Simpson’s Paradox Visually! @MathVisualProofs

Uploaded November 2025 | Updated September 2026, 2 weeks ago

In this short video, we show how to think about Simpson's paradox visually in terms of vector arithmetic. In particular we show that ratios can be represented by slopes of lines (or slopes of vectors) and then we can have an interesting slope reversal when adding as you would add proportions or statistics (not usual fraction arithmetic).

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The visual proof in this video is based on a proof without words by Jerzy Kocik from the December 2001 issue of Mathematics Magazine ( jstor.org/stable/2691038 page 399).

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$Simpson’s Paradox Visually! In this short video, we show how to think about Simpsons paradox visually in terms of vector arithmetic. In particular we show that ratios can be represented by slopes of lines (or slopes of vectors) and then we can have an interesting slope reversal when adding as you would add proportions or statistics (not usual fraction arithmetic). If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! The visual proof in this video is based on a proof without words by Jerzy Kocik from the December 2001 issue of Mathematics Magazine ( https://www.jstor.org/stable/2691038 page 399). #mathshorts #mathvideo #math #statistics #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #paradox #simpsonsparadox #simpson #derekjeter #davidjustice #baseball #proportion #vectors #vectoraddition #battingaverage #data To learn more about animating with manim, check out: https://manim.community$

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$Chaos Game finds the Mandelbrot Quintet In this video, we show how to use a random process of iteratively applying five affine transformations in the real plane to generate a 5-rep-tile known as the Mandelbrot Quintet. What happens if you do something similar with different affine transformations? Here is a bit longer version (without words): https://youtu.be/rLxx6b-oJGo Check out these videos for related constructions: https://youtube.com/shorts/dklWNdM9WSg https://youtu.be/rLxx6b-oJGo https://youtu.be/NBI_5GdvqUo If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! This animation was inspired by an article written by Lorelei Koss that appeared in the Proceedings of Bridges 2015: https://archive.bridgesmathart.org/2015/bridges2015-423.pdf . For more information, you should also check out the related article Fractal Tilings in the Plane by Richard Darst, Judith Palagallo and Thomas Price from the February 1998 Mathematics Magazine: https://www.jstor.org/stable/2691339 #chaos #chaosgame #quintet #mandelbrot #mathvideo #math #mtbos #manim #animation #theorem #iteachmath #mathematics #dynamicalsystems #iteratedfunctionsystem #dynamics #fractals To learn more about animating with manim, check out: https://manim.community$