statpics

Just Marginal Joints

2011-08-15T11:24:00.000-04:00

Here is a joint distribution of wear on the counter top of a Home Depot. The counter top was originally white. This has worn away to reveal various layers of shading in the laminate and further into the underlying wood of the table. The innermost area has been actually gouged out by many tools, cans of paint, and other heavy hardware. We see nested triangular patterns of wear revealing the joint distribution of tool placement on the counter and their movement across the checkout scanner.

But wait. There's more, as they say on infomercials. Not only do we get the joint distribution of wear, we also get one marginal distribution of wear along the front edge of the counter. As customers drag their purchases onto or off of the counter they leave a bell-shaped pattern of use along that front edge.

Our Video

2011-08-08T22:21:00.004-04:00

Award for Best Evidence of Inspiring Students at the 2011 Joint Statistical Meetings in Miami Beach. Double click on video for full screen.

YADWFD: Yet Another Door Wear Freqency Distribution

2011-08-04T21:49:00.003-04:00

This is an edge-on view of an open door. Notice the wear pattern along the edge. Another bell-shaped frequency distribution of wear.

Mc-Bell-Shaped

2011-08-02T21:43:00.005-04:00

Wear caused by hands (fingers?) holding a door? Perhaps left hand fingers in the PULL slot and thumbs wearing away on the door edge. More frequent wear near the middle and less above and below. We've seen this pattern before, like here. There will be more to come. This pattern is quite common. Find one for yourself and share.

Skyscraper Frequencies

2011-06-01T18:39:00.006-04:00

A sculpture of a keyboard with the key's height proportional to its letter's frequency of use in English. Looks like a small city block full of skyscrapers. How would the block look different if the frequencies of use were in another language. Via Geekologie. Thanks to Laura.
I examined related frequency and language questions here.

Automated Histograms c. 1962

2011-05-23T14:00:00.001-04:00

This is a device, from Nature in 1962, to construct a histogram during an experiment of stimulus-response times. The histogram forms by the careful timing of the release of ball-bearings into plastic bins. As a stimulus is given to a subject, the machine comes to life, starting a motor and engaging an electro-magnet. The motor hums, driving a treadmill-type belt at a constant rate. A ball-bearing is then projected onto the underside of the belt by a solenoid. The ball-bearing is held fixed at a point along the moving belt by the magnet. Once the subject responds to the stimulus, the electro-magnet is switched off, and the ball-bearing drops into the appropriate bin indicating the response time. The histogram grows as more response times are measured. It is suggested that the mean can then be found by balancing the display, and the variance by finding its moment of interia.

Earthquake/Population Density Map

2011-04-02T17:44:00.001-04:00

A map of global earthquake intensity, showing magnitude and density of seismic activity weighted by population (larger version here). According to Views of the World this map allows us "to understand the earthquake intensity in relation to today’s population distribution, and thus gives an idea of where most people are of risk related to seismic activity." The algorithm uses kernel density estimation followed by a density equalizing algorithm.
Via The Map Room.

Friday Fun: Comparing Apples & Oranges

2011-03-25T20:39:00.000-04:00

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!

2011-03-19T11:41:00.009-04:00

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

2011-03-13T12:55:00.001-04:00

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

2011-03-09T15:27:00.000-05:00

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

2011-03-01T21:03:00.006-05:00

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

2011-03-01T18:58:00.000-05:00

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

2011-02-27T19:23:00.001-05:00

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!

Galton's Bayesian Machine

2011-02-25T08:30:00.003-05:00

Chance magazine has an article by statistician and statistics historian Stephen Stigler on Galton's visualization of Bayes Theorem. He describes Galton's Bayesian machine, likely made up of beads, bins, and glass although the original device doesn't survive. These are, of course, familiar materials for Galton's statistical demonstrations.

At the top level, beads are arrayed in deep vertical histogram bins representing the prior distribution, p(θ). A knob is turned and some fall into a bell-shaped horizontal room, representing the likelihood: f(x|θ). The room's back wall bulges away from us placing larger likelihood on central values of θ. If this room were moved more to the right, it would place larger likelihood on larger values of θ. At this second level, those beads falling to the front are retained, inside the bell curve wall, but some beads are rejected falling to the back, outside the wall. This performs the product: f(x|θ) p(θ). Of course at this level some bins are wide and deep, some are very shallow. The knob at this level is then turned and the beads are dropped to the bottom into vertical bins of equal width, rescaling them into a histogram proportional to the posterior distribution: f(θ|x)= f(x|θ) p(θ). Very clever and invented in 1877!

"Mnemonic" is itself a (Poisson) mnemonic

2011-02-24T10:45:00.005-05:00

See The Futility Closet. I can now use the Poisson distribution to help me remember how to spell "mnemonic"!

Bathroom Exits

2011-02-23T11:03:00.004-05:00

This is a view of the inside exit door of the men's restroom at a movie theater in Germantown, Maryland. (I had to be careful with the camera in there!)

Notice the spatial pattern of wear on the main part of the door and the vertical wear pattern on its left-hand edge. This illustrates a bivariate frequency distribution of hand placement along with a marginal frequency distribution (on the left) of just the vertical hand placement.

Users of this restroom exit by pushing on the door and proceeding around to the right towards the theater. As the men do so, they don’t seem use the metal push panel provided. It doesn't seem to be designed properly for mens' heights. Instead, the men seem to push higher on the door wearing off the red paint. We see a two-dimensional spatial distribution of their hand placement. The wear pattern shows both the horizontal and vertical placement of their hands as they push the door to exit.

But the picture also shows more. As the men exit the door, they proceed out to the right, rubbing their hands on the edge of the door. The resulting wear pattern shows the marginal distribution of the vertical position of their hands. They push the center of the door and then scrape their hands on the edge producing both the two-dimensional spatial distribution followed by a one-dimensional marginal distribution.

