Home▸Data Science▸Simpson's Paradox in 2D: When Grouped Trends Reverse

Simpson's Paradox in 2D: When Grouped Trends Reverse

Interactive 2D data-science lab: watch a negative trend inside every subgroup flip into a positive trend once the groups are pooled together — a real, reproducible statistical illusion caused by a confounding variable, plotted directly on an X-Y scatter you can pan and zoom.

Data Science2DAdvanced60 FPS📱 Mobile-adapted⇄ 3D version

Details

CategoryData Science

RenderingCanvas 2D

DifficultyAdvanced

Target FPS60

ControlsSliders set the number of subgroups, the within-group slope, the confound strength and the noise level; a resample button redraws the random points, two toggle buttons show or hide the per-group regression lines and the pooled regression line, drag pans the scatter plot and scroll/pinch zooms it, and a reset-view button restores the default pan/zoom.

statisticsdata-scienceregressioncorrelationconfounding-variable

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Every subgroup in this dataset shows the same negative relationship between X and Y — yet pool all the points together and the trend can flip to positive. This is Simpson's Paradox, a real and reproducible statistical phenomenon caused by a confounding variable that drifts together with both the predictor and the group label. The simulator generates several subgroups of synthetic data, fits a genuine least-squares regression line to each one individually and to the pooled dataset, and renders both directly on a 2D scatter plot (pan and zoom to inspect) alongside a bar-chart panel that puts the within-group and pooled slope/correlation side by side so the reversal is unmistakable.

⚙ Under the hood

Watch a negative trend inside every subgroup of a dataset flip into a positive trend once the groups are pooled together — a real statistical illusion driven by a confounding variable, plotted directly on a pannable, zoomable 2D scatter with live regression fits and a side-by-side bar comparison.

statisticsdata-scienceregressioncorrelationconfounding-variable

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install