• What if you have a 900 square foot area? Might look between nearby points.
• Or a 100 square foot area? Only one nearby point.

Is there a relationship you can use?

(Text figure’s source: Carey, Morris, and James. Home Improvement for Dummies, IDG Books.)

• A first thought is to use a line.
• People often build items to fit lines; it’s how we tend to think.
• But the relationship here doesn’t look like a line, does it?

• As a first step, get rid of the bars.
  • The areas have no meaning.
  • But they aren’t bad here, more on that later.
• We haven’t changed the data, so this still does not appear to be a line.

• Trying a statistical line fit: Definitely no line here.
• But look at the x axis.
• Are the points spaced appropriately?

• Spread the points out, and suddenly we do have a line.
  • The BTU measurements likely are rounded, so not a perfect line.
• Now we can predict the BTUs needed for any size without having to poke at nearby points and estimate differences.

• Bar charts like these often are tables and not graphs.
• Inductive reasoning: Keep track of your assumptions when extrapolating visual relationships.

• Remember in the bar chart: Areas did not matter.
• People are very, very bad at judging areas.
• Given the one baloon represents 12%, how large is the one next to it?

(From the Onion (//www.theonion.com:http://www.theonion.com))

• Given the one baloon represents 12%, how large is the one next to it?
• 22%
• This is the Onion, but the graph is to scale.
• Not by area, but by length.
• But you see area first\mathop{\mathop{…}}

(From the Onion (//www.theonion.com:http://www.theonion.com))

• Also beware graphs with too much of a “slant”.
  • (multiple meanings here)
• In a “pie chart”, areas are the data.
• But people are very, very bad at judging areas.
• Which is larger, 19.5% or 21.2%?
• Who is the 19.5% in this image?
• Avoid 3D effects!

(at Macworld 2008, photo from Ryan Block of Engadget (//www.engardget.com:http://www.engardget.com))

• Never be afraid of using small tables.
• Is there a problem with other being the second largest?
• other: LG, Samsung, Ericsson, \mathop{\mathop{…}}
• Knowing your premises:
  • US-only.
    • Nokia is #1 world-wide (40%)
    • Samsung is #2 (15%)
    • Motorola is #3 (10%)
  • No history in this table, no idea about future.

• Purpose: Display all our experimental data without much interpretation.
• Too much data for a simple table?
• On the left: algorithms and data cases (plain v. exceptional)
• Blocks: Specific processors
• Below: CPU/processor cycles per array entry
• Dotted vert. line: CPU cycles for a critical operation
• Colors and symbols: “direction” of algorithm and data cases (repeated!)
• Graph allows simple comparisons of our raw data.

(from Marques, Riedy, and Vömel. Benefits of IEEE-754 features in modern symmetric tridiagonal eigensolvers)

• Purpose: Determine if CPUs impose penalties on certain arithmetic features.
• Each algorithm (green bars) uses a different feature.
• Ratio of “careful” over “plain” shows a slow-down.
• Find outliers by looking down and across:
  • One direction (“progressive”) encounters more problems than the other (“stationary”)?
  • Missing data here: “stationary” ran far more slowly, slow-down hidden by total cost.

(from Marques, Riedy, and Vömel. Benefits of IEEE-754 features in modern symmetric tridiagonal eigensolvers)

• Purpose: Begin interpreting the data to determine which single algorithm should be used.
• Chose one algorithm, “B”, to normalize others (2.2, 2.4).
  • Reviewers (and authors) missed a typo. “B” should be 2.3.
• Could this have been a table?
  • More than a page of data in tabular form.
  • Can be summarized by statistics (median and percentiles).
  • Summaries were in the text.
• Does this serve its purpose?
  • With hindsight, not really.
  • Summary in the text was better.
  • This plot was unnecessary.

(from Marques, Riedy, and Vömel. Benefits of IEEE-754 features in modern symmetric tridiagonal eigensolvers)