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## One Data Point

The name of this blog was originally not “Many Worlds Theory”.

I was going to call it, at first, “One Data Point”.  I know: not very exciting.

I still think that’s a good name;  it gets to the heart of what I want to say in this blog, for reasons I’ll discuss in a moment.  But I went with “Many Worlds Theory” for purely selfish, economic reasons.

(Here’s the monologue that went on inside my head: “Man, I bet I could have made some money if I had registered bigbangtheory.com a few years ago.  That TV show is quite clever.  My wife says I’m a bit like Leonard.  Anyway it would be nifty if I could register a name that would show up on Google searches… Let me play a round a bit and see what happens on Google.  Holy crap, no one has registered manyworldstheory.com?  How’d that happen?”)

I know, I know.  The chance of making money off a blog is about the same chance that the Carolina Panthers’ coaching staff makes good coaching decisions this coming week.  (Is this a topic for a future blog?)  But the name “Many Worlds Theory” is too good to pass up.  In some universe, this domain name really pays off for me.

So.  Back to “One Data Point”.  I got the idea from a physics lab I taught a few years back.  The lab was about the simple pendulum.  What variables affect the period of the pendulum’s motion?   The instruction up front was minimal; the students were supposed to design the experiment themselves.  They were to vary things like mass, initial angle, string length, and see which parameters were important.  (If you’re curious about the outcome, why don’t you try the experiment yourself?)

Fast forward about a week.  A student turns in a lab write-up, and I am grading it.  And I notice: their graph of “Period as a Function of Mass” has only one data point.

One data point.

Their conclusion is that period doesn’t depend on mass.  And to their credit, they have actually drawn a horizontal line through that one data point to make their case.

Here’s a reconstruction of the subsequent conversation I had with the student:

ME: [Pointing] So, do you see anything wrong with this graph?

STUDENT:  Uh, no?

ME: Well, there’s only one data point.

STUDENT: So?

ME: So how were you able to draw a line through it?

STUDENT: Well, I knew it had to be a horizontal line—

ME: You were supposed to verify that it was a horizontal line, with data, not assume the line was horizontal to begin with.

STUDENT: But it was horizontal.

ME: Only because you drew it that way!

STUDENT: Well, no, it was horizontal because it went through the data point we had.

ME: [Stifling laughter] But couldn’t you have drawn a line going in any direction you like, with only one data point?

STUDENT: But it was horizontal.

I’ll stop here; you get the idea.  It reminds me of the bit about the volume “going to eleven” in This is Spinal Tap.

This sort of reasoning is much more common that you might imagine.  I call it the “one data point” fallacy because I am not knowledgeable enough to know what it’s really called (or too lazy to look it up).  The idea is this: most people seem to be unaware that it takes two points to define a line.

Examples:

• “Hurricane Sandy is awful!  Global warming must exist.”
• “My friend Joe lost his job.  Therefore the economy is getting worse!  ”
• “The drinking water must cause cancer, because our neighbor’s son got cancer.”
• “The streets are getting more dangerous!  I know because I got mugged.”
• “TV is getting worse!  Just look at that Honey Boo Boo show.”

I hope you can see that all of the reasoning here is completely ludicrous.  That doesn’t mean that all of the statements are wrong; I happen to agree with exactly two of the statements.  But in each case a conclusion was drawn from one data point.

You know that you can draw a line in any direction, consistent with a single point?  That basically means that you can draw any conclusion you like from any of the above examples.

For instance:

“My friend Joe lost his job.  Therefore the economy is getting better!”

How so?  Well, what if Joe were the only person in the entire country to lose his job?  Then that one data point would be a sign of 0.0% unemployment!

The “one data point” fallacy is so pernicious that you have to stop yourself from using it.  It crops up everywhere.  Politicians love it: it is reasoning by anecdote.  “North Carolina is hurting.  Alice lost her job at the factory and had to go onto food stamps.  Vote for me.”  This stuff drives me crazy.

It almost makes you think that people can’t reason worth a damn.

But then again, I need more data to draw a definitive conclusion.

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### 2 Responses

1. …and hence the need for an inquiry approach in teaching science to kids.

2. […] talked about this before.  You can’t really draw any conclusions about anything from one data point.  And yet, people do […]