William Kruskal Remembered

Statistic al Scienc e 2007, V ol. 22, No. 2, 275– 276 DOI: 10.1214 /0883423 06000000402 Main article DO I: 10.1214/0883 42306000000420 c  Institute of Mathematical Statisti cs , 2007 William Krusk al Rememb ered Stephen M. Stigler I knew Bill Krusk al as a dear friend and coll eague for o ver 30 years, but I also knew him as a citi- zen of his departmen t and univ ersit y , a statesman of the statistics profession and a researc her in math- ematical statistics. In all of t hose roles Bill show ed c h aracteristics he m ust ha v e dev elop ed at an early age: unshak able integrit y , consideration for others, painstaking atten tion to detail and an op en, ques- tioning scienti fic m ind. In what I h op e would b e a spirit of social science inquiry that Bill would ha v e sanctioned, I w ant to begin b y asking a question of Bill t hat he a sked so often of others. F or 30 years, wh enev er our department met in priv ate session to face a d ecision on a ten u re case, Bill would ask of his colleagues some v ersion of this question: “T ell me,” he wo uld ask, “what s p ecific significan t new idea w ould yo u associate with the candidate; w hic h of the candid ate’s w orks or p ub- licatio ns are truly imp ortant?” Bill’s pu rp ose wa s clear—he w an ted fo cu s; he did not wa nt to hear a recital of general impressions, h e wan ted evidence that would con vince him, would convince the dean, w ould con vince the prov ost and president. I will ask Bill’s question ab out Bill h imself, and adv ance some answ ers. My first answ er is that Bill will b e rememb ered longest for a particular p iece of researc h work dur - ing the 1950s. Bill was first app oin ted as an instru c- tor in our newly form ed department in 1950. Th e b est kno wn of his w orks is the Kru sk al–W allis test, a rank test for the analysis of v ariance he prop osed in 1951 and then develo p ed with Allen W allis into a Stephen M. Stigler is Ernest DeWitt Bur ton Distinguishe d Servic e Pr ofessor and Chairman, Dep artment of Statistics and t he Col le ge, and memb er of t he Committe e on Conc eptual and Hist oric al St udies of S cienc e, U niversity of Chic ago, Chic ago, Il linois 60637 , USA e-mail: stigler@galton.uchic ago.e du . This is an electr onic reprint of the orig inal a rticle published by the Ins titute of Mathematical Statistics in Statistic al Scienc e , 20 07, V ol. 22, No . 2, 27 5–276 . This reprint differs from the orig inal in pagination and t yp ogr aphic deta il. famous article pu blished in 1952 (K r usk al and W al- lis, 1952 ). This s im p le p ro cedure has had a remark- able r un. If you wish to kno w the exten t of its fame, I suggest visiting Go o gle News , as I did a few times shortly after Bill died. There th e name Krus k al pro- duced from 5 to 15 h its on the Go o gle News pages (i.e., the searc h r estricted to news sources of the past mon th) and almost all of th ose were to the use of the Krusk al–W allis test in several different, newly released scienti fic studies. Indeed it is astonishing that a simple test p rop osed ov er a half cen tury ago is still in current n ews. If a Go o gle News coun t of 5–15 strikes you as meager, I suggest you try the same test on Go o gle News using the name Gauss or Neyman or P earson or K olmogoro v; in my trial all of th ese were either absent or m er ely sin gle hits. If y ou tr y the f u ll extent of Go o gle ’ s co v erage, there are o v er 900,000 pages for K r usk al–W allis. F or this article alone Bill will b e r emem b ered as long as there are web pages, statistica l softw are or textb o oks. If y ou pr otest (as Bill p erh aps would) th at the test is no more than a p art of a prop er analysis, and a small part at that, I sa y that misses m y p oint . This longevit y is significant evidence of Bill’s mar- v elous ab ility to explain so clearly and d ev elop his topic so thoroughly that in half a cen tury no one has sup erceded him as a reference, in the manner that Rob ert K. Merton called “obliteration b y incorp ora- tion.” Bill’s was th e first wo rd and th e last word. Of course th is w as not h is only ma jor researc h success; he also made imp ortant con tr ibutions to th e mea- surement of asso ciat ion, some with Leo Go o dman, and to co ordinate-free linear mo dels and other ar- eas. But Bill’s qu estion to his colleagues only asked for one idea: he wa nte d focu s and the consequent detail. I was careful in d escribing this test of Bill’s as the w ork for which h e will b e longest rememb ered. I do not b eliev e it w as his most imp ortant contribution. T o m y mind Bill’s greatest cont ribu tion was the fu r- therance of scientific colleg ialit y in our department, in the Un iv ersit y of Chicago, in the profession of statistics and indeed in the br oad inte llectual com- m unity of the nation. I would refer to th e imp or- tance of h is role in this as “inestimable,” b ut I am 1 2 S. M. S TIGLER sure Bill w ould protest b eca use of course I am going to try to estimate it. In all these spheres h e w as the soul of collegial- it y . He nurtured junior facult y . He help ed students for w h om h e had no formal resp onsibilit y , with ref- erences and p roblem suggestions. He shared class- ro om examples and exam questions. By