{"id":3310950,"date":"2006-02-14T14:07:00","date_gmt":"2006-02-14T14:07:00","guid":{"rendered":"http:\/\/su.blog.bunty.tv\/2006\/02\/14\/Hiawatha\/"},"modified":"2007-11-26T03:37:43","modified_gmt":"2007-11-26T03:37:43","slug":"Hiawatha","status":"publish","type":"post","link":"http:\/\/su.blog.bunty.tv\/?p=3310950","title":{"rendered":"Hiawatha"},"content":{"rendered":"<div class='sustuff'>Stumbleupon <a href='http:\/\/horsewithnobunty.stumbleupon.com\/review\/3310950\/'>Review<\/a>\n<\/div>\n<p> <\/p>\n<ul><\/p>\n<pre><br \/>\r\n                Hiawatha Designs an Experiment<br \/>\r\n<br \/>\r\nHiawatha, mighty hunter,<br \/>\r\nHe could shoot ten arrows upward,<br \/>\r\nShoot them with such strength and swiftness<br \/>\r\nThat the last had left the bow-string<br \/>\r\nEre the first to earth descended.<br \/>\r\n  This was commonly regarded<br \/>\r\nAs a feat of skill and cunning.<br \/>\r\nSeveral sarcastic spirits<br \/>\r\nPointed out to him, however,<br \/>\r\nThat it might be much more useful<br \/>\r\nIf he sometimes hit the target.<br \/>\r\n\"Why not shoot a little straighter<br \/>\r\nAnd employ a smaller sample?\"<br \/>\r\nHiawatha, who at college<br \/>\r\nMajored in applied statistics,<br \/>\r\nConsequently felt entitled<br \/>\r\nTo instruct his fellow man<br \/>\r\nIn any subject whatsoever,<br \/>\r\nWaxed exceedingly indignant,<br \/>\r\nTalked about the law of errors,<br \/>\r\nTalked about truncated normals,<br \/>\r\nTalked of loss of information,<br \/>\r\nTalked about his lack of bias,<br \/>\r\nPointed out that (in the long run)<br \/>\r\nIndependent observations,<br \/>\r\nEven though they missed the target,<br \/>\r\nHad an average point of impact<br \/>\r\nVery near the spot he aimed at,<br \/>\r\nWith the possible exception<br \/>\r\nof a set of measure zero.<br \/>\r\n  \"This,\" they said, \"was rather doubtful;<br \/>\r\nAnyway it didn't matter.<br \/>\r\nWhat resulted in the long run:<br \/>\r\nEither he must hit the target<br \/>\r\nMuch more often than at present,<br \/>\r\nOr himself would have to pay for<br \/>\r\nAll the arrows he had wasted.\"<br \/>\r\n  Hiawatha, in a temper,<br \/>\r\nQuoted parts of R. A. Fisher,<br \/>\r\nQuoted Yates and quoted Finney,<br \/>\r\nQuoted reams of Oscar Kempthorne,<br \/>\r\nQuoted Anderson and Bancroft<br \/>\r\n(practically in extenso)<br \/>\r\nTrying to impress upon them<br \/>\r\nThat what actually mattered<br \/>\r\nWas to estimate the error.<br \/>\r\n  Several of them admitted:<br \/>\r\n\"Such a thing might have its uses;<br \/>\r\nStill,\" they said, \"he would do better<br \/>\r\nIf he shot a little straighter.\"<br \/>\r\n  Hiawatha, to convince them,<br \/>\r\nOrganized a shooting contest.<br \/>\r\nLaid out in the proper manner<br \/>\r\nOf designs experimental<br \/>\r\nRecommended in the textbooks,<br \/>\r\nMainly used for tasting tea<br \/>\r\n(but sometimes used in other cases)<br \/>\r\nUsed factorial arrangements<br \/>\r\nAnd the theory of Galois,<br \/>\r\nGot a nicely balanced layout<br \/>\r\nAnd successfully confounded<br \/>\r\nSecond order interactions.<br \/>\r\n  All the other tribal marksmen,<br \/>\r\nIgnorant benighted creatures<br \/>\r\nOf experimental setups,<br \/>\r\nUsed their time of preparation<br \/>\r\nPutting in a lot of practice<br \/>\r\nMerely shooting at the target.<br \/>\r\n  Thus it happened in the contest<br \/>\r\nThat their scores were most impressive<br \/>\r\nWith one solitary exception.