I noticed the open exit door on the women's room. I couldn't get the picture there. But the women's door had much less wear on the door. They seemed to use the metal push plate to open the door. It was mounted more correctly for their height or perhaps the women were in less of a hurry.

BMI Over Time

2011-02-05T13:51:00.004-05:00

Much like Gapminder highlighted in a previous post, the Washington Post has created a scatterplot of national body mass indices (BMI) overtime. Can you find a country whose national BMI decreased over a stretch of time contrary to almost every other country?
For an individual, body mass index is not the most valid index of how overweight you might be, despite the claims of the Centers for Disease Control. Keith Devlin points this out well in his column for the MAA.

NYTimes Investment Graphic

2011-01-04T10:51:00.002-05:00

This NYTimes graphic makes me feel better about my very conservative investments.

Interactive Age Distributions

2010-07-27T11:31:00.005-04:00

Great interactive histograms of the age distributions in selected countries since 1950 and projected out to 2050. From GE via information aesthetics

Plotting a Newer Court

2010-07-14T11:48:00.011-04:00

The Washington Post has again published a similarity matrix of Supreme Court Justices voting. Three years ago I posted about using a multidimensional scaling procedure to convert this similarity into a visual plot. Since that time Rehnquist and Souter have left the Court replaced by Roberts and Sotomayor. Before Elena Kagan completes the Senate's review process to replace Justice Stevens, here is a plot of the newer Court. Again an arbitrary algebraic sign places Justices Stevens, Sotomayor, Breyer, and Ginsburg on the left of our plot and Justices Scalia, Thomas, Roberts and Alito on the right. Again, Justice Kennedy is the most centrist justice falling just a little right of center.

CEO's can sure drink a lot

2010-07-13T15:21:00.007-04:00

A data comparison of average US salaries, represented by a Styrofoam cup, and average US CEO's salaries, represented by many champagne glasses for 1965 and then 40 years later in 2005. The ratios are 1:25 in 1965 and 1:275 in 2005. Part of many more interesting data comparisons, with videos, in the exhibit "Common Sense - An Art Exhibit About the American Dream" at the College of Creative Studies, Taubman Center in Detroit.

So Close Yet So Far

2010-07-12T11:05:00.008-04:00

I went to the Corcoran galley of Art this past weekend to see the exhibit of artist Chuck Close. An amazing array of mosaic or block portraits made with paint, paper pulp, thumb prints,...Stand far away and the portrait is obvious, but the closer you look (no pun intended) the portraits turn into a jumble of abstract marks, symbols, colors, and textures. After the visit I did a little research and found this article from Science about this effect. In a 1999 article by psychologist Denis Pelli, "Close Encounters - An Artist Shows How Size Affects Shape," shows the following graph and its caption from an experiment. They had viewers stand close to a Close portrait and more away, noting when a facial feature (the nose) eventually emerged.

The nose test. The critical face width of Close's portraits plotted against the number of marks across the face. The regression lines, one for each of five observers (accounting for half of the variance), are plots of the results for judging nose emergence on each of the 33 gridded portraits from the Chuck Close retrospective (except the Keith/Six Drawings Series) (2). X and O are raw data for two observers. Size independence predicts a vertical line. All five lines have log-log slopes close to 1 (mean 1.0, SD ± 0.2), showing that the perceived shape does depend on size.

I would think a better plot would have face width as the explanatory variable and marks across the face to be the response. Independence would then be testing for a slope of zero (a more standard way for statisticians to represent it). Here is the original graph flipped to see the scatter.
Of course the lines drawn here are not the regression lines of the marks regressed on the face width. In fact, it appears that a new regression of marks on face width would have slopes much closer to zero! Is it significantly different from zero? I'd have to digitize the data off the graph to check for sure, but was the original graph chosen to emphasize the conclusion that size and shape are dependent?

How Mariano Rivera Dominates Hitters

2010-06-30T15:48:00.007-04:00

Here is an excellent animation from the New York Times showing how Mariano Rivera has been such a dominant closer in baseball. It shows how his similar deliveries result in drastically different ball placement at the plate. They analyzed nearly 1300 of his pitches over the 2009 season. The scatterplots show the location of the ball as it goes over the plate. He is amazingly adept at keeping the ball on the corners and away from the middle of the plate, where a hitter would have the best contact.

The First Published Random Walk?

2010-06-29T15:32:00.005-04:00

According to Alex Bellos in his new book "Here's Looking at Euclid", this is the world's first graph of a random walk, published by John Venn in his book "The Logic of Chance" in 1888. Venn produces this path using the digits from 0 to 7 from the first 707 digits of π. Venn writes,

"Of these, after omitting 8 and 9, there remain 568; the diagram represents the course traced out by following the direction of these as the clue to our path. Many of the steps have of course been taken in opposite directions twice or oftener. The result seems to me to furnish a very fair graphical indication of randomness. I have compared it with corresponding paths furnished by rows of figures taken from logarithmic tables, and in other ways, and find the results to be much the same."

Here are the directions Venn uses and the results from the first ten decimal digits.

2010-06-28T16:29:00.004-04:00

This is an pair of automatic entry doors to the terminal at Dulles airport outside of Washington, DC. Although the doors open automatically as you approach, passengers pushing luggage carts ahead of them hit the bottom edge of the doors when they open too slowly. This leaves a distinctive wear pattern on each door. Most carts hit the same spot, some cause wear a little higher, some cause wear a little lower. This could be from different cart heights or different loads on the carts or from the slight dents in the door from the repeated bumpings, causing the carts to hit more off the center target. A bell-shaped frequency distribution is left behind. Most wear in the center less towards the extremes.

2010-06-04T11:48:00.004-04:00

Not so much an image this time, but a quote I like from the book "The Great Influenza" by John M. Barry that I am currently reading.

"To be a scientist requires not only intelligence and curiosity, but passion, patience, creativity, self-sufficiency, and courage. It is not the courage to venture into the unknown. It is the courage to accept -- indeed, embrace -- uncertainty."

