# Testing

• ### Hypothesis Testing is Fun!

Lyric copyright by Gary Cziko
may sing to tune of "Mr. Bojangles" (Jerry Jeff Walker)

Well, I didn't think I'd ever like statistics,
and I don't know why.
But I had to take it sometime soon to graduate,
so I gave it a try.
And I've changed my mind, yes I've changed my mind,
'cause it's clear to me now,
Hypothesis testing, hypothesis testing, hypothesis testing is fun!

Oh, you state your null hypothesis and don't forget,
your alternative one, too.
It may be directional that means it has one tail,
but usually two.
You decide on alpha, oh, don't forget alpha,
to control errors Type I and II.
Hypothesis testing, hypothesis testing, hypothesis testing is fun!

Then compute your z or t or F or chi-square,
and compare it to the table.
To decide the fate of your own null hypothesis,
you reject it if you're able.
If you're lucky you reject it, don't try to accept it,
it's not logical to do.
Hypothesis testing, hypothesis testing, hypothesis testing is fun!

So statistics really can be quite enjoyable,
if you study all along.
And I want to world to know about the joy I've found,
so I wrote this song.
And I hope you'll sing it, yes hope you'll sing it,
in a voice clear and strong.
Hypothesis testing, hypothesis testing, hypothesis testing is fun!

• ### What P-Value Means

Lyric ©2005 Lawrence Mark Lesser;
May sing to tune of "Row, Row, Row Your Boat"

It is key to know
What p-value means --

It's the chance
(with the null)
you obtain
data that's

At least that extreme!

• ### I Will Find U

Lyric copyright by Kate McFarland
may sing to tune of "I Will Find You" (Peter Hammill)

Trapped by your habit when you must compare,
Two-sample t-tests that blind you
I have a better way;
each observation pair,
I'll assess, greater/less; I will find U.

(For) independent samples X and Y,
Mann-Whitney's test, I'll remind you,
Is so simple--add a half for every tie,
Else just sum, naughts and ones, and you'll find U.

Far away in a normal test
You'll find you don't have so much freedom;
Don't run away to a normal test.

Don't be afraid should it be unknown
What distribution's before you.
Don't be afraid (with) symmetry alone,
Lose no more, (than) point-one-four, if you find U.

Far away in a normal test
Things cannot be much more efficient;
Don't run away to a normal test...

Trapped by your habit when you must compare,
Two-sample t-tests that blind you
I have a better way;
each observation pair,
I'll assess, greater/less; I will find U.

• ### Chi-Square For Us

Lyric copyright ©2006 by Lawrence Mark Lesser
may be sung to the tune of "Aquarius" (James Rado, Gerome Ragni, Galt MacDermot)

When you have qualitative data
And you need to test goodness of fit
Or do a test of independence,
Then this fine tool is it!
This is the dawning of the age of chi-square for us,
Age of chi-square for us,
Chi-square for us!
Chi-square for us!

It's the oldest test we use now--
In nineteen-hundred, Pearson showed us how
Reasoning with simple rat'os
yield expected frequencies that go in formula summation
note degrees of libera-ation:
chi-square for us, Chi-square for us!

(repeat first section)

• ### It's .05

Lyric copyright by Marc Coram and Matthew Finkelman
may sing to the tune of "My Boyfriend's Back" (Robert Feldman, Gerald Goldstein and Richard Gottehre)

The p-value's low and I'm gonna get it published
Heh-na, heh-na, it's .05

The p-value's low and the journal isn't rubbish
Heh-na, heh-na, it's .05

Yeah, my paper got accepted
Null hypothesis rejected
Heh-na, heh-na, it's .05

The effect is microscopic but I got four thousand patients
Heh-na, heh-na, it's .05

Now people will forget my bad TA evaluations
Heh-na, heh-na, it's .05

Yeah, my paper got accepted
Null hypothesis rejected
Heh-na, heh-na, it's .05
Heh-na, heh-na, it's .05
Heh-na, heh-na, it's .05

• ### Test on Mu (to the other side)

Lyric copyright by Dennis K. Pearl
may sing to the tune of "Break on Through (to the other side)" (The Doors)

You know the tail's to the right
Root-n divides the s
Tried the left
Tried the right
Test on mu to the other side
Test on mu to the other side
Test on mu to the other side, yeah

We placed our measures here
valid measures there
But can you still recall
Testing just one side
Test on mu to the other side
Test on mu to the other side

Yeah!
C'mon, yeah

Both ways reject my null
Both ways reject my null
mean was low
mean was high
mean was low
mean was high

I landed an alternative
Both ways can give
Evidence to claim
The null's a lie
Test on mu to the other side
Test on mu to the other side
Test on mu, oww!
Oh, yeah!

