Correlations of Google Search Rankings with State Statistics

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

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

Aggregated Images of Emotions

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

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

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

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

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

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

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

via: reddit
Nothing more need be said!

Election References

A display of the frequency of references to the candidates.

Interactive Bar Chart

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

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

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

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

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

Very cool interactive graphic from the New York Times.

The Office : Not Mutually Independent

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

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

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

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

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

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