ECON 309
Lecture 3: Use and Abuse of Graphs
I. Basic Guidelines for Graphs and Other Visual Aids
The purpose of a graph, or other visual representation of data, is to make information
easier to understand, not harder. That means having clear labels (including units of
measure), plus an explanatory title. It also means not employing “snazzy” effects that
impede understandability, such as 3D effects and pictographs that make it difficult to tell
relative sizes. (More on this later.)
Relatedly, a graph should be easy to look at. Don’t just accept Excel’s default settings!
Change fonts of labels, legend, and axis markers to make them easy to read. Change
colors, spacing of gridlines, etc., to make them look nice.
State your sources under the graph, under the title, or somewhere else nearby. Don’t bury
your source in the text (although it’s okay to leave other details in the text, such as the
precise methodology used to collect the data).
Most importantly, know the point you want to make. Graphs should not be included
simply to look smart. They should be included because they help you convey
information better or more quickly than text. And what information you wish to convey,
or what kind of story you want to tell, with your graph will determine the specific kind of
graph you use. In short: Have a point, pick the right data to support your point, and pick
the right graph to display your data.
II. Pie Charts
A pie chart is best used to display and compare percentages of a whole. This means there
are two important principles for using a pie chart: (a) the total must be meaningful, and
(b) you cannot leave out anything that forms a part of that total; this may necessitate
including an “other” category.
[Use graphs1.xls to demonstrate. The pie chart of my family’s ages (Pie 1) is silly,
because the total has little meaning – it’s the total number of years lived by members of
my family. The pie chart of the top four market shares (Pie 2) is bad, because the total
should be 100% of market share, which means that an “other” category (as in Pie 3) is
needed. Using an exploded pie (Pie 4) is snazzy but unnecessary, and it makes it more
difficult to do comparisons. All that matters is the size of the top surface, but the eye
wants to look at the whole 3D slice, which is obscured for the back slices but not the
front ones. The orientation of the 3D exploded pie also matters; if Pie 4 had been rotated
a little clockwise, we could have seen more of the side of the “other” slice.]
How to create a pie chart in Excel: Highlight the data that you wish to chart. Go to the
Insert menu, and click the Pie Chart icon. Choose the kind of pie – usually the 2D, nonexploded variety. Use right-click “Select Data” to make changes to the use of data in the
pie chart; this will usually be necessary. If your highlighted data includes data you don’t
want in the pie, you can delete one or more series of data in the left-hand panel. (For
instance, to create the pie chart for 2020 data after highlighting ten years’ worth of data, I
had to delete all the series for each of the other 9 years.) After you’re finished with the
Wizard, make changes to fonts, colors, etc. as necessary. [Demonstrate using PRA data.]
III. Bar Charts
A bar chart is any chart that shows values for different categories using bars with lengths
corresponding to values. The bars can be horizontal or vertical; Excel calls bar charts
with vertical bars “column charts.”
Histograms, which we’ve already used, are bar charts where the values represented are
frequencies.
Bar charts are best used when you want to compare actual values, rather than percentages
of a total, across categories. (You can use them to compare percentages of a total, too,
but a pie chart is usually better for that.)
When you use a stacked bar chart, you’re stacking different types of value, so that each
color in a bar is a different kind of value. If you do this, the total of those different types
of values should mean something. Stacking allows easier comparison of the totals, but it
also makes it more difficult to compare the component values.
[Use graphs1.xls to demonstrate. Bar 1 is fine. Bar 2 has stacked sales and
expenditures, but the sum of sales and expenditures has no meaning. Bar 3 uses
unnecessary 3D effects that make it more difficult to see the values associated with the
bars.]
Bar charts are best used for a relatively small number of categories – say, ten or fewer.
For a larger amount of information, a table is better. [Use interestrates.xls to
demonstrate. Bar 1 shows a bar graph with too many categories.]
IV. Line Charts
Line charts are best used for tracking change over time. That means the horizontal axis
will be time. They can also be used when there is a natural order to the items on the
horizontal axis – for instance, the ranking of finishers in a marathon.
Line charts can be used for other purposes, but it’s usually misleading to do so. There is
a bad example in Donnelly, p. 43, where he uses a line graph to show the relationship
between number of showers and monthly utility bills. He uses a line graph to show the
general upward direction. A scatterplot with a best-fit line would have accomplished this
better. A naïve reader might get the false impression that these points represent an
upward trend in utility bills or showers over time. A look at the source data in the table
above the chart shows this is not the case.
[Use graphs1.xls to demonstrate. Line 1 shows a line graph of the ages of family
members, as though to show the change in age that occurs when one family member
becomes another. This is a poor use of a line graph. Also look at interestrates.xls. Line
1 shows a line graph with categories instead of time on the horizontal axis. This creates
the illusion of big changes occurring.]
Line graphs can be used to show change in various ways. One way is simply to graph a
total value for each time period. In this kind of line graph, the amount of change over
time is shown by slope or the amount of fluctuation in the line. [Use graphs1.xls to
demonstrate. Line 2 shows total sales for two firms over ten years. This shows how
much both companies have grown with the industry; also, you can see the continuing
dominance of one firm.]
Or you can do a line graph in which you track percent change in a value relative to the
previous year’s value. To do this, you’ll need to create a data series for each period’s
total figure as a percentage of the previous period’s total figure. [Use graphs1.xls. Line
3 shows percent change in sales. The fact that all values are positive means the firms’
sales have been growing, but the overall downward slope means the growth rate has been
declining.]
Or you can do a line graph in which you track percent change in a value relative to a base
year; this is called indexing. To do this, you’ll need to create a data series for each
period’s total figure as a percentage of the base year’s total figure. This is called
normalizing a variable. [Use graphs1.xls. Line 4 shows an index of sales, using 2011 as
the base year. In this case, we can see that both firms have grown by several hundred
percent, but one firm has grown a lot more than the other. Notice that this is actually the
smaller firm.]
Which type of line graph should you use? It depends on the point you want to make.
V. Misleading Uses of Graphs
There are innumerable ways in which graphs can be misleading, but here are some of the
most common.
Missing labels. What is being measured, and what are the units? Are we looking at
totals, percent changes, or an index relative to a base year?
Example from Huff, p. 50. How is energy release being measured?
Example from Huff, p. 51. What is being measured at all?
Manipulative ranges. You can fiddle with the range of vertical values to dampen or
exaggerate the variation in whatever is being measured.
Example from Huff, p. 61-63. A mild upward trend is made to look gigantic.
Example from Huff, p. 65. Are government payrolls skyrocketing?
Example from Huff, p. 65. Here, a bar chart gets the treatment. Notice that the
ratio between bar heights no longer has meaning.
Manipulative pictograms. A pictogram represents amounts using little pictures (stick
men, bottles, etc.) to represent quantities of something. This is fine if each picture
represents the same amount, so that a larger amount is shown by having a larger number
of the same-size picture. But it can be highly misleading if a larger amount is shown with
a larger picture. Why? Because if the picture is increased proportionally in both
dimensions, its total area will increase by the square of the proportional increase in one
dimension.
Examples from Huff, p. 71, 72, and 73. In all these cases, the quantities or values
being represented are represented by the height only. But the eye notices the
whole area of the picture, which implies a much greater amount of difference.
[Demonstrate more contemporary examples of misleading and/or confusing graphs using
charts.ppt.]