Bar charts can also be used to represent frequencies ofdifferent categories. A bar chart of the iMac purchases is
shown in
. Frequencies are shown on the Y
axis and the type of computer previously owned is shown on theX axis. Typically the Y-axis shows the number of observations
rather than the percentage of observations in each category asis typical in pie charts.
Bar chart of iMac purchases as a function of
previous computer ownership.
Often we need to compare the results of different surveys,or of different conditions within the same overall
survey. In this case, we are comparing the
distributions of responses between the surveys
or conditions. Bar charts are often excellent forillustrating differences between two distributions.
shows the number of people playing card
games at the Yahoo website on a Sunday and on a Wednesday on
a day in the Spring of 2001. We see that there were moreplayers overall on Wednesday compared to Sunday. The number
of people playing Pinochle was nonetheless the same on thesetwo days. In contrast, there were about twice as many people
playing hearts on Wednesday as on Sunday. Facts like theseemerge clearly from a well-designed bar chart.
A bar chart of the number of people playing different
card games on Sunday and Wednesday. The bars in
are oriented horizontally
rather than vertically. The horizontal format is useful whenyou have many categories because there is more room for the
category labels. Such
horizontal bar charts may
be contrasted with
vertical bar charts like the
one in
.
We'll have more to say about bar charts when we consider
numerical quantities later in this chapter. (See
Bar Charts .)
Some graphical mistakes to avoid
Don't get fancy! People sometimes add features to graphs that
don't help to convey their information. For example,3-dimensional bar charts like the one shown in
are usually not as effective as their
two-dimensional counterparts.
A three-dimensional version of
. Here is another way that fanciness can lead to
trouble. Instead of plain bars, it is tempting to substitutemeaningful images. For example,
presents
the iMac data using pictures of computers. The heights of thepictures accurately represent the number of buyers, yet
is misleading because the viewer's attention
will be captured by areas. This can exaggerate the sizedifferences between the groups. In terms of percentages, the
ratio of previous Macintosh owners to previous Windows ownersis about 6 to 1. But the ratio of the two areas in
is about 35 to 1. A biased person wishing to
hide the fact that many Windows owners purchased iMacs wouldbe tempted to use
instead of
!
Edward Tufte coined
the term
lie factor to refer to the ratio of the size of the
effect shown in a graph to the size of the effect shown in thedata. He suggests that lie factors greater than 1.05 or less
than 0.95 produce unacceptable distortion.
A redrawing of
with a lie factor
greater than 8. Another distortion in bar charts results from setting the
baseline to a value other than zero. The baseline is thebottom of the Y-axis, representing the least number of cases
that could