Peak to Peak
Way to weigh
Power to Power
State and negate
z's the guide
Test on mu to the other side
Test on mu to the other side
Test on mu
Test on mu
Test on mu
Test on mu
Yeah, yeah, yeah, yeah
Yeah, yeah, yeah, yeah, yeah

• ### Oops! ... I Picked The Wrong Test

Lyrics © by Jen Simonds
may sing to tune of "Oops! ... I Did It Again" (Britney Spears)

I think I did it again
I made you believe,
I had what I need
Oh, Chuck, I have run a Z-test,
But that doesn't mean I know what's best
But to lo-ose my σ, that is just so typically me
Oh baby baby

Oops I did it again
I picked the wrong test
Got invalid results
Oh, baby baby
Oops I ran a two-tailed
When I wanted just one tail
For my hypothesis

You see my problem is this
I'm running t-tests
Wishing my groups they were independent
I cry watching the curve
'Cause if I reject, I've got nerve
But to lose degrees of freedom
That is just so typically me
Oh, baby, Oh baby baby

Oops I did it again, I misread the graph
Where's the interaction?
Oh, baby, baby
Oops, are those parallel lines
And where are the main effects
Is this even an ANOVA?

[Dream Sequence]
Chuck: Britney, Britney, I got these for you.
Britney: But I thought the old lady archived these down in the basement of the library
Chuck: I went down and got them for you.
Britney: Awww, you shouldn't have...
Chuck: No, you really need these

Oops I ran a Pearson's for my test
I tried to correlate categories
Oops you think that I needed a Χ²
For my nominal data

Oops I did it again, rejected the null
Didn't understand p
I thought bigger's better
Oops I misread the "sig."
On my SPSS output
I'm not that innocent

Oops I did it again
I picked the wrong test, got invalid results
Oh, baby baby
Oops I ran a two-way
When I wanted a three-way
For my hypothesis.

Watch the video

• ### Scientific Jam

Lyric and music copyright by Jeff Hale

You ask a good question and wonder what the answer is.
If you guess at the answer, that's a hypothesis.
The scientific method can make you very smart.
If you want to solve a problem, that's a good place to start.

chorus :
Is your hypothesis wrong or right?
Do a test that will shed some light.
If your experiment goes as planned.
You've answered your question with the scientific jam.

You've collected all the data. Now your searching for a clue.
You just might want to graph it so you'll have a picture too.
With careful observations you've really thought it through.
The answer finally hits you. Now your ready to conclude.

chorus :
Is your hypothesis wrong or right?
Do a test that will shed some light.
If your experiment goes as planned.
You've answered your question with the scientific jam.

bridge
Make a guess, hypothesize, do a test and experiment.
Think it through, analyze, then conclude with a great surprise

Now just in case you made a major breakthrough,
do the test again just to make sure it's cool.
Some other science dudes just may want to do your gig
A repeatable experiment is something they can dig.

repeat chorus

• ### If Only P were greater

Lyrics copyright by Denise Tran
may sing to the tune of "Drops of Jupiter (Tell Me)" (Patrick Monahan, Robert Hotchkiss, James Stafford, Scott Underwood, and Charlie Colin)

Backed by evidence, I've made a new guess
My alternative hypothesis, hey--
I thought you said you still loved me too
But I've rejected this null, it just ain't true, hey--
Why do I care for you when I've
Found the p-value is less than point-oh-five, hey-- hey--

But tell me, is there practical relevance
To stop reaching out to you?
Though statistical significance,
A circumstance unlikely due to chance

Tells me, I don't mean much to you
And there's nothing left to do
Sometimes the difference seems small at best
Should I run another test?

Well if p is low, I guess null must go
Although I'd much prefer Ho to stay--
But the chances you feel the way I do
Are under five percent (wish it wasn't true), hey--
If my results are right, I'm not quite sure
Perhaps I made a Type I error? hey-- hey--

But tell me, to stop reaching out to you,
Is there practical relevance?
Though statistical significance,
A circumstance unlikely due to chance

Tells me, I don't mean that much to you
And there's nothing left to do
I feel the difference is small at best
Maybe I'll run another test?

Could you imagine no Type I error,
Saying things are out of place and the feelings are gone
Even when they're really not

Could you imagine if p was really high
And I did not have to question
The significance of the results
Or your love for me

Tell me, does significance mean a thing?
If there exists another possibility
I'll need some new hypotheses

And tell me, is there practical relevance?
Between results I'd expect from null
And those I actually got
Is the difference smaller than I thought?

Tell me, 'cause I'm not so sure
If I made a Type I error
Feelin' so lonely, guess,
I'll need to make another test

Maybe I made a Type I error
Should I still reject Ho?
Still reject Ho?
Or maybe I should set my alpha at less than point-oh-five

• ### ANOVA Table's Coming to Town

Lyric copyright © by Dennis K Pearl
May sing to the tune of "Santa Claus is Coming to Town" (John Frederick Coots and Haven Gillespie)

You better watch error;
they better be tight.
Better be normal,
or it don't work right.
ANOVA Table's coming to town!

It's summing those squares,
And checking 'em twice;
Variance 'tween or within a slice.
ANOVA Table's coming to town.
ANOVA Table's coming to town.
ANOVA Table's coming to town!

It sees the data you've been keeping;
...but not if they are fake.
It knows if they're within or between;
So between for goodness sake!

Oh - You better watch error;
they better be tight.
Better be normal,
or it don't work right.

ANOVA Table's coming to town.
ANOVA Table's coming to town.
ANOVA Table's coming to town!