Fun_People Archive
20 May
Hiawatha Designs an Experiment

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From: Peter Langston <psl>
Date: Mon, 20 May 96 14:29:49 -0700
To: Fun_People
Subject: Hiawatha Designs an Experiment
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                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 a feat of skill and cunning.
 Several sarcastic spirits
 Pointed out to him, however,
 That it might be much more useful
 If he sometimes hit the target.
 "Why not shoot a little straighter
 And employ a smaller sample?"
 Hiawatha, who at college
 Majored in applied statistics,
 Consequently felt entitled
 To instruct his fellow man
 In any subject whatsoever,
 Waxed exceedingly indignant,
 Talked about the law of errors,
 Talked about truncated normals,
 Talked of loss of information,
 Talked about his lack of bias,
 Pointed out that (in the long run)
 Independent observations,
 Even though they missed the target,
 Had an average point of impact
 Very near the spot he aimed at,
 With the possible exception
 of a set of measure zero.

 "This," they said, "was rather doubtful;
 Anyway it didn't matter.
 What resulted in the long run:
 Either he must hit the target
 Much more often than at present,
 Or himself would have to pay for
 All the arrows he had wasted."

 Hiawatha, in a temper,
 Quoted parts of R. A. Fisher,
 Quoted Yates and quoted Finney,
 Quoted reams of Oscar Kempthorne,
 Quoted Anderson and Bancroft
 (practically in extenso)
 Trying to impress upon them
 That what actually mattered
 Was to estimate the error.

 Several of them admitted:
 "Such a thing might have its uses;
 Still," they said, "he would do better
 If he shot a little straighter."

 Hiawatha, to convince them,
 Organized a shooting contest.
 Laid out in the proper manner
 Of designs experimental
 Recommended in the textbooks,
 Mainly used for tasting tea
 (but sometimes used in other cases)
 Used factorial arrangements
 And the theory of Galois,
 Got a nicely balanced layout
 And successfully confounded
 Second order interactions.

 All the other tribal marksmen,
 Ignorant benighted creatures
 Of experimental setups,
 Used their time of preparation
 Putting in a lot of practice
 Merely shooting at the target.

 Thus it happened in the contest
 That their scores were most impressive
 With one solitary exception.
 This, I hate to have to say it,
 Was the score of Hiawatha,
 Who as usual shot his arrows,
 Shot them with great strength and swiftness,
 Managing to be unbiased,
 Not however with a salvo
 Managing to hit the target.

 "There!" they said to Hiawatha,
 "That is what we all expected."
 Hiawatha, nothing daunted,
 Called for pen and called for paper.
 But analysis of variance
 Finally produced the figures
 Showing beyond all peradventure,
 Everybody else was biased.
 And the variance components
 Did not differ from each other's,
 Or from Hiawatha's.
 (This last point it might be mentioned,
 Would have been much more convincing
 If he hadn't been compelled to
 Estimate his own components
 From experimental plots on
 Which the values all were missing.)

 Still they couldn't understand it,
 So they couldn't raise objections.
 (Which is what so often happens
 with analysis of variance.)
 All the same his fellow tribesmen,
 Ignorant benighted heathens,
 Took away his bow and arrows,
 Said that though my Hiawatha
 Was a brilliant statistician,
 He was useless as a bowman.
 As for variance components
 Several of the more outspoken
 Make primeval observations
 Hurtful of the finer feelings
 Even of the statistician.

 In a corner of the forest
 Sits alone my Hiawatha
 Permanently cogitating
 On the normal law of errors.
 Wondering in idle moments
 If perhaps increased precision
 Might perhaps be sometimes better
 Even at the cost of bias,
 If one could thereby now and then
 Register upon a target.

W. E. Mientka, "Professor Leo Moser -- Reflections of a Visit", American
Mathematical Monthly, Vol. 79, Number 6 (June-July, 1972)

See also "Applied Dynamic Programming" by Bellman and Dreyfuss, prior to 1962.

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