Sankey Motion Pictures
Topology-stable flow transitions with explicit layout and reproducibility.
Open Sankey Motion Pictures →
CENTRAL QUESTION
WHAT CHANGED?
DATA & AI · SCIENTIFIC VISUALIZATION
Scientific evidence through distributions, time, networks and meaningful motion.
Topology-stable flow transitions with explicit layout and reproducibility.
Open Sankey Motion Pictures →Transform, inspect and compare evidence through typed state, statistical inference, contracts and diagnostics.
Enter the interactive lab ↓STATISTICAL VISUAL REASONING STUDIO
An interactive inference layer built from the same visual grammar: distributions, samples, sampling distributions, confidence intervals, test statistics, A/B decisions, power, assumption diagnostics and multiplicity.
Distribution loaded. Adjust a control to update the visualization and its numerical summary.
Visualize empirical reference distributions, exchangeability assumptions, bootstrap coverage and randomization-based p-values.
Rank tests, robust location and scale, trimmed estimators and sensitivity views when classical assumptions are fragile.
Connect coefficients, uncertainty, predicted-vs-observed structure, residuals, influence and model comparison to the same evidence contract.
Make sequential looks, exclusions, missing-data handling, sample-size planning and analysis provenance visible before a result becomes polished.
MATHEMATICAL STATISTICS · FOUNDATIONS ATLAS
The final reference set goes one level deeper: moments, degrees of freedom, unbiased estimation, covariance, probability bounds, derived reference distributions and regression geometry. These are now explicit rather than hidden behind test names.
Expected value summarizes the center of a random quantity and composes cleanly across sums, even when variables are dependent.
Bernoulli: E[X]=p. Poisson: E[X]=Var(X)=λ. For rare Binomial events, λ≈np links the two families.
After the sample mean is estimated, only n−1 deviations can vary freely. Bessel's correction makes the usual sample variance unbiased.
Bias is E[θ̂]−θ. Unbiasedness is useful, but precision, robustness and consistency still matter.
Covariance measures joint deviation. Normalizing it gives correlation; dividing by Var(X) gives the simple-regression slope.
Correlation is dimensionless association, not causation. Regression adds a conditional prediction model and residual assumptions.
Markov and Chebyshev trade sharpness for very weak assumptions. They show what can be guaranteed from moments alone.
Bounds are conservative; they are useful when the exact reference family is unknown or intentionally left unspecified.
Many classical test distributions are constructed from standardized normal variables and degrees of freedom.
Degrees of freedom control tail weight and skew. As df grows, t approaches Normal and χ² becomes less skewed.
The fitted line represents E[Y|X]. The vertical spread around it is the residual distribution, whose structure carries model diagnostics.
Residual shape, variance and dependence determine whether standard errors and tests from the fitted model are trustworthy.
PYTHON CODE COMPANION
RESEARCH → SOFTWARE
The first release limits scope to six chart forms so typed state, correspondence, transitions and reproducibility can be tested before expansion.
Types, state, scene, contracts, correspondence, serialization.
Dot, line, slope, interval, histogram/density, heatmap.
GraphState, node-link, matrix, node/edge events, view transitions.
Statistical, cyclic, chord, multiscale, spatial, and field motion only after validation.