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confidence-intervals #

Animates repeated sampling: each new sample produces a point estimate θ̂ and a confidence interval θ̂ ± z·se(θ̂). Intervals stack over time and are colored by whether they cover the true parameter θ, illustrating that the method has a long-run coverage rate (not that any single interval has a 95% probability of containing θ).

canvasclick to interact

⏮◀◀▶▶STEP0.25x1xZOOM

t=0s

practical uses #

• 01.Reporting uncertainty around an estimated mean/proportion (A/B tests, surveys)
• 02.Communicating precision of model parameters (regression coefficients, effects)
• 03.Quality control and experimentation: deciding if measurements are consistent with a target θ

technical notes #

Uses a lightweight deterministic PRNG + Box–Muller to simulate θ̂ ~ Normal(θ, se). New intervals emit every ~0.42s; older ones fade. Canvas coordinates are snapped to a grid for a blocky aesthetic; responsive scaling via scale = min(w,h)/240. True θ is a vertical line; hit/miss intervals use GREEN_DIM/GREEN.

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