Day 33: Heart of Mathematics

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Announcements:
- Your Dynamics assignment is due today.
- Homework for the graphs unit:
  - Problem #30, p. 608; and then adapt the exercise by replacing the word "statistics" with the word "graphics". Due Wed., 11/19.
- Show-n-Tell topics should be something you've seen, something you've thought about, something you've encountered that means more because of this class. If you need ideas, stop in and see me some time...
"Lying with Graphs"...
- There are several take-home messages that we want to become aware of:
  1. Scales on graphs:
    - Where do they start?
    - Why do they start there?
    - How do they grow?
    - Why do they grow that way?
    - Does size matter?
    - There are several different kinds of scales:
      - Categorical (just names or categories)
      - Ordinal (ordered, e.g. lowest to highest)
      - Numerical (with relative order essential)
    - Let's look at some examples:
      1. Consider our authors' example on page 589: two histograms of heights.
      2. Let's revisit our financial dynamical systems to see how scales were used.
      3. This site describes a personal experience with a graphic along the same lines as my financial graphics above -- only with a scaling twist.
      4. Here is a humorous view of scales that also illustrates something about those lyin' statistics.
      5. In the "Does size matter?" category, we have the following emotionally charged graphic (and several alternatives), representing abortion
      6. Here's another, with less emotional content, about the Shrinking value of a dollar
        What determines the brain/eye's perception: length, or area?
      7. Here's another one: The Incredible Shrinking Doctor
      8. And another, slightly different, and slightly worse!: Alcohol and Tobacco Use
      9. And finally, often it's not our objective to lie, but rather to clarify, that leads us to "change scales". For example, let's consider how to choose bin size to view a histogram:
        
        Cicada-killing wasps and their prey
  2. Dimensions of content:
    - Issues:
      - How many dimensions of information does a graph contain?
      - Are they the right dimensions, or could they be combined?
      - Is the graph overloaded?
    - A bar or pie chart contains only one dimension of information; a histogram, or scatterplot of two variables x and y, contains two (e.g. Fat and Your Risk of Colon Cancer; although labels give additional "dimension" (but usually only categorical).
      But graphs can easily contain more than two dimensions.
    - It's easy to make a bar chart do double duty, as we see here in this graph of Energy use versus population.
    - The classic example of a good graphic (containing more than two dimensions -- at least four dimensions, in fact) is
      
      Napoleon's March to Moscow, by Charles Joseph Minard
      Edward Tufte, who is a great fan of this graph, talks about "simple design, intense content". This graphic illustrates it. This might be Tufte's version of "Our goal is to create an image that reveals the structure that the data contains."
      Charles Joseph Minard did a similar map for the
      March of Hannibal from Spain to Italy
    - Here's a sort of variant of those, about the Shrinking Farm Food Dollar. It's nice to put a little humor into a graph, if it doesn't get in the way....
    - A few others:
  3. The type of graphic: (we have choices, after all!)
    - Our authors propose pie charts: others argue against them
      Notice that pie charts use areas proportionally to the values represented (not heights or widths, as we saw in the doctor and dollar graphics above).
    - It is little known that Florence Nightingale, nurse extraordinaire, was also the creator of a sophisticated version of the pie chart. She is called "... a pioneer in the visual presentation of information and statistical graphics."
  4. "Emotional content" of a graphic:
    - We have to be careful to refrain from letting our statement or aesthetic issues get in the way of presenting the data. For example, this illustration of the disparity between the CEO and the average worker.
    - Here's one that I think is done beautifully: U.S. Private Wealth in Perspective. This may be due in part to the change in the Tax Rates Over Time in the US.
- Tufte fights not just for "simple design, intense content", but also against the flattening of information that has occurred with the advent of PowerPoint. Here is a classic example of PowerPoint abuse.

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