January 13, 2009

Statistical Wear

Marks on objects can provide intriguing statistical glimpses of usage patterns. The darkened leaves of a well-thumbed book may point to favorite passages; the distinctive hollows of oft-traversed steps suggest the characteristic tread of countless feet.

Last year, while I was at East Tennessee State University, I happened to notice a particularly striking example of such "statistical wear" on the door to the men's restroom, just down the hall from my office. Entry to the restroom was by a swinging door, which opened inward with a push.

Countless hands pushing on the door had worn away the brown stain in one particular area, reflecting where men had preferred to place a hand. The result was a roughly circular spot—a two-dimensional statistical distribution—with the most wear in the middle and progressively less wear away from the center.

Countless hands have worn away the stain in one particular spot on the swinging door to a men's restroom. Photos by I. Peterson.

Two factors probably contributed most to the two-dimensional pattern: the height of the individuals pushing on the door and perhaps some preference for how much force to apply (less force would be required to push open the door farther away from the hinges). Curiously, the pattern largely misses a brass plate that was likely supposed to be the target.

What pattern would you expect to see on a nearly identical swinging door to the women's restroom?

The pattern is similar, but it is lower and a little closer to the door's edge, reflecting a lower average height and a greater preference for pushing with less force. As a result, the pattern has a significantly greater overlap with the door's brass plate.

The door to the women's restroom also has a distinctive two-dimensional wear pattern.

Statistician Robert W. Jernigan of American University has been collecting such "visualizations" of statistical concepts for many years, from the pattern created on a brick wall by a leaking downspout to oil stains on a parking lot. His fascinating "Statpics" blog is devoted to images that illustrate statistical ideas.

Jernigan's paper, "A Photographic View of Cumulative Distribution Functions," appeared in the March 2008 Journal of Statistics Education.

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