Bell-Shaped Animals

2010-05-31T21:25:00.008-04:00

Adapted from a graphic in Life magazine October 10, 1955 showing speeds of various animals. The artist has displayed the animals sampled on a horizontal scale of speed. There are few slow animals on the left, many more medium speed animals in the middle, and few fast animals on the right. The outline of the cloud of animals shows the essence of a roughly bell-shaped frequency distribution with a little skewness to the right. But take out the elephant and much of the skewness goes away also.

Artificial Population Sampler

2010-05-27T23:17:00.001-04:00

I found this brochure in an old file. It dates from 1978. It shows a physical model for teaching sampling and quantitative methods in ecology. Click on the images for larger views. Developed by Arnold M. Schultz, a Professor of Systems Ecology at the University of California, Berkeley and used as a teaching tool beginning in 1958. His 1961 patent application seen here was awarded in 1965.

The model contains two plates of plastic containing arrangements of vinyl discs of various sizes and colors that represent populations in a square region of the Cartesian plane. One plate is called the random population plate made up of six colors that seem to be distributed uniformly over the square. The other plate is called the nonrandom population plate made up of 19 colors that are arranged in rough clusters to illustrate more contiguous, local populations. Instruments are provided for measuring locations and size. Along with color they provide both qualitative and quantitative data for estimating means, variances, density, diversity from various random sampling methods. The population parameters are fixed in each of the plates allowing assessment of measurement error and bias. A paper by Schultz et al. from the Journal of Range Management (1961,v14,n5,pp 236-242) illustrates its use. I've found one listing of the color distribution (from the paper "A comparison of techniques for assessing dispersion patterns," D.W. Goodall and N.E. West, Vegetatio, (40)1:15-27, 1979) but other than a reference to it having six sizes, nothing explicit about the size distribution.

A real hands-on approach to sampling that is very useful for both teaching and research. An example in teaching is illustrated here. Its use in ecological research in 2006 is shown here.

Compositional Eating

2010-05-26T11:53:00.003-04:00

Are you eating right? This site has dinner plates that graphically help you to keep to certain eating proportions. Of course, you must be careful not to pile-on and overload one section and skimp on others. The area devoted to your food choices might be a good reminder, but it's more the mass of each component that's important to your nutrition.

Footsie?

2010-05-20T11:53:00.006-04:00

Distributions of foot placement, sitting on a bench, in a casino "on the Boardwalk in Atlantic City"

Old School Rules: A Normal Slide Rule

2010-05-17T15:30:00.020-04:00

Here's a normal slide rule. Yes, it's very old technology, but it helps to see some workings that other high-tech black boxes hide.
Of course you can even get much more extensive stat calculators for your IPhone See StatsMate. Still this is fun.

Find the BIG TIF file at this link (or click on the illustration below). And, as requested, here is a smaller pdf version. Print it out on heavy card stock.

Cut off the slider on the left and set it aside. On remaining front section, cut out the normal curve and the results window. Fold back the top and bottom. Then slide in the slider with the numbers down and the blue rectangle up.
Pick your z-score and read the area of the blue shaded region.

Data Jewelry

2009-11-05T09:59:00.003-05:00

Here is a novel data representation, high and low temperatures over the course of a year are laser-cut into small house-shaped slices that encircle the bracelet. Also shown are small circular holes with area proportional to the monthly rainfall. A flattering year's worth of weather data to wear on your wrist. See details here.

Time Series Heat Map in R

2009-11-03T13:40:00.006-05:00

The Revolutions blog gives information on the statistical programming language R. Heat maps are shown in a recent post. A calendar is displayed horizontally with days of the week in rows and months arranged in jagged columns (since not all months have the same number of days). A color is plotted on each month's day for the magnitude of a time series variable (in this case the stock price for Microsoft) over several years of calendars. The site gives R code developed by Paul Bleicher, MD PhD, Chief Medical Officer at Humedica for producing these plots.

A Normal Sidewalk?

2009-08-13T12:17:00.003-04:00

I've seen this pattern in many sidewalks. A crack forms at the seam of two pieces of concrete. Over time and use the crack crumbles away portions of the sidewalk in a bell-shaped pattern. What process or differential equation might define the resulting bell-shaped pattern of wear?

The Density of Space Trash

2009-08-13T11:04:00.003-04:00

Here is an image showing the density of space debris in low earth orbit. Notice that this density has a very long, and likely heavy, tail that is not shown. Geo-synchronous satellites orbit at 36,000km well off the upper range of this graph (2,000km). There would be a large bump in the density at 36,000km. From The Washington Post.

A Pearl: a Balanced Median Necklace

2009-08-12T14:54:00.004-04:00

The September issue of The College Mathematics Journal has this balance point view of the median by Mark Lynch of Millsaps College.

2009-07-27T13:59:00.002-04:00

Wine consumption for various countries proportional to the area of each circle. Strangemaps.wordpress.com has an interesting discussion of trying to make sense of the numbers in this map that has no legend to tell you what the numbers mean. Why is Luxembourg so big?

A Sad Tally Indeed

2009-07-27T13:48:00.003-04:00

Discrete distribution of Golden Gate Bridge Suicides. Locations plotted to the nearest light pole. The bay side is more popular than the ocean side. Any conjectures as to why? From strangemaps.wordpress.com via sfgate.com

A Mean Streak Across the Country

2009-07-27T13:43:00.003-04:00

The mean center of population for the US. From the US Census Bureau: “the point at which an imaginary, flat, weightless and rigid map of the US would balance perfectly if weights of identical value were placed on it so that each weight represented the location of one person on the date of the census.” From strangemaps.wordpress.com

Delay

2009-07-27T13:41:00.001-04:00

Sorry for the long break. Life interfered.

It's Easy as 1,2,3

2009-02-24T12:02:00.003-05:00

Graphical rating of movie trilogies. From Danmeth via notcot.

