PRESIDENTIAL ESSAY NO. 1: APRIL 2021 Notorious: Anscombe’s Warning about Diagrams By Chris Pritchard (
[email protected]) Consider the following four data sets: Rothamsted (founded under R A Fisher decades earlier). Later he moved to the States, to Set 1 Set 2 Princeton in 1956 and then on to Yale to lead the statistics department. Here he became a leading x y x y exponent of the use of computers in statistical 10.0 8.04 10.0 9.14 analysis. (One of his colleagues at Yale was John Tukey who gave us box plots and other graphical 8.0 6.95 8.0 8.14 tools; in fact, Anscombe and Tukey married the 13.0 7.58 13.0 8.74 sisters Phyllis and Elizabeth Rapp.) 9.0 8.81 9.0 8.77 The paper in which the data sets appeared is 11.0 8.33 11.0 9.26 entitled ‘Graphs in statistical analysis’. Published in The American Statistician and it is online at 14.0 9.96 14.0 8.10 www.sjsu.edu/faculty/gerstman/StatPrimer/an 6.0 7.24 6.0 6.13 scombe1973.pdf 4.0 4.26 4.0 3.10 Anscombe started by arguing that we pay far too 12.0 10.84 12.0 9.13 little attention to graphs in statistics, having been ‘indoctrinated with these notions’, which he lists: 7.0 4.82 7.0 7.26 numerical calculations are exact, but graphs 5.0 5.68 5.0 4.74 are rough, for any particular kind of statistical data, Set 3 Set 4 there is just one set of calculations constituting a correct statistical analysis, x y x y performing intricate calculations is virtuous, 10.0 7.46 8.0 6.58 whereas actually looking at the data is cheating.