<br \/>\r\nThis, I hate to have to say it,<br \/>\r\nWas the score of Hiawatha,<br \/>\r\nWho as usual shot his arrows,<br \/>\r\nShot them with great strength and swiftness,<br \/>\r\nManaging to be unbiased,<br \/>\r\nNot however with a salvo<br \/>\r\nManaging to hit the target.<br \/>\r\n  \"There!\" they said to Hiawatha,<br \/>\r\n\"That is what we all expected.\"<br \/>\r\nHiawatha, nothing daunted,<br \/>\r\nCalled for pen and called for paper.<br \/>\r\nBut analysis of variance<br \/>\r\nFinally produced the figures<br \/>\r\nShowing beyond all peradventure,<br \/>\r\nEverybody else was biased.<br \/>\r\nAnd the variance components<br \/>\r\nDid not differ from each other's,<br \/>\r\nOr from Hiawatha's.<br \/>\r\n(This last point it might be mentioned,<br \/>\r\nWould have been much more convincing<br \/>\r\nIf he hadn't been compelled to<br \/>\r\nEstimate his own components<br \/>\r\nFrom experimental plots on<br \/>\r\nWhich the values all were missing.)<br \/>\r\n  Still they couldn't understand it,<br \/>\r\nSo they couldn't raise objections.<br \/>\r\n(Which is what so often happens<br \/>\r\nwith analysis of variance.)<br \/>\r\nAll the same his fellow tribesmen,<br \/>\r\nIgnorant benighted heathens,<br \/>\r\nTook away his bow and arrows,<br \/>\r\nSaid that though my Hiawatha<br \/>\r\nWas a brilliant statistician,<br \/>\r\nHe was useless as a bowman.<br \/>\r\nAs for variance components<br \/>\r\nSeveral of the more outspoken<br \/>\r\nMake primeval observations<br \/>\r\nHurtful of the finer feelings<br \/>\r\nEven of the statistician.<br \/>\r\n  In a corner of the forest<br \/>\r\nSits alone my Hiawatha<br \/>\r\nPermanently cogitating<br \/>\r\nOn the normal law of errors.<br \/>\r\nWondering in idle moments<br \/>\r\nIf perhaps increased precision<br \/>\r\nMight perhaps be sometimes better<br \/>\r\nEven at the cost of bias,<br \/>\r\nIf one could thereby now and then<br \/>\r\nRegister upon a target.<br \/>\r\n<br \/>\r\n<\/pre>\n<p>W. E. Mientka, &#8220;Professor Leo Moser &#8212; Reflections of a Visit&#8221;<\/p>\n<p>\nAmerican Mathematical Monthly, Vol. 79, Number 6 (June-July, 1972)<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Stumbleupon Review Hiawatha Designs an Experiment Hiawatha, mighty hunter, He could shoot ten arrows upward, Shoot them with such strength and swiftness That the last had left the bow-string Ere the first to earth descended. This was commonly regarded As &hellip; <a href=\"http:\/\/su.blog.bunty.tv\/?p=3310950\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":""},"categories":[1381],"tags":[400569],"_links":{"self":[{"href":"http:\/\/su.blog.bunty.tv\/index.php?rest_route=\/wp\/v2\/posts\/3310950"}],"collection":[{"href":"http:\/\/su.blog.bunty.tv\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/su.blog.bunty.tv\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/su.blog.bunty.tv\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"http:\/\/su.blog.bunty.tv\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3310950"}],"version-history":[{"count":0,"href":"http:\/\/su.blog.bunty.tv\/index.php?rest_route=\/wp\/v2\/posts\/3310950\/revisions"}],"wp:attachment":[{"href":"http:\/\/su.blog.bunty.tv\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3310950"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/su.blog.bunty.tv\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3310950"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/su.blog.bunty.tv\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3310950"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}