Supplement to “ Comments on the Neyman - Fisher Controversy and its Consequences ”

This supplement contains our reworking of Neyman's calculations. It is important to note that, although our proofs may not be technically elegant, they are designed to reveal explicitly the errors of Neyman (1935). A.1 Randomized Complete Block Designs Consider N blocks and T treatments, with each block having T experimental units, and treatments randomized to experimental units independently across blocks. We define W ij (t) = 1 if unit j in block i is assigned treatment t, 0 otherwise. x ij (t) = X ij (t) + ij (t), where X ij (t) ∈ R is an unknown constant and ij (t) ∼ [0, σ 2 ] are iid and independent of treatment indicators W = {W ij (t)}. The potential outcomes are decomposed into x ij (t) = ¯ X ·· (t) + B i (t) + η ij (t) + ij (t), where B i (t) = ¯ X i· (t) − ¯ X ·· (t), η ij (t) = X ij (t) − ¯ X i· (t). Define y i (t) as the observed response of the unit assigned treatment t in block i, y i (t) = T j=1 W ij (t)x ij (t),