# The Bootstrap Begins

may sing to the tune of "American Pie" (Don McLean)

Long long time ago,
Ingram can still remember when
ANOVA used to be the thing.
Small samples were all that we had
And of the Normal we were glad
And we all said R.A. Fisher was our kin
But my data would never fit,
No matter how I transformed it.
Significance was too low;
I did not know where to go.
My referees all called it "crap",
When a thought hit me with a slap:
"You should try out the bootstrap."
That's how I got published.

CHORUS (slow):
My, my, this assumptions a lie,
But if we bootstrap we can use it and the paper will fly.
We'll resample and kiss the normal goodbye
Singing "Theory is too hard for this guy".

Well Tukey in the olden days
Used to sing the Jack-knife's praise
'Though no-one knew exactly what it did.
Mann and Whitney and Signed Ranks
When non-normality could not be hid.
But if the data was over-dispersed
And transforms seemed to make it worse:
The Chi-squared wouldn't work
The doctors went berserk!
But Brad told us to resample,
A few hundred times should be ample;
Use the histogram empirical
We'll call that the bootstrap.

CHORUS

Do you know that our confidence
Can be put in places that make sense
Even when the distribution is unknown?
Do you have processing power
To run this scheme within an hour
And find a result that's not yet been shown?
Any applied statistician
Will almost always say "I can!"
"We'll bootstrap anything."
A distribution we can plot
For any statistic you've got;
You've stepped into the perfect shop
Here's the best thing on the lot.

CHORUS

Twenty-five long years have come and gone
Since Efron's idea came along
And now you see it everywhere.
With computers now so very fast
Simulation is a blast
And for all that theory we don't really care.
Though Donoho still rails away
At the lack of rigor found today;
Models are complicated,
Distributions are not stated.
And though there is no guarantee
That the truth is what we'll see,
When consulting comes to me
I'll still say "Let's bootstrap".

CHORUS (x2: soft then fast)