The Super Big Bowl Game

2009-01-31T16:13:00.005-05:00

The Super Bowl, excuse me, I should have said The Big Game, (since the NFL restricts their copyrighted name from all but their officially endorsed advertising), is tomorrow. The Pittsburgh Steelers play the Arizona Cardinals in Tampa. The Steelers home is Heinz Field shown in this view from Google Earth in 2006. Look at the two prominent areas of wear along each sideline of the field. These sidelines are where the players, coaches, and trainers watch, wait, and often pace as the game progresses. These areas of wear show us the frequency distribution of this sideline action. Coaches and players move up and down along the sideline following the action on the field. As they do so their steps wear away the turf underneath leaving a record as frequency distributions; more wear indicating a greater frequency of use.

If you look closely you can also see a wear pattern of the team's use of the field during play.

Microbes illustrate Simpson's Paradox

2009-01-30T17:35:00.004-05:00

An article in Science by Chauang, Rivoire, and Leibler illustrates Simpson's paradox with a microbial system. They describe the principles with the illustration above from their paper. On the right three subpopulations undergo decreases in their percentage of green, but because of unequal weighting of the subpopulations the global population undergoes an increase.

Correlations of Google Search Rankings with State Statistics

2008-12-12T20:03:00.006-05:00

This StateStats site is fun. The states are shown in relative rankings of an entered search term. Here I searched for the word "beatles". Spearman rank correlations are then calculated for these search rankings and state ranking of statistics such as population density, income, or percent voting for Obama. States with the most searches for the word "beatles" are negatively correlated with those states that voted for Bush in 2004 and positively correlated with those states that voted for Obama in 2008. Examples on the site reveal interesting correlation patterns for searches for terms like, prius or nascar. The site warns that correlation is not causation.

Show the World Resized

2008-11-13T13:17:00.002-05:00

Show World allows you to resize countries based on selected variables. See also Gapminder.

Aggregated Images of Emotions

2008-11-03T08:31:00.011-05:00

What colors are most often associated with various emotions? A bar chart. Plus, aggregation of drawings of answers to the question: Do your emotions have directions? If yes, draw arrows. From Emotionally Vague. See also What Color is PG-13?.

So Many a Second

2008-10-30T08:42:00.004-04:00

Visualizations of raining trees, cars, births, deaths showing how many happen in the world per second. Even more from infosthetics.

Two Colorful Examples of Smoothed Bivariate Density Functions

2008-10-29T21:56:00.007-04:00

Seen this week, smoothed scatterplots showing the density of locations of basketball shots taken by Phoenix Suns players. More information is here. Via the Statistical Modeling blog of the Stat Department at Columbia University.

Also this week:

Smoothed scatterplots showing where subjects first looked in recognizing faces. The nose knows. More here.

Bivariate Histogram from Maya Lin

2008-10-21T19:34:00.006-04:00

From Maya Lin, the designer of the Viet Nam Veterans Memorial, a sculpture in wood called 2X4 Landscape. It looks like a bivariate histogram. It is showing now at the de Young museum in San Francisco until mid January 2009. After that it is coming to the Corcoran in Washington, DC according to this site.

Joint and marginal distributions in Legos

2008-10-09T13:49:00.002-04:00

Here are Lego approximations to a joint probability density function and its two marginal probability density functions. The marginals are built just by stacking the Legos in their appropriate row or column. Notice the Legos modeling the quadratic marginals. In one case concave up, and the other concave down.

US Population in Grains of Rice

2008-09-25T09:12:00.003-04:00

A UK exhibit showing the population of the US in grains of rice. 1 person = 1 grain of rice. From Of All the People in The World via NotCot. Lots more at the Flickr site.

Continental Marginal

2008-09-23T22:30:00.004-04:00

From Brazilian artists Angela Detanico and Rafael Lain via strange maps shows the marginal distribution of the continental land masses. The northern hemisphere has the predominance of globe's land.

The Ultimate Pie Chart

2008-09-18T09:44:00.003-04:00

via: reddit
Nothing more need be said!

Election References

2008-09-16T10:49:00.003-04:00

A display of the frequency of references to the candidates.

Interactive Bar Chart

2008-09-16T10:44:00.003-04:00

Here is an interactive bar chart in a museum where people take tokens depending on how they answer a question. The frequencies of their responses can be seen as the columns get diminished with each selection.

Pentagon 9-11 Memorial

2008-09-11T10:17:00.002-04:00

Today the Pentagon 9-11 Memorial is dedicated. Benches dedicated to each victim are arranged by the victim's age. Age lines start at 1930 for the oldest (71 years) and continue to 1998 for the youngest (three years old). An age wall runs along one edge from a height of 71 inches down to a height of 3 inches. Here is an interactive virtual tour of the memorial from the Washington Post.

Also Today, an unsettling normal distribution

2008-09-11T10:16:00.005-04:00

According to an old article in the NY Times (April 2, 1946, p12) this is a copy of an official captured German map found by Allied intelligence officers sometime after WWII. It shows a bulls-eye target in the middle part of lower Manhattan. The concentric circles show concentrations of destruction from multiple V-2 type rockets or special orbital bombers. Elsewhere the map is topped with the normal curve modeling the east-west error distribution of these multiple attacks.

A Model of a Characteristic Function

2008-08-15T10:56:00.011-04:00

I was looking at a CD holder and noticed that it could represent the unit circle and provide a model of a characteristic function. It reminded me of a paper by Epps, available here, whose abstract begins: "The value of a characteristic function of a random variable X at some real number t is the center of mass of the distribution of tX wrapped around the unit circle in the complex plane." I have cut the sides of the CD holder to leave a normal distribution wrapped around a circle. The balance point of this model is the center of mass mentioned by Epps. As t gets smaller, approaching zero, the wrapped distribution gets more concentrated around a modal point. Also, the balance point moves toward the edge of the unit circle, directly under the mode of the wrapped distribution. The rate at which this balance point moves, at the edge of the unit circle, is the mean of the the random variable X.

