Revisiting Fisher's n ‐D statistical vision: From algebraic abstraction to modern visualization

We revisit early foundational results in mathematical statistics derived by Ronald A. Fisher. They involve sampling distributions of statistics calculated from independent and identically distributed Normal observations, namely the root mean square deviation; the mean absolute deviation, conditional on already knowing the value of the root mean square deviation; and the converse. The purposes of this note are to illustrate (i) Fisher's remarkable ‐D geometric vision, (ii) how modern visualization reveals the geometric structure underlying Fisher's proof, (iii) how today's users can “see” what lies underneath—and simplify and more readily understand—proofs and derivations, and (iv) how these tools can allow mathematical statistics courses to supplement traditional algebraic manipulations with numerical investigations and geometric visualizations.