This non-parametric sandbox was generated by Claude (Anthropic) for the STAT 101 course materials. Every number on it is computed in your browser and recomputed on every knob change: the whole kernel density estimate (a real Gaussian-kernel sum over a fine grid), Silverman’s bandwidth, the fitted normal’s mean and SD, the LOESS curve (a weighted least-squares fit at every grid point), the global OLS line, the ranks, and both Pearson’s r and Spearman’s rho. Nothing on this page is sketched.

Spearman is computed as Pearson-on-ranks, with ties given average ranks. The shortcut rho = 1 − 6Σd²/(n(n²−1)) is exact only when there are no ties; the page shows it but reports the general value, which is correct under ties. Because Spearman depends only on order, it is 1 for any monotone-increasing relationship — even y = x³, where Pearson is well below 1 — and a lone outlier that drags Pearson leaves it almost unmoved.

Kernel density estimation, LOESS and Spearman’s rho are standard non-parametric methods. The bandwidth, span, dataset shape and seed are illustrative inputs you set; the arithmetic done on them is exact. Seeded generator: mulberry32 (public domain). No number on this page came from a real dataset — the presets are simulations whose shape is chosen and whose draws are reproducible from the seed.