Understanding p-values

A couple of days ago I was trying to nail down p-value, significance levels and null hypotheses. I know that if the p-value is lower than 0.05, the result is significant and the null hypothesis is rejected – but that’s just memorization. I wanted to understand it, know when it should be applied, and be able to explain it to others. I turned to my trusty co-worker, R., to help in this endeavor. (If you prefer you can skip the dorky “Brianne comes to understand p-values” conversation and go right to the “why this shit is important” section below.)

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Understanding p-values
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Calculus: The Musical

On Tuesday a friend invite me to join him for a show at Huge Improv Theater called Calculus: The Musical. It was a small production. Two actors portrayed many different characters, there was no intermission, and there were several frenzied costume changes during the show. Both actors played guitar at points, and one had several pieces on an electric keyboard. It had all the elements that I love in a musical comedy: Witty characters, fast-paced dialogue and action, a dash of slapstick, various overdone accents, a multimedia presentation, a blending of musical styles (from classical to rap and a lot in between), and a man playing Sir Isaac Newton talking to a little action figure of himself (“Little Isaac”) and then having the action figure answer back in a higher-pitched version of his true voice. Okay, that last was specific to Calculus: The Musical and not at all something I look for in musical comedies.

As the name might imply to those among you who are particularly quick-witted, it was about calculus. As a mathphobe who never made it all the way through a calculus course I was worried that all of the jokes would go right over my head. I did miss some of them; several times my friend’s giggling indicated that something humorous had transpired on stage after some dialoguey gobbledygook about derivitives, functions, limits and infinite series. But the writer managed to incorporate calculus without making the storyline completely unintelligible to the uninitiated.

You can listen to songs from the musical at maththeater.com. Here are the lyrics from the only song that I can actually claim to have understood entirely. It’s called 5 Sizes of Numbers:

There are 5 sizes of numbers,
Big Infinity and small Zero,
And the Finite in the middle,
They’re the ones, I’m sure you know.

But now we look between Finite and Zero.
To numbers so small, they’re nothing at all,
But still a little larger than a Zero.
Their name is Infinitesimal.

On the other side of Finite,
There are numbers too large to say,
Infinites are what we call them,
They are big, in every way.

But they will never quite be Infinity,
They’re not quite as big, not even close.
We’ll use all of these numbers in Cal-cu-lus,
The numbers, I love the most.

It only gets nerdier from there. They have a song about Bernhard Reimann in the style of Eminem’s Without Me. Just sayin’.

Calculus: The Musical has been touring nationally for six years, and it stopped in Minneapolis only for a couple of days. But they have shows scheduled from now through May of 2012 in different parts of the country. I had a good time, maybe even learned a thing or two, and it reminded me that I really need to stop procrastinating and start reading that copy of Jennifer Ouellette’s Calculus Diaries that I got for Christmas and have left languishing on my bookshelf for the last year!

Calculus: The Musical