his example he taught u s th e imp ortance and sho wed us the in- tellectual rew ards of dedicated atten tion to teac hing at all lev els. He instilled in th e mem b ers of ou r de- partmen t b oth collegi al m utual resp ect and a sense of in tegrit y in furthering the mission of our univer- sit y in wa ys that still guid e us to d a y and still set us apart from most statistics departments, indeed most academic d epartmen ts in an y discipline. Our s is still Bill’s department. A signal qualit y of Bill’s w as th e wa y he b uilt bridges b etw een mem b ers of the facult y who shared in terests in wa ys they might otherwise nev er h av e realized. When I prepared a manuscript, h e w ould offer copious d etailed su ggestions and insist th at I send it to a half dozen other p eople he w as su re w ould b e in terested. When our present prov ost, a historian of ancien t Rome, arrived as a new asso- ciate p r ofessor 20 yea rs ago, it w as Bill who sent me a cop y of his pap er on the use of anecdotes as data in ancien t times. Bill’s ab ility to forge links preceded Go o gle b y o ver 40 y ears and exceeded it in inte llec- tual depth and the abilit y to recognize related ideas. No w , not every one who encountered Bill to ok im- mediately to his w a y of helping. Not every author of a ten-page d ouble-spaced pap er is grateful for ten single-spaced p ages of typ ed commen ts, making su g- gestions, ev en gen tle suggestions, ranging from allu- sions to work in areas you had neve r heard of, to grammar and sp elling. At Bill’s 70th b irthday part y 15 yea rs ago, F red Mosteller told the story of h ow he greeted such a very long letter from Bill by sitting do wn and starting to wr ite an equally long letter bac k, explaining why in ev ery instance he had done things the w a y he had. J immie S a v age learned of this and wr ote F red a short note: “Dear F reddie, stop answe ring Bill’s letter and fix the MS.” In going through some of Bill’s pap ers I came up on a 1952 refereeing file th at sh o w s neatly ho w some p eople came to accept and ev en appreciate, h o w ev er reluctan tly , th is capacit y of Bill’s. A pap er had b een submitted to The Annals of Mathematic al Statistics b y a well kno wn W est Coast statistician, and it was sen t to Bill f or review. Before th e whole p r o cess was finished there w ere tw o more revisions and three ref- eree’s rep orts from Bill: first r ep ort, t w o p ages; sec- ond rep ort fiv e pages, th ir d rep ort, eigh t pages. Th e follo win g extracts fr om the author’s replies to these rep orts tell a story: The referee. . . mistak enly b eliev es I am w orking on a simp ler problem. . . . I am not w illing to mak e an y fu rther al- terations ju st to please a p erfectionist ref- eree. Life is to o s hort to waste it on con- tin ual r efi nemen ts of a pap er. And finally a letter fr om the asso ciate editor: The author has just written that h e n o w realizes that his confi d ence co efficien t is in error and wish es to withdra w the pap er to revise it. He is very ap ologetic ab out his rejection of y our rep ort earlier. With a less careful or observ ant job this error w ould hav e slipp ed through into pr in t to ev ery one’s em barrassment. I ha ve some sym path y for that au th or. Bill’s p er- fectionism and ins atiable in tellectual cur iosit y taxed ev en him, as t wo unfinished and unpublished man uscripts he left on co ord in ate-free linear mo d- els and on c hi-square statistics w ill attest. Happ ily , generations of Chicago stud en ts b enefited from his courses on this material, and more recen tly our col- league Mic hael Wic hura has tak en the first of these sub jects and dev elop ed it far b eyo nd w h at Bill had done, into a fi n e textb o ok (Wic hura, 2006 ). I w ork ed with Bill for nearly tw o decades on an idea of his to explore the roles and app earances of the word “nor- mal” in statistics. W e d id fin ally manage a mo d est pap er (K r usk al and Stigler, 1997 ) on the topic, but it co vered only a tiny fr action of the accum ulated material Bill had un earthed — an d that p ap er w ould ha v e joined the other unpub lish ed man u scripts if Bill had follo wed his preference and pur sued sev eral other a v en ues he susp ected wo uld b e revea ling. Bill was a dear friend and trus ted guide. He was a true gen tleman; a man of firm opinions and strongly held v alues gen tly expressed, and he was op en to other views and could abide all but th e true scoun- drels of life. His counsel will b e missed, but h is influ- ence on me and on our department will long su rviv e him. WILLIAM KRUSKAL REMEMBERED 3 REFERENCES Krusk al, W. H. and Stigler, S . M. (1997). Normativ e ter- minology: “Normal” in statistics and elsewhere. In Statis- tics and Public Policy (B. Spencer, ed.) 85– 111. Oxford Univ. Press. Revised in S. M. Stigler (1999). Statistics on the T able . The H istory of Statistic al Conc epts an d Meth- o ds Chapter 14 277–2 90. Harv ard Un iv. Press, Cambridge, MA. MR1712969 Krusk al, W. H. and W allis, W. A. (1952). Use of ranks in one-criterion v ariance analysis. J. Amer . Statis. Asso c. 47 583–621 . (Correction 48 907–911.) Wichura, M.J. (2006). The C o or dinate-F r e e Appr o ach to Line ar M o dels . Cambridge Un iv. Press. MR2283455