulas alone rarely convey.