Hiawatha Designs an Experiment

Maurice G. Kendall

Hiawatha, mighty hunter
He could shoot ten arrows upwards
Shoot them with such strength and swiftness
That the last had left his bowstring
Ere the first to earth decended.
This was commonly regard
As a feat of skill and cunning.

One or two sarcastic spirits
Pointed out to him, however,
That it might be much more usefull
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 follow men on
Any subject whatsoever,
Waxed exceedingly indignant
Talked about the law of error,
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 Yeats 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.

One or two 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)
Randomized his shooting order
Used factorial arrangements
And the theory of Galois
Field of ideal polynomials
Got a nicely balanced layout
And successfully confounded
Second-order interactions.

All the other tribal marksmen
Ignorant, benighted creatures
Of experimental set-ups
Spent 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 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
Did analyses of variance
Of designs experimental
Finally produced the figures
Showing beyond preadventure
Everybody else was biased
And the variance components
Did not differ from each other
Or from Hiawatha's.
(This last point, one should acknowledge,
Might have been much more convincing
If he hadn't been compelled to
Estimate his own components
From experimental plots in
Which the values all were missing.)
Still, they didn't understand it
So they couldn't raise objections
This is what so often happens
With analyses 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
Made primeval observations
Hurtful to the finer fellings
Even of the statistician.

In a corner of the forest
Dwells alone my Hiawatha
Permanently cogitating
On the normal law of error
Wondering in idle moments
Whether an increased precision
Might perhaps be rather better
Even at the risk of bias
If thereby one now and then could
Register upon the target.

Copyright © 2012

Schuyler W. Huck
All rights reserved.

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