# 21. Graphs II: The Worst and Better Graphs

At times, I strive to be an educated Simpleton.

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OK, we know that a great graph can Sing!!!  But do we know anything about what conveys information the best?  Yes.  Many psychology studies have been done to tell us what is good and what is ineffective.  The information I’ll be conveying will be from Naomi B. Robbins book Creating More Effective Graphs from Wiley (2005) and from a seminar she gave to the Deming Conference in December 2005.  The book is written in an exceptionally clear manner and goes over the worst and best of graphs.  It is both educational and entertaining.  She expects to reprint it this winter.  I highly, highly recommend it.  Her company’s website is http://www.nbr-graphs.com/.  I’ll attempt to summarize some of her suggestions and summary of the literature.

First, her goals:  “For our purposes, Graph B is considered more effective than Graph A if the quantitative information contained in Graph B can be decoded more quickly or more easily by most observers than of Graph A (from the 2005 seminar).”

Are there any graph types which are ineffective?  Yes, probably the most frequently used type of graph ever used – the pie chart.  Why?  Information in a pie chart is based on the angles of each wedge.  1) People can’t judge angle differences easily.  2) acute angles are underestimated and obtuse angles overestimated.  3) Angles on the horizon are overestimated relative to angles on the verticals.  One expert, Edward Tufte said, “Given their low data-density and failure to order numbers along a visual dimension, pie charts should never be used.”

Let me give an example from Dr. Robbins’ book:

What do you conclude from Figure 2.3 (sorry, about my first graph being 2.3, but that was her number)?

According to an graph expert William Cleveland, the following is the order from the best to worst (graph types on the same line [e.g., angle and slope] are approximately equal):

• Position along a common scale
• Position along identical, nonaligned scales
• Length
• Angle – Slope
• Area
• Volume
• Color hue – Color saturation – Density

If I said pie charts are poor, what can make them poorer?  Bling!  One no longer includes 3-D 32-pointed stars indicating direction (e.g., North) on maps; nor sea dragons or Neptune; nor curlicues.  Yet 3-D block charts, such as 2.3 above, are common.  Worse than 3-D block charts are 3-D block charts at an unusual angle and the bar not up against the scale.  The following is an illustration from Dr. Robbin’s book:

What is the height of bar 1?  Is it about 1.3 (from the front top)? Is it 1.7 (from the back top)? Is it 1.5 from the middle?  No!  No!  No!  If you pushed the bar back to where the scale begins, its height would be 2.0.  The eye was fooled by the downward looking prospective of the above graph.  Pseudo 3-D graphs are tasteless bling!

As mentioned above the best way to convey information is using a common scale.  Let me return to the percentages from pie-chart, Figure 2.3, and represent it using bars.

Did you conclude from pie chart, Figure 2.3, that the left most wedge was 40%?  That the other three wedges were all equal and all were 20%?  OK, enough said, pie charts are only useful for throwing into the faces of comic statisticians (an oxymoron, if I ever heard of one).

Going upward in Cleveland’s hierarchy is length.  Let me illustrate that with a stacked bar graph, in Figure 2.11.  What can you conclude from the top-most stacked bar, from ‘All Other OECD’?

Most people can’t judge the height of a bar ‘floating’ very easily.  So one simple solution is to pull out the information from ‘All Other OECD’ into its own figure, Figure 2.12.  Now, can you see a downward trend in the data.  Morale:  “it is very difficult to judge lengths that do not have a common baseline (Naomi Robbins, page 31).”

Dr. Robbins, also presented each of the subgroups side by side, so for year 77, she presented the US bar, the Japan bar, the West Germany, and the All Other OECD, followed by the four for 78, etc.  However, due to the clutter, it was more difficult to see any patterns.

I think that the above 2.12 is quite clean and understandable.  So if you have sub-groups which you want to present, it makes sense to ‘waste’ paper and present the sub-group alone with a common scale and without any other cluttering information.  Simple is often the best.

OK, simple is the best.  One last comment for this blog, the simple presentation of the key information is the best.  When dealing with the gold-standard active vs placebo study, the key information is not a plot of the active and placebo means.  No.  The key piece of information is the difference in the means.  People are frequently unable to discern visual differences.  Take the following top plot.  What can you conclude about the difference in balance of trade?

Yes, we can easily see the large difference between 1720 and 1740.  But did you pick up the spike after 1760 presented in the bottom plot?  “We miss it because our eyes look at the closest point, rather than the vertical distance (Naomi Robbins, p 37).”

Simple truth:  If we are interested in the difference between active and placebo, then we need to plot the difference between active and placebo.

If this was the difference between active and placebo over time, then the only tweak I might make is to include the 95% CI on the difference, with a horizontal line at 0.0 to see if the lower CI bar ever is above zero (i.e., is statistically significant).

Primary lesson:  Keep it simple, keep it to the point, stress the key objectives of the research.

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