Markov's Inequality Without Words

2008-08-14T17:06:00.009-04:00

A very clever derivation by Pat Touhey of Markov's Inequality from The College Mathematics Journal, September 2008 published by the Mathematical Association of America.

Olympic Medal Plots

2008-08-05T22:44:00.004-04:00

Very cool interactive graphic from the New York Times.

The Office : Not Mutually Independent

2008-07-30T13:45:00.007-04:00

Here is a movie of your new office building. The building is made of office cubicles and glass. It faces a river on one side and a red road on another. There are nine offices in the building that are available for use. The most desirable offices have windows that face the river or face the road. Of course, two windows are better than one, and a top floor office with two windows is the prize selection. But unfortunately, you cannot choose. You are assigned randomly to one of the offices and all are equally likely to be your assigned office.

Although in this building, river views, road views, and top floor offices are pair-wise independent they are not mutually independent, since they are not also three-way independent. Can you determine how?

A Colorful Normal Distribution

2008-07-30T11:20:00.007-04:00

I ran across this normal distribution on Flickr. It is outside the Rodin Museum in Paris. A close-up can also be seen here. Of course sometimes people get carried away. Here for example or here. And yet another here. See even more by searching "Rodin stickers" on Flickr.

Cumulative Distribution Tabs

2008-06-10T14:56:00.004-04:00

The image above shows a cumulative distribution function that can be seen and understood with relative ease. This is a side view of the pages of the paperback version of the Oxford Advanced Learners’ Dictionary. Small colored squares for each letter are shown on the edge of each page. These colored squares act as tabs running from the top of the page for letters early in the alphabet to the bottom of the page for those letters that come later. These printed alphabetical marks on the edges of the pages help speed the look up of words and their definitions. This is really one of the first search engines.

When the dictionary is placed on its side, these colored tabs produce a cumulative distribution function for words from the English language. We have a visual and understandable image of a cumulative distribution function. We can quantify this by noting, for example, that 93 pages of this dictionary are devoted to the letter "A", so 93 pages have tabs colored to act as guide tabs to words starting with "A". The last page number of each letter’s tab indicates the number of pages devoted to words that begin with letters occurring, in alphabetical order, before that tab. Let G(x) denote the page number of this last page for each letter x in the set {A,B,C,…,Z}. These are the cumulative counts of pages for words beginning with each letter in the English alphabet. The maximum of G(x), call it M, is just the number of the last page of the dictionary for the letter "Z". Define F(x) to be G(x)/M. Then F(x) represents the cumulative relative frequency of letters of the alphabet. This is the alphabet’s cdf. Learn more from my paper "A Photographic View of Cumulative Distribution Functions" in the Journal of Statistics Education.

Earliest Living Histogram

2008-05-01T13:59:00.008-04:00

Here is the earliest "living histogram" picture that I have found. It is from a paper by C.B. Davenport in The Popular Science Monthly, September 1901. It is more easily found on-line at Google books in the text Graphical Methods for Presenting Facts by Brinton(1914) on page 165. Davenport placed forty University of Chicago students into columns according to different height classes. What we see are the top of their heads or rather their hats!
My previous earliest finding of a living histograms occurred in a paper by Blakeslee(1914). A link to it is available in the references of a genetics review paper by Crow.
The term "living histogram" was coined by Joiner(1975) in the International Statistical Review. Joiner's image, Blakeslee's image, and an update by Strausbaugh(1996) can also be seen in a paper by Schilling, Watkins, and Watkins "Is Human Height Bimodal?" from The American Statistician.

Skewz Me

2008-04-02T16:02:00.006-04:00

Here is Skewz.com a website that lets readers rate news stories on a personal liberal-conservative scale. Results are summarized by story and by media. In the story above 37 reader's ratings are summarized. This gives an indication of the political bias or, less pejoratively, the point of view of the article.

Although you can see all the ratings that I have squished below, I would prefer to see the histogram of all the ratings as I have inserted lower. Like this: Did that one guy who rated this story as the most liberal really understand the scale?
What is even more informative is the Cloud View you can get for a media comparision.

How biased is your source of news?

Bad Baseball Graphics

2008-04-02T15:59:00.002-04:00

So what's wrong with this picture.
See here for the answer.

The Sound of a Chair

2007-11-06T09:22:00.001-05:00

Not really statistical and not totally visual, but here is an interesting 3D representation of data. Using time, frequency, and volume this tone yields a 3D graphic in the form of a chair. Click on the link to designer Matthew Plummer Fernandez then click on sound/chair to hear the sound of a chair.

State of the Union Statistics

2007-10-18T11:32:00.000-04:00

Here is an interactive view of the State of the Union addresses from all the US Presidents. Larger word clouds indicate the words that were used more frequently. You can select a President and compare his address (in red) with another's (in white). Up and down arrows can help eliminate word clustering. The bar chart at the bottom indicates the total number of words in each address. A very nice use of frequency statistics.

George W. Bush has a fondness for Julie, shown on the right. This is Julie Aigner-Clark who developed the Baby Einstein videos and cashed in when she sold out to Disney. Of course, the videos have now been shown to be ineffective. Hear the NPR story.

Beware correlations on averages

2007-10-05T15:02:00.000-04:00

A recent article on Cuba brought to mind how correlations on averages can be very different from correlations on individuals. Due to unfortunate economic conditions, the 1990s found the Cuban people both low on food and fuel. They ate less, (daily energy intake declined from 2,899 kcal in 1988 to 1,863 kcal in 1993) and they exercised more as a result of widespread use of bicycles and walking as alternative means of transportation.

As a result, obesity declined, as did deaths attributed to diabetes, coronary heart disease and stroke. This corresponds with much of what is known about increasing the length of life through caloric restriction. Laboratory tests on many organisms have shown a negative correlation between caloric consumption and length of life. The example from Cuba is a natural experiment on humans that appears to indicate that daily calorie intake is negatively correlated with life expectancy. Of course, the Cuban example has a confounding variable of increased exercise. So we can't say directly that the less you eat the longer you live. But contrast this with data from the UN through the FAO on average daily calorie intake and average life expectancy by country, shown above. The correlation is positive 0.72. Of course, this correlation is confounded with wealth, health care, etc.

