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Lyrics & Music © 2016 Monty Harper

We've got our kids in the choir 
The kids in the choir 
We measured their heights
To see how they changed
And on the average
Our kids got shorter 
We took it for a fact
Yeah, it was all arranged, but...

CHORUS:
No one counted on Simpson's Paradox
Yeah no one counted on Simpson's Paradox
Nobody counted on Simpson's Paradox
To turn our numbers upside down

We took the boys in the choir 
And the girls in the choir
We were thinking they were shorter
Like the average had said
But the boys got taller
And the girls got taller
How could this happen?
Had we lost our heads?

[REPEAT CHORUS] 

Well we had more girls this year
And fewer boys this year
And girls are mostly shorter 
Than boys as a rule
So our girls got taller
And our boys got taller
While our choir got shorter
And we all got schooled, because

[REPEAT CHORUS] 

Lyrics © 2016 Lawrence M. Lesser
may sing to the tune of the Beatles' "Lucy in the Sky with Diamonds"

Picture statistics in the newspaper
With context all missing or half summarized;
Somebody chose just who would be surveyed
And the order the items arise.
Stats are each chosen and given a setting, polished and cut for a view:
Look for the angle that reaches your eyes when they're done.

CHORUS: This is how stats are like diamonds,
This is how stats are like diamonds,
This is how stats are like diamonds, ahhh……

Follow the chain of a long calculation
For students who view stats as math mechanized.
But when you tell them "all stats are constructed",
Their eyebrows will rise up so high!

Newspaper numbers appear on page 4, labelled and grouped for display:
Like a nice gem, this story now sparkled, unlike rocks. (Repeat Chorus)

Picture a stat with no error or bias,
Without a confounder that's lurking disguised.
Take care that you see how that stat is presented:
Most jewels have a flaw to apprise. (Repeat Chorus twice)

Lyrics and music ©2012-2013 by Lawrence Mark Lesser

I heard of chance in math class while glancing at Sue from afar;
Ev'ry outcome equally likely, rolling a die or drawing cards.
And that gave me hope: she'll either love me or she won't,
So chances must be 1 in 2 that I'll win Sue!

Now I got me a ticket for the lottery: either I hit jackpot or I don't.
So easy to win: I'm ready to spend, and I'll try hard not to gloat
From my mansion, financed by this 50-50 chance
To make my dream come true - - me and Sue!

But odds were "odd" 'cause who would guess
Having 1 in 2 chances, twice with no success?!

It's just as well we never jelled: I know divorce hits 1 in 2.
And lottery's no draw for me: my ping pong ball days are through (they were numbered)!
Yeah, I'm movin' on - - what I knew was wrong:
There's more to chance I must pursue, like 1 in 2. Will skies be blue? 1 in 2.

Lyrics and Music © 2015 Lawrence M. Lesser

0.007  is the p that we get.
That's smaller than the alpha we set.
So when it comes to the null we reviewed,
 Reject the null we conclude!

Lyrics and music ©1997, 2007 Lawrence M. Lesser​

Sportscaster bragged all night
'Bout the one prediction he got right:
He said, "The more they've scored, the more they've won."
Probability of A given A is 1.
Probability of A given A is 1.

Writer made his Bible a find-a-word:
"TWIN", "TOWERS" and "PLANE" converged
When he let computers run.
Probability of A given A is 1.

You'll find reason, you'll find fate explaining why your side won
Like nothin' to do if nothin's new under the sun.

"Fear breeds fear, war breeds war,"
Said the call-in poll on Channel 4:
Father's legacy to son.
Probability of A given A is 1.
Probability of A given A,   
Possibility of A given A,
All the same to me: always points to one.

Lyrics by Dennis Pearl.  May sing to the tune of "The House of the Rising Sun" popularized by the Animals

There is a mouse with odd new genes
They’re all analyzing that one.
And it’s been the ruin of many a poor lab
Reproducible results are none.

My mother went to Baylor
Where she studied new transgenes.
My father was a Gramblin’ man
Down near New Orleans.

Now the only thing a study needs
are cases to match controls.
And the only time that’s satisfied
takes dice and all their rolls.

Oh teachers, tell your students
Not to do what I have done.
Spend your lives experimenting
on a mouse, analyzing just one.

Well my bioinformatics platform
Is impossible to train.
I’m going back to splicing genes
having samples to obtain.

They built a mouse with odd new genes
to solve a rare disease.
A statistician asked for a hundred more
And God, I hope he said “please.”

Music and Lyrics © 2015 Tom Toce (Retrograde Music)

For deviation, you need the root
Don't permute
Take the root
Sample growth is one thing
That's absolute
Your  Standard Error  lags, it shrinks like –
 Standard Error  lags, it shrinks like –
 Standard Error  lags, it shrinks like –
The root.
The  square root !

Lyrics copyright by Robert Carver
may sing to the tune of "Runaround Sue" (Ernie Maresca and Dion DiMucci)

Here's my story, sad but true
About a sample that I once drew
It raised my hopes, but now I'm a wreck
'Cause the assumptions I forgot to check.

(vamp: Ho, Ho, Ho, Ho-Ho-Ho-Ho, etc.)

Ah, if I had just looked at the very start
My stats professor would have thought me smart
Now listen people what I'm telling you
A-keep away from a sample that's skewed.

I ran my t-test in the proper way
Thought I'd reject H-nought for H-a
But my sample was small, so now I'm screwed
I was misled by a sample that's skewed

(vamp: Ho, Ho, Ho, Ho-Ho-Ho-Ho, etc.)

Ah, the mean can travel around
When a long tail pulls it up or down
Now people, let me put you wise
Check conditions when you hypothesize.

Here's the moral of the story from a guy who knows
Pay attention to what you suppose
It makes a diff'rence, I'm telling you, dude:
A-keep away from a sample that's skewed.

{reprise}

Ah, the mean can travel around
When a long tail pulls it up or down
Now people, let me put you wise
Check conditions when you hypothesize.

Here's the moral of the story from a guy who knows
Pay attention to what you suppose
It makes a diff'rence, I'm telling you, dude:
A-keep away from a sample that's skewed.

Lyrics © 2018 Larry Lesser

Sung to the tune of "The Alphabet Song" ("Twinkle, Twinkle, Little Star")

I will order A, B, C:
There's A-B-C and A-C-B,
B-A-C, B-C-A,
C-A-B, and C-B-A!
I've permuted A, B, C:
Next time, won't you sort with me?

Music and Lyrics © 2016 Monty Harper

Suppose you study 12 different herds of  elephants 
Can the differences in their average weights 
be explained by random error?
Or do any herds have weights that are truly different?
It's a difficult conundrum
Lucky for you there's a test that will help you compare!

CHORUS:
ANOVA, ANOVA
ANOVA, ANOVA
ANOVA, ANOVA
Analysis of Variance

The variance of the average weight 
between the different herds 
Is matched against the variance of
weights within each set
The ratio of "between" against
"within" gives your statistic
If the average weights are all equal, how
unlikely is the "between" / "within" ratio you get?

[REPEAT CHORUS] 

If the variance between your herds 
Dominates that within
You can reject the null hypothesis
And let the real work begin
At least one herd of your elephants features
weights  of a different mean
But ANOVA gives no details -
It's a one trick multiple mean comparing machine.

[REPEAT CHORUS] 

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