Cochran’s theorem: Results on quadratic forms in normal variates were shown by the Scottish statistician William Cochran in 1934 when he was a 24-year old graduate student at the University of Cambridge, studying under the supervision of John Wishart. He left Cambridge without completing his Ph.D. degree to work at Rothamsted Experimental Station, recruited by Frank Yates after R. A. Fisher left to take a professorship at University College, London. In the 1934 article, Cochran showed that if x1, …, xn are iid N(0, 1)

and ∑

i x2 i = Q1 + ⋯ + Qk for quadratic forms having ranks r1, … ,rk, then Q1, …, Qk are independent chi-squared with df values r1, …,rk if and only if r1 + ⋯ + rk = n.