If individuals generally respond to decreased caloric intake the same way that the citizens of Cuba did, then hypothetical scatterplots for individuals within each country would have a negative correlation:

Here the ellipsoidal regions indicate confidence regions for the mean caloric intake and length of life for individuals in each country. The tilt in the ellipses indicate the negative correlation. Now I don't have such data. But the Cuban example suggests that the correlations may well be negative within a country but positive across the countries of the world.

A nice example that tells us again to beware of correlations on averages. They may not reflect the correlations on individuals.

Normal Dining?

2007-10-03T10:38:00.000-04:00

Here is an image of a bell-shaped distribution on the baseboards of booths at a restaurant in Bethesda, Maryland. Could it be that the pattern is caused when the wait staff set, clear,or deliver food to the table? Imagine a server scuffing the baseboards with his shoes, rubbing the wood smooth in a pattern that shows typical foot placement. Or is the pattern the residual polish left after customers scuff the wood next to their seats as they slide into the booth? I think I prefer the former explanation.
What do you think?

Gapminder

2007-09-24T16:56:00.001-04:00

An amazing interactive Flash implementation shown here of scatterplot graphics related to world development. Multiple dimensions, variable transformations, geographic anchors, time series visualization, etc. An outstanding interactive graphic!

World's Income Distribution

2007-09-24T16:44:00.000-04:00

An interactive Flash demonstration showing the distribution of the world's income and the percentage of the world's population that falls under the poverty line of $1 a day and how it changes over time and by region.
From www.gapminder.org

A 6-Dimensional Conditional Slice

2007-09-24T16:19:00.001-04:00

Here is a graphic from the US Geological Survey via the World Wildlife Fund. It shows 6 dimensions of data across a conditional slice of the US at latitude 35% N. Similar to an earlier post of rainfall.

Power of the Histogram

2007-08-12T21:21:00.000-04:00

The new CBS game show called "Power of 10" has contestants estimate what Americans think. The host of the game is comedian Drew Carey. One question posed to a contestant was "What percentage of Americans think Drew Carey is a presidential candidate and not a comedian?" The contestant must provide a guess. Low valued questions allow for a relatively large margin of error. For example, a $1000 question has a margin of error of 40%. The next power of 10 question for $10000 has a margin of error of 30% etc. up to $10,000,000 where the exact answer is required. One contestant has already won $1,000,000 on the show. To help them with their guesses contestants are given the results of an audience poll. This is given in the form of the histogram show above.

For the Drew Carey question, the modal guess is 10%, the mean and median are in the 20's.

By the way, the answer to the question above was 9%, well within the contestant's range of 2% to 42%. She won $1,000. Of course the audience's modal answer was much closer, showing the wisdom of crowds.

A distribution in the clouds

2007-08-06T11:53:00.000-04:00

Here is an endpaper from a book displayed at a site on the Visual Telling of Stories via www.strangemaps.wordpress.com. The book is likely about travel across the US with commentary on geology, geography, etc. A close-up is shown here. The elevation profile towards the bottom has, above it, a frequency distribution (in clouds) of the annual rainfall in each part of the country.

Statistical Clock

2007-08-03T21:17:00.000-04:00

Using data from the World Health Organization, the CIA factbook, the US Census Bureau and other sources you can get an unsettling look at the world. The up-to-the-second version is at poodwaddle.com.

Cake Chart

2007-07-31T11:07:00.001-04:00

You've heard of pie charts. Here are Cake Charts. The cake's decoration is designed to be the proportions of each cake's ingredients. As the site says, "Decoration becomes information."

Such data are called compositional data. The previous post had compositional data on national flags. Here is one of my research papers on modeling compositional data.

Pie Flags

2007-07-20T13:13:00.001-04:00

Here is a site that shows the flags of the nations of the world as pie charts of their flag's colors. Click on the site's charts to see what country it belongs to.

What color is PG-13?

2007-07-19T10:52:00.000-04:00

Here's someone who has attempted to compare the frequency distributions of the colors on movie posters given their MPAA rating. As you might expect the more kid-friendly the movie, the more bright colors you see. NC-17 and R rated movies are more "dark and fleshy".

Plotting A Divided Court

2007-07-11T11:31:00.002-04:00

On July 5, 2007 the Washington Post published the table above in the article “Parsing a Divided Court.” This is a similarity matrix. Displayed for each pair of Supreme Court Justices are the percentages of time that they agreed in non-unanimous rulings. We can use the method of principal co-ordinates by Gower "Some distance properties of latent roots and vector methods used in multivariate analysis" (1966, Biometrika, 53, pp. 325-338) to obtain points in Euclidean 2-space whose distances approximately mirror these similarity scores (distance^2 = 2(1 – similarity)). Justices with high similarity scores are plotted as points close together. Justices with low similarity scores are plotted as points far apart.

The method starts with a similarity matrix A. The diagonal elements of A are ones, indicating a justice’s perfect similarity with themselves. (Alternatively, a distance matrix D = (d[i,j]) could be used to build A, with diagonal entries equal to zero and the a[i,j] off diagonal entries equal to -½*d[i,j]^2).

The matrix A is transformed by subtracting out of each row the mean of that row of A, then subtracting out from each column the mean of that column of A, then adding the overall mean of A to each entry. The eigenvectors and eigenvalues of this transformed version of A are then computed. The elements of the first two eigenvectors multiplied by their respective eigenvalues give the co-ordinates of the nine justices in 2-space. This provides the visual representation of the original similarity matrix shown above. A measure of goodness of fit is given by the sum of the first two eigenvalues divided by the trace of the transformed A. Here about 75%.

