A281614 Number of examples for Simpson's paradox with data items in [n].

0, 0, 0, 0, 4, 232, 1370, 8126, 28252, 86140, 222252, 543520, 1130136, 2331916, 4411418, 7931834, 13716480, 23235304

Offset

0,5

Comments

Number of octuples (a,b,c,d,w,x,y,z) in [n]^8 with a*d > b*c, w*z > x*y and (a+w)*(d+z) < (b+x)*(c+y).

All terms are even. If (a,b,c,d,w,x,y,z) is an example then (w,x,y,z,a,b,c,d) is a different example.

Links

Table of n, a(n) for n=0..17.

Wikipedia, Simpson's paradox

Example

a(4) = 4: (2,1,4,3,2,4,1,3), (2,4,1,3,2,1,4,3), (3,1,4,2,3,4,1,2), (3,4,1,2,3,1,4,2).

Maple

a:= n-> (g-> add(add((h-> `if`(h[1]*h[4] < h[2]*h[3], 2, 0))(
         g[i]+g[j]), j=1..i-1), i=2..nops(g)))(select(f->
         f[1]*f[4] > f[2]*f[3], [seq(seq(seq(seq([w, x, y, z],
         w=1..n), x=1..n), y=1..n), z=1..n)])):
seq(a(n), n=0..8);

Crossrefs

Cf. A281700.

Sequence in context: A145767 A206352 A024057 * A132551 A333864 A358158

Adjacent sequences: A281611 A281612 A281613 * A281615 A281616 A281617

Keyword

nonn,more

Author

Alois P. Heinz, Jan 25 2017

Status

approved