Monday, October 1, 2012

Proportionality and Disproportionality: Not just words with too many syllables!

This dog’s legs are disproportionately short for his body!

A proportion relates two different objects via size or some other characteristic.

To evaluate a proportion, establish three factors:
1)      The original object/group
2)      The object/group of comparison
3)      The underlying cause/relationship (if any)

Proportions go awry when someone tries to draw an incorrect conclusion from the data.

Let’s go through some goofy examples:

Example #1: A disproportionate number of physicists die from rock climbing.

Rock shoes and "Quantum Mechanics" textbook

We’re comparing:
1)      the percentage of physicists who die from rock climbing
2)       the percentage of the general population who die from rock climbing
3)     Both physics and rock-climbing are types of problem-solving so I’m not surprised that physicists are drawn to rock-climbing (or vice-versa).

Example #2 (based on my experience): A disproportionate number of (male) particle physicists have ponytails so growing a ponytail will make you better at particle physics.
1)      Percentage of particle physicists with ponytails.
2)      Percentage of the general male population with ponytails.
3)      Guys with ponytails are usually jerks; particle physicists are often jerks. Hence, ponytails and particle physics are correlated, but one does not cause the other so growing a ponytail will probably just make people think you’re an jerk.

Example #3: There are a disproportionate number of women in physics so women are worse at physics.
1)      The percentage of women in science (almost none)
2)      The percentage of women in the general public (50%!)
3)      The reasons behind this could probably be an entire blog by itself. Sexism is probably one cause (http://www.pnas.org/content/early/2012/09/14/1211286109), and I think there's no way that it's because women are worse at physics.

Proportionality affects everyone when it comes to clothing because clothes are sized according to some mythical “average person”. Because of this, everyone is forced to measure their bodies and proportions against this average person so we end up making statements like:

Example #4: My legs are disproportionately long for my body.
My awesome paint drawing of legs with short pants.

1)      The length of my legs
2)      The leg length of the average  person
3)      The underlying cause here is the clothing industry in America. If we use this criterion, everyone is disproportionate to their own bodies. This criterion renders the statement meaningless, but I still use it because almost everyone has the framework of the average person in their minds.
Example #5 (completely made-up): 10% of baseball players die of cancer so baseball causes cancer!
1)      The percent of baseball players that die of cancer (10%).
2)      The percent of the general public that dies of cancer (unknown in this headline).
3)      In this case, this fact is presented as a disproportionality. However, without knowing the cancer rate in the general public, you can’t actually conclude that baseball causes cancer.

As long as you keep the comparison parameters straight in your head, you can’t get fooled!

If you want some more examples, check out this cool photo collection: http://formyhour.com/photo-project-disproportionate

PS: Some of you may have noticed that much of this post deals with correlation and causation without directly mentioning those two words. Don’t worry, it’s a topic for another blog post!

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