An arbitrary algebraic sign places Justices Stevens, Ginsburg, Souter, and Breyer on the left of our plot and Justices Thomas, Scalia, Roberts and Alito on the right. Justice Kennedy is the most centrist justice falling just a little right of center.

An anagram note: The first letter of the justice’s last names: KGB’S STARS
(May 2010: My mnemonic KGB'S STARS for the justice's last names has held out through two replacements on the Court. Rehnquist left and Roberts replaced him. Souter left and Sotamayor replaced him.
But now it may fail. Stevens left and Kagan is the current candidate to replace him. Perhaps STARK KGBS. Not very good.)

Do Women Really Talk More Than Men?

2007-07-06T12:14:00.001-04:00

In their article published today in Science, "Are Women Really More Talkative Than Men?" Mehl, et al. address what has become a cultural "truth" quantified in the book "The Female Brain" by Brizendine. There it is claimed that women use about 20,000 words a day while a men use about 7,000. But Mehl and colleagues have studied the actual conversations of nearly 400 people over the past 8 years. The histograms above from their online supplement display the findings. Women spoke an average of 16,215 words a day with a standard deviation of 7301 words. Men spoke an average of 15,669 words a day with a standard deviation of 8633 words. A one-sided t-test results in a p-value of 0.2479. Hardly a significant finding. Each group spoke about 16,000 words a day with large individual variation. This illustrates perfectly the quote by novelist Ivy Compton-Burnett, "There is more difference within the sexes than between them."

Cycle Man

2007-07-03T10:29:00.000-04:00

On Friday, June 29, 2007 Aubrey Huff first baseman for the Baltimore Orioles hit for the cycle. In one game, he had a single, a double, a triple, and a homerun. This has happened 276 times in major league history, only three times for the Baltimore Orioles and it is the first time it has happened at home in Baltimore and at Oriole Park at Camden Yards. In the major leagues he is the third player to hit for the cycle in 2007. So what is the distribution of such an event?

Interestingly, just this year Huber and Glen have modeled the distribution of such rare events in their article, “Modeling Rare Baseball Events – Are They Memoryless?” in the Journal of Statistics Education. They model three baseball events as a Poisson Process: no-hit games, triple plays, and hitting for the cycle. Using data from 1901 through 2004 they get the distribution shown above of how many cycles are seen in a given season. The observed results are a bit short on seasons with exactly 2 players hitting for the cycle, and there are a few more seasons than expected with exactly 1 player hitting for the cycle. The expected results are shown in red: a Poisson distribution with the observed mean of 2.19.

Over the time period examined, nearly 160,000 games were played, and only 0.14% of these games had a player hit for the cycle. As Huber and Glen found the cycle is rarer than a triple play but not as rare as a no-hitter.

So how closely does this match a Poisson process? One measure is a Poissonness Plot developed by Hoaglin (American Statistician 1980). If f[k] represents the observed frequency of a random count k then the log of the Poisson density would essentially be -λ+klog(λ)-log(k!). So that in a plot of log(f[k])+log(k!) against k, a straight line would indicate a good fit to a Poisson distribution. The slope of this line is an estimate of log(λ). Here log(λ) is 0.9583, so that an estimate of λ is 2.607. Of course the maximum likelihood estimate is simply the mean number of cycles per season 2.19. Since the variance of a Poisson distribution is also equal to λ, this would provide another estimate of 2.90. Note the Poissonness plot estimate falls in between the two.

Another way of checking for a Poisson process is to check the inter-arrival times, that is, the number of games between any two players hitting for the cycle. These inter-arrival times should follow an exponential distribution. The figure below shows the cumulative relative frequency of the observed time between cycles for the period 1901 through 2004. Also shown is the theoretical exponential cumulative probability distribution with a mean equal to the observed mean of 719.533 games. This indicates that the cycle process is memoryless. Even if there have been 1000 games without any major league player hitting for a cycle, you would still have to wait on average over 719 games more before one does.

For Aubrey Huff it was certainly a special night. Not only did he hit for the cycle he also had the 1000th major league hit and the 200th double of his career. Even with all that the Orioles still lost the game to the LA Angels 9 to 7.

Shooting a Fence

2007-06-25T16:23:00.000-04:00

"Fig. 10.—When deviations in all directions are equally probable, as in the case of shots fired at a target by an expert marksman, the "frequencies" will arrange themselves in the manner shown by the bullets in compartments above. A line drawn along the tops of these columns would be a 'normal probability curve.' Diagram by C. H. Popenoe."

From a 1918 book by Popenoe and Johnson titled "Applied Eugenics". Even though that field has been discredited, they have a clever way of motivating the normal distribution.

"Suppose an expert marksman shoots a thousand times at the center of a certain picket in a picket fence, and that there is no wind or any other source of constant error that would distort his aim. In the long run, the greatest number of his shots would be in the picket aimed at, and of his misses there would be just as many on one side as on the other, just as many above as below the center. Now if all the shots, as they struck the fence, could drop into a box below, which had a compartment for each picket, it would be found at the end of his practice that the compartments were filled up unequally, most bullets being in that representing the middle picket and least in the outside ones. The intermediate compartments would have intermediate numbers of bullets. The whole scheme is shown in Fig. 11. [actually Fig. 10] If a line be drawn to connect the tops of all the columns of bullets, it will make a rough curve or graph, which represents a typical chance distribution. It will be evident to anyone that the distribution was really governed by "chance," i.e., a multiplicity of causes too complex to permit detailed analysis. The imaginary sharp-shooter was an expert, and he was trying to hit the same spot with each shot. The deviation from the center is bound to be the same on all sides."

A Skewed Runway

2007-06-11T12:00:00.000-04:00

This is a composite picture obtained from the United States Geological Survey. The top picture is a view of the runway called 1L at Washington-Dulles International Airport. Look at the tire skid pattern from the landing airplanes.

The real runway is many times longer than it is wide. The images shown here have been stretched across the width of the runway and shrunk along the length to better see the pattern of use. Aside from this mild distortion, the tire skid pattern has not been altered.

