Last week Cora and I explained how to read a simple stock chart, also known as a table that displays a line graph. This week, I promised to bring you some chart problems that often mislead readers. This information is important if you or your children use software programs that allow you to display statistical data as visuals, because it helps to remember that simple is often best. More importantly, if you and your children understand how companies (or news feeds) use charts to display data, the companies that use complicated charts may suddenly appear unreasonably complicated as well.

The graphics that companies or news feeds use to display statistical data can either be clear and meaningful or unnecessarily complicated. Even well-made graphic displays can mislead readers who don't know how to interpret them. Below is a short list about problems to notice when you view or create visual graphs and charts.

Perceptual Distortions: Drawings that contain distorted visuals illustrates one of the most common types of misleading information. Say that you come across a display that shows three hands, and each hand holds a candy bar. The goal for this chart is to show readers how the size of the candy bar has shrunk over the past twenty-five years. In this display, the hands are all the same size, and they line up vertically along the page.

The first hand, located at the top, holds the largest candy bar. The figures printed alongside this hand read, "1980 = 100%." In other words, the information on this chart is based on the year 1980, and the candy bar represents a relative size of 100%. The second hand, located below the 1980 hand, has a slightly smaller candy bar and the figures along the side of this hand state, "1995 = 60%." The candy bar, then, shrank 40% between 1980 and 1995 (100% - 60% = 40%). The final hand, which represents 2005, is the lowest hand on this vertical display. The candy bar in this hand is very small, and the figures typed in along the side of this hand and its candy bar state, "2005 = 48%."

The problems in this particular graph include:

1. Visual distortion makes the smaller candy bar appear even smaller than the actual size, and the larger candy bar appear even larger than the actual size. Often, the actual graphic is smaller than the data shown. For example, the 2005 candy bar is 48% of the 1980 bar, but the actual drawing may be less than 25% of the original drawn candy bar.
2. The years are uneven, and this error makes the candy bar appear to shrink rapidly. Instead of "1980-1995-2005," the years should show "1980-1985-1990-1995-2000-2005" to illustrate reasonable and even space between years.

Perceptual distortion was so common during the late 1800s that German researchers gave it a name, roughly translated as "the old goosing up the effect by squaring the eyeball trick."* I call it, "telling a lie with distorted graphics."

Data Distortion: We covered this information last week, but I'll quickly refresh you on the problem. When you look at stock charts, for instance, and if none of them begin at "0" along the vertical left-hand side of a chart (where the cost and volume were listed at the BUYandHOLD charts), then the information was NOT distorted. However, the information contained in a chart that doesn't begin with zero and that doesn't end at "100" (or 100%), may look far less dramatic. This doesn't mean the information isn't correct, though.

But - when the information along this left-hand vertical side of a chart is unevenly spaced, then you have problems. Say the candy bars and the hands in the example above were removed, but the data remained. What's left? The years "1980, 1995, and 2005" would be arranged along the bottom horizontal area of a chart, and the percentages, "100%, 63%, and 48%" would be placed along that left-hand vertical side of the chart.

The remedies to this problem are easier to impart than the problems?the years need to be spaced evenly, as mentioned in the previous example. Additionally, the percentages need to begin at "0" and end at "100" or 100%. Then, the chart would represent a clearer picture of how that candy bar shrunk over the years.

Percentage Problems: The New York Times printed a graph in their 6 October 1999 issue to explain rising costs for public and private colleges against the rate of increase in these same costs. The illustration contained two charts, one above the other. The top chart contained a bar graph, or a graph that used vertical colored bars to demonstrate changes. The second table, located directly beneath the first one, contained two line graphs similar to the ones in the cost charts at BUYandHOLD.

At first glance, the lower graph gives the impression that college costs fell steadily throughout the 1990s. However, a closer look reveals that the vertical axis showed percentages increases, so the downward-sloping lines show only that the rate of increase in college costs decreased, not the actual costs. The actual costs, shown in the top graph, revealed that the actual costs rose substantially. Without reference to the actual text in the body copy, the charts seen alone seem contradictory. This chart wasn't meant to be misleading, but the way that it was presented remains confusing.

From the examples above, then, a reader can look out for image distortion, data distortion, and percentages used as categories in the vertical axis, rather than actual figures. Other problems are also visual. When you see a chart that contains 3D graphics, drop-shadows, or graphs that show pictures rather than simple line, bar, or pie charts, then you know that the data may at least seem distorted. Next week we'll show you (and the kids) how to create a simple chart. Then, you might wonder why companies and news feed choose to display distorted data to their audiences.

Until Then,
Linda Goin

* Jeffrey O. Bennett and William L. Briggs, Using and Understanding Mathematics, a Quantitative Reasoning Approach, 2nd ed (Boston: Addison Wesley, 2002), 333.