Hiawatha

                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)