Monday, April 20, 2009

Never a Center Without a Spread

By Skip Kifer

When I ask my classes “who runs faster boys or girls,” someone would, after having decided it is not a trick question, say “boys.” If one is talking about averages or centers of distributions that is the correct answer. If one is talking about how fast people can run, it misses the mark substantially. How many men in the world can run faster than Marion Jones?

Education talk is filled with centers when it should be filled with spreads and, on the best of days, centers, shapes and spreads. Let me give you a couple of examples:

Which of the following two pictures, based on the same data, describe an achievement gap?

An answer is, of course, they both do. But what do they portray and which is the better description? And, are there better descriptions?

The recent entries concerning equity in educational funding in the Commonwealth portray kinds of centers. Here is another picture that contains the data and spreads as well.

I do not see the equity in funding. In fact, spreads, a measure of inequity, may have increased.

Anytime I see reported only averages or only percentages I am immediately suspicious. There are simply better ways to portray data and to make it possible for persons to understand better what the data may be saying.

(Editor's Note: Correction made in text April 21.)

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