Critical Thinking
Across the
Curriculum Project

Charts and Graphs:

In analyzing statistical arguments, often times the data is represented visually for increased impact. People are often able to understand or grasp more quickly the "meaning" behind data when it is presented visually. This has spawned all sorts of graphing programs or functions within programs with simplify this task. Unfortunately, it has also made it much easier to mis-represent the data so that conclusions (generalizations) can be drawn from the date which otherwise might not be warranted. For example, suppose I have data which tracks the status of a group of stocks which have been designated as those stocks which are the Leading Economic Indicators for the U.S. economy. The data for the first five months of the year are as follows:

• January - +0.04
• February - +0.03
• March - +0.01
• April - -0.01
• May - +0.09

Well, that doesn't show much, does it? We need to do something to make the change in the data visible. Plotted this way, we cannot even see the data points. Besides that, there is no visual interest. Let's address the scaling problem first. Instead of using a 0-100% scale, why don't we reduce the top end of the scale to 1% and extend the bottom of the scale to -.1%. With these changes to the plot, we get this graph:

That helps a little - at least now we can see the data and the changes from month to month. But there is still no visual interest. Why don't we try a 3-D plot?

Now that is better - not only can we see the data, but it looks much better than our 2-D plot. The problem is, I cannot make any valid conclusions about the economy from this data - people would realize, by looking at the graph, that the change from April to May was not that great. Let's reduce the scale of the upper range of the Yaxis from .1% to 0.04%.

Now that looks impressive. Now I can write an article in the financial section claiming that the economy is on the rise - people should buy stocks now to get in on the boom! (of course, I never mention the margin of error in this study) Remember, when I decreased the range of the Y axis, I increased the size of the difference between the data points proportionately.

What does this information tell us? Notice that the age ranges are not constant. What relevance do the size of the matches have?
 

Here is one of my favorite ones - Notice the source and the fact that none of the countries represented on the map compare to the U.S. school system. If you counted in summers and the December break, how many weeks of vacation do you suppose U.S. teachers enjoy? (14-16weeks) What conclusions do you suppose we are supposed to draw given this data? That U.S. teachers should get more paid vacation?

What does this tell us? Does this mean if I move to these zip codes I will be richer? What sort of average is a median score? Is this the same as the mean average? Would the difference between the two make any difference in our conclusions?

Gee, do you suppose there would be any reason to inflate these figures? (Where is the most money to be made in the future?) Does the size of the bars (those you can see) reflect the difference in the percentages? We also have to be wary - these are projected use figures. How did they do the projection? What time frame is this projection to? One year? Five years?

This is an interesting graphic. The headline seems to indicate that the percentages represent the number of students per computer in the respective school districts. Thus, Wyoming will have 7.0 students per computer (on average, I assume). A problem arises with at least three of the school districts, however - what is 7.6 students? What is 0.6 of a student? The real interesting thing about this graphic are the conclusions reached by the author of the accompanying article on the USA Today web site:

Computers seem to be taking over the world these days and no where do they seem as important as in our schools. But the availability of computers in the schools is spotty at best. Some of the lowest computer to student ratios are in the West. Some of the highest are in the East.

The first conclusion was that school districts in the East of the U.S. were doing better at providing computers to their students than those in the West. The author concluded this based on the percentages of computers per student in each school district. Now if we read the percentages as computers per students the conclusion is correct, but I doubt anyone would say that Wyoming is doing badly by providing 7 computers per student. This, however, seems highly unlikely. It is more likely that the percentages in the graphic represent the number of students per computer, in which case the conclusion that the Western states lag behind the Eastern states is unwarranted. In addition, the conclusion is based on figures from only 4-5 states. Is this a representative sample?

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Inquiries to: michael.connelly@mcckc.edu
Last modified: 03/02/04