The aiming point for landing pilots is indicated by two broad white rectangular marking stripes about 1,000 feet from the end of the runway. Touchdown zone markers are groups of one, two, or three rectangular bars every 500 feet arranged on either side of the runway center line.

This runway at Washington-Dulles airport is so long (11,500 feet) that pilots need not land exactly on the aiming point for safe operation. This along with the fact that they definitely don’t want to land short of the runway accounts for the skewed tire skid pattern. Note that although the skid pattern is skewed along the length of the runway it is symmetric across the width of the runway.

The skewness along the length of the runway shows that most of the airplanes land within 1,000 feet of the aiming point, but some land, as indicated by the skid pattern, much further down the runway. The symmetry across the width of the runway is, of course, due to the two sets of wheels of the landing gear and how accurately the pilots hit the centerline of the runway.

The second runway picture shows the entire 1L/19R runway (albeit distorted to fit the page). Notice now the U-shaped distribution of tire skids, as we see the accumulated skid marks from airplanes landing from both directions.

Poisson Parking

2007-06-11T11:53:00.001-04:00

The picture shows an aerial photograph, courtesy of the United States Geological Society, of the main visitor’s parking facility of business in Maryland on a Sunday morning in April. Look at the line of 13 parking spaces at the bottom of the picture. Notice the pattern in the oil stains leaked from the cars that park in those spaces. More oil is leaked in the spaces closest to the building.

Parking lots permit both the dynamic and static viewing of statistical processes. A time lapse film of customers entering and leaving a parking lot could allow us to estimate arrival rates, lengths of stay, or number of parked customers as time progresses. But automobiles, not being the cleanest of vehicles, leave their mark. This process is often modeled by a Poisson distribution. The actions of this process can be seen in static pictures as well.

Being Sunday no one is visiting the company, but the many previous visitors have left their marks. Notice the oil stains in the parking places. Much more oil is leaked and deposited in the places used most often. These places are the ones closest to the building. The one parking space closest to the building is a place for drivers with handicaps. Skip this space and examine the pattern starting with this first non-handicapped parking space. This first space will have oil stains when there are one or more cars in the lot. The second space will have oils stains when there are two or more cars in the lot, and so on. Thus, as the distance from the office front door to the car increases, then the amount of leaked oil decreases. This shows the steady state distribution of a multi-server queue. It takes the form of a truncated Poisson distribution, distributing Poisson probability only among the first few positive integers corresponding to the number of parking spaces.

Tri-modal distributions

2007-06-11T11:43:00.000-04:00

This is an image of tennis courts at Wimbledon via earth.google.com. Examine the wear pattern in the grass along the baselines.

In most of these courts three distinct areas of wear are obvious. Two are on each corner of the baseline to deliver the ball into the service boxes. The third is a more centrally placed area near the baseline where the players position themselves to anticipate the return volley. Additional wear up and down the baseline is added as the games progress. These are examples of tri-modal distributions, with three prominent areas of most frequent use. Other areas of wear can also be seen inside each of the service boxes, perhaps indicating wear due to doubles play.

Two of these courts seem to have more bi-modal wear patterns indicating mainly the serving positions of the players. Are they not playing a baseline game on these courts? Are these courts used exclusively for service practice?

Quincunx: a designer's view

2007-06-07T16:28:00.000-04:00

A very interesting qunicunx or Galton board illustration by Bob O'Keefe and Springer publishers from a few years back. Most obvious is the segregation of the colors. What could cause this? Perhaps a magnet? May the force be with you!
More subtle is the resulting distribution. It should look more bell-shaped rather than this triangular shape. You could get a triangular distribution from the sum of two uniform random variables, but it would require not pins to jostle the balls, no central hole for them to fall through, and a more symmetric supply of black and white balls. Something like this..

Imagine someone has loaded the balls in the equal-sided diamond-shape shown. The balls are held, waiting to fall above the the v-shaped retainer. Suppose the the entire retainer is removed, all at once. The balls fall straight down, through the slots, into the waiting bins below. The retainer is then replaced and refilled with balls. This is the image we see. This would achieve the resulting triangular distribution.

This, of course, still doesn't explain the segregation of the colors!

Highway Spacing Proportional to Population Density

2007-06-07T15:52:00.000-04:00

A map of the US Interstate System from Chris Yates via www.strangemaps.com
Note how the spacing is directly related to the population density. The distance from Daytona Beach to Tampa, Florida is only 132 miles. Compare that to the distance from San Antonio to Los Angeles: 1202 miles.

Galton's Quincunx

2007-06-07T14:04:00.000-04:00

A Qunicunx at the Instituto Butantan, São Paulo, Brazil.

The model was the invention of Sir Francis Galton, one of the English gentry scientists of the 19^th century. Galton was a cousin of Charles Darwin, and like Darwin, devoted himself to scientific explorations. He made significant contributions to meteorology, forensic science, and statistics. In the 1870s Galton developed a device to study dispersion of random events. His device consists of an array of pins that allows lead shot, encased behind glass, to cascade through. As a ball of shot falls it strikes a pin and falls randomly to the right or to the left, each equally likely. From there, the shot falls to the next level of pins where it repeats this random walk downward. The shot is collected in separate bins at the bottom of the device. The pattern of shot accumulated in the bins illustrates the variability associated with this simulation of a binomial experiment. He called his device a quincunx, due to the arrangement of pins like the pips on the number five side of a die. An illustration of Galton’s original quincunx can be found at the Galton Institute.

A Watery Histogram

2007-06-07T11:22:00.000-04:00

A view of the side of an office building in Washington, DC after a rain shower.

What to look for:

Notice the water on the wall, leaking from the downspout.

Statistical Concept: A histogram showing the pattern of leaking water similar to the way a Galton board, also called Galton's Qunicunx or binomial board, is used to illustrate the binomial probability distribution, also a diffusion pattern demonstrating horizontal spread as the water seeps horizontally and down into the porous brick wall.