mathematics

Statistics & Inference

Hypothesis tests, confidence intervals, and the statistical tools that separate signal from noise — from p-values to ANOVA to regression to the mean.

statisticshypothesis testingp-valueconfidence intervalANOVAchi-squaredregression to the mean

Statistics is the science of learning from data under uncertainty. It provides the rigorous framework that medicine, psychology, economics, and every empirical science relies on to distinguish real effects from random noise. Yet statistical reasoning is famously counterintuitive — p-values are chronically misunderstood, confidence intervals are misinterpreted, and regression to the mean fools experts and laypeople alike.

These simulations let you build intuition by experimenting with the core tools of statistical inference. Generate samples, run hypothesis tests, watch confidence intervals shrink as sample sizes grow, and see why extreme observations naturally regress toward the average. Interactive exploration makes abstract formulas tangible.

5 interactive simulations

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Analysis of Variance (ANOVA)

Compare means across multiple groups with one-way ANOVA — visualize between-group and within-group variance to understand the F-test

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Chi-Squared Test for Independence

Build contingency tables and run chi-squared tests to determine whether two categorical variables are independent or associated

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Confidence Intervals & Sample Size

Visualize how confidence intervals shrink with larger samples and see why a 95% CI does not mean 95% probability the parameter is inside

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Hypothesis Testing & P-Values

Simulate hypothesis tests to understand p-values, Type I and Type II errors, and why statistical significance doesn't mean practical significance

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Regression to the Mean

Visualize why extreme observations tend to be followed by less extreme ones — the statistical phenomenon that fools coaches, doctors, and policymakers