Monday, August 27, 2012

Paint, Tom Sawyer, and Errors

Today’s post is about the difference between random error (http://en.wikipedia.org/wiki/Random_error) and systematic error (http://en.wikipedia.org/wiki/Systematic_error). Another analogy awaits you. (This blog could probably be entirely about errors.)

Imagine painting a wall. You finish your first coat of paint. Before passing out from the paint fumes, you notice that there are spots missing paint. Furthermore, you notice there seem to be two types of areas without paint.

Random spots: the spots you can’t control. The spots have no pattern. They arise from chance when your brush sticks, the paint clumps up, etc.
Solution: To fully cover the wall, you paint more than one coat. With multiple coats, the random spots will average out because it’s unlikely that the brush will stick in the exact same spots the second or third time around.

Systematic spots: The right or left side of the wall has spots because of your handedness (unless you’re some mutant who’s ambidextrous). When you’re in the corner, your hand hits the other wall so you can’t paint fully into the corner.
Solution: More coats will not help in this case. Fortunately, you know the source of the error! Two options: 1) You can switch hands and awkwardly paint with the off-hand. 2) Pull a Tom Sawyer and get a friend with the opposite handedness to paint for you.

So how does this relate to science? (See this website for a nice description, http://www.physics.umd.edu/courses/Phys276/Hill/Information/Notes/ErrorAnalysis.html.)

Well, taking scientific measurements is like painting a wall, but painting it blindly or painting with invisible paint. You have no idea how much of the wall you’ve actually covered after you’re done.

To account for random error: scientists take repeated measurements (just like adding more coats of paint). In fact, for every $n$ measurements, the error usually goes down by $\sqrt{n}$.

The sources of random errors are often related to precision (see http://parsingscience.blogspot.com/2012/07/five-hidden-facets-of-numbers.html).

To account for systematic error: If you’re lucky, the systematic error will be something simple like your handedness.
Unfortunately, systematic errors are often harder to identify and you may never determine the true source of the error.

Takeaway message: if you ever want to picture how difficult science is, imagine painting a wall with invisible paint. Have some sympathy for the scientists in your life and buy them a drink or a new paintbrush.

Funny example of systematic error: I knew a research team who was taking measurements in the basement of a physics building. They kept having errors in their measurements and discovered that it was correlated with the toilets being flushed!

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