Stanford is not an Ivy League school. The Ivy league consists of eight colleges: Brown, Harvard, Princeton, Dartmouth, Cornell, Columbia, Yale and the University of Pennsylvania. The Ivy league is a intercollegiate athletic conference.
The first “Ivy Group Agreement” was signed in 1945 and applied only to football. The Ivy league was officially founded in 1954, but the first season of athletic competition was in 1956 and '57. The term “Ivy colleges” was first used by Stanley Woodward of the New York Herald in 1933, while the exact term “Ivy League” was first used on Feb. 8, 1935, by AP sports editor Alan Gould.