Editing Simpson's paradox (section)

==Vector interpretation==
[[File:Simpson paradox vectors.svg|thumb|Vector interpretation of Simpson's paradox]]
Simpson's paradox can also be illustrated using a 2-dimensional [[vector space]].<ref>{{cite journal|author=Kocik Jerzy|year=2001|title=Proofs without Words: Simpson's Paradox|url=http://www.math.siu.edu/kocik/papers/simpson2.pdf |archive-url=https://web.archive.org/web/20100612220747/http://www.math.siu.edu/kocik/papers/simpson2.pdf |archive-date=2010-06-12 |url-status=live|journal=[[Mathematics Magazine]]|volume=74|issue=5|pages=399|doi=10.2307/2691038|jstor=2691038}}</ref> A success rate of <math display="inline">\frac{p}{q}</math> (i.e., ''successes/attempts'') can be represented by a [[vector (geometry)|vector]] <math>\vec{A} = (q, p)</math>, with a [[slope]] of <math display="inline">\frac{p}{q}</math>. A steeper vector then represents a greater success rate. If two rates <math display="inline">\frac{p_1}{q_1}</math> and <math display="inline">\frac{p_2}{q_2}</math> are combined, as in the examples given above, the result can be represented by the sum of the vectors <math>(q_1, p_1)</math> and <math>(q_2, p_2)</math>, which according to the [[parallelogram rule]] is the vector <math>(q_1 + q_2, p_1 + p_2)</math>, with slope <math display="inline">\frac{p_1 + p_2}{q_1 + q_2}</math>.

Simpson's paradox says that even if a vector <math>\vec{L}_1</math> (in orange in figure) has a smaller slope than another vector <math>\vec{B}_1</math> (in blue), and <math>\vec{L}_2</math> has a smaller slope than <math>\vec{B}_2</math>, the sum of the two vectors <math>\vec{L}_1 + \vec{L}_2</math> can potentially still have a larger slope than the sum of the two vectors <math>\vec{B}_1 + \vec{B}_2</math>, as shown in the example.  For this to occur one of the orange vectors must have a greater slope than one of the blue vectors (here <math>\vec{L}_2</math> and <math>\vec{B}_1</math>), and these will generally be longer than the alternatively subscripted vectors&nbsp;– thereby dominating the overall comparison.