Teaching Basic Quantitative Concepts with Visualizations

Data do not speak. As has famously been noted, data and especially data displays –whether maps, statistics, or word clouds– can lie or at least be deceptive. Access to easy methods for generating visualizations and analyses may be as dangerous as liberating, unless we are careful as both producers and consumers.

The following three maps all show exactly the same data, but look very different—due to the choices made in display.

The first map uses natural breaks in the data to separate categories. The second uses quartiles, a measure based on medians. For this the states are separated into 4 equal piles and the most densely-populated states are given the darkest color. Note how much variation this group exhibits. While the least dense two groups have only a small range, the range for the most densely populated is huge. Continue reading →

Using Cartograms as a Visualization Tool: An Interactive Tool for Exploring Fertility Rates

Cartogram of the world based on population size.

Cartograms are spatial depictions that rely on quantitative attributes other than area to size their units. The most common cartograms show the world, and distort it by population or by wealth, but any geographic entity can be transformed into a cartogram. Because they force us to view the map in unfamiliar ways, cartograms provide dramatic visual portrayals of geographic, political, and socio-economic relationships. A look at a cartogram of the world based on population (above) quickly shows the potentially dominant places of India and China in Asia with respect to Russia and the significance of Korea and Japan as well.

The world sized by Gross National Product (GDP).

Quite a different picture is presented by the world sized by Gross Domestic Product (GDP).  Here the U.S. and Europe dominate.  China is still large,Russia is still small, and the importance of Korea and Japan is still evident.

 No weighting variable: the estimate is that about 50% of the population knows that the Jewish Sabbath starts on Friday. Appropriately weighted data: The estimate changes by about 5 percentage points, suggesting that only 45% of the population knows the correct start time.

Full disclosure: I approach this topic simultaneously from the perspective of a social scientist and as the instructor of a traditional introductory statistics class for over twenty years. I am, thus, myself part of the problem. While I am mainly following the dictates of some of the most popular text books, it is fully within my power to diverge from the book. When I do not do so, it is really my own fault—a sheep following the sheep dogs.

Our worst failure as statistics teachers is to teach as if all or most of the data that our students will engage with in their future careers are from simple random samples. Continue reading →