Friday Fun: Comparing Apples & Oranges

A totally fair, balanced, unbiased comparison. Really. No really! See more of this chart at: smarter.org via junkcharts.

March Madness: It Didn't Happen Again!

Since 1985, when the NCAA Division I Men's Basketball Tournament expanded to 64 teams, a team seeded (or ranked) 16 (last in each of the four regions) has never beaten a team seeded first. Over the 27 years from 1985 to 2011, (108 pairings) the number 1 seed has won by as much as 58 points (in 1998, Kansas(1) over Prairie View(16) 110-52). But twice over that time, both times in 1989, the number 1 seed narrowly edged out the number 16 seed by only 1 point (Georgetown(1) over Princeton(16) 50-49 and Oklahoma(1) over East Tennessee State(16) 72-71.

The histogram above shows the winning point margins. It closely fits a normal distribution with a mean of about 25 and a standard deviation of about 12. This gives us an estimate of the probability that a 16 seed could beat a number 1 seed, as just the probability that this normal distribution is less than zero. Here, we get a value of about 2%.

Wait 'til next year!

P.S. (3/20/2011)
A colleague observed that since a 16 seed has never won over a 1 seed in 108 trials of men's basketball (although it has happened in women's in 1998, 16 seed Harvard over 1 seed Stanford 71-67) that a 2% probability of an upset is perhaps too high and the probability should be less than 1% (1/108). But this treats a trial as only a success or failure and ignores how close the score was to an upset. A value near 1% is likely too small.

Multiple Regression Model c. 1911

A multiple regression model from George Undy Yule's "An Introduction to the Theory of Statistics" (1911) page 242. The residuals can be seen in the edge-on view.

Contours of Use

Here are scatterplot contours of hand placement in opening a door at a health center stairwell. The door itself is the darkest color shown, but it has been painted over with white, blue, and peach(?) colored paint. As thousands of hands push the door open they slowly rub away some of the paint, leaving bivariate contours of greatest use. Horizontal and vertical frequency of hand placement can be readily seen in the paint wear pattern.

3D Punching Bag Scatterplot

A 3D scatterplot made of 1300 punching bags (click picture for larger view) by artist Michael Kalish from Wired, with an impressive 2D marginal scatterplot of Muhammad Ali.

Matching Normal Densities

An image of the wear on exit doors at a Barnes and Noble bookstore in Rockville, Maryland. Most wear is located a little below shoulder height as customers push on the door with outstretched arms as they exit. Or are they holding open the door with fingers as they enter? It turns out it's both. (Yes, I stood there and watched!). It's both uncomfortable and inefficient to open the door much higher or much lower. We're left with a greater frequency of use centrally located with less and less wear above and below: a unimodal frequency distribution of wear. Considering that human height is approximately normally distributed, the patterns here should reflect that normality. It's interesting to note that the left hand door seems to have a frequency distribution of wear that sits slightly above that for the right hand door.
Any ideas as to why?

Musical Stacked Histograms

This graphic has gotten a lot of play in the past few weeks. It purports to show the collapse of the global music industry. The image is discussed on Junk Charts where attention is directed at the mystery of the decline in CD sales around 2001. An interesting image, but as Michael DeGusta of Business Insider shows not all is what it seems. He details the graphic's recent history and notes several problems: It's really only US sales figures and it's not adjusted for inflation, among other problems. He provides other images of music sales data and this correction of the chart in 2011 dollars:
Here we see a problem with interpreting such an image. One commenter on Junk Charts notes:

"We might be able to tell if the Digital Sales area was not hidden behind the CD Sales area. Hence the problem with area charts."

To which another responds with the correct answer:

"Digital sales isn't hidden behind the CD sales - its stacked on top. I know it looks like a range of mountains, but it isn't. I think. That's the perceptual problem with charts stacked like this."

Yes, it is not one curve sitting behind another, like a range of mountains. The histogram information is stacked on top of the other curves. Stacked histograms are often used when displaying time dependent data, like for following. But not always.
Here is an image of a "living histogram" that organizes men and women of different heights into frequency classes. The men's histogram is easily seen. The women (dressed in white) are added or stacked onto the men's histogram classes. It does give an indication of the population heights for both, but it's more difficult to view the women's histogram alone. The same holds for the graphic of music sales. But I want to see the time axis extended further into the past, showing sales of 45s, 78s, and then even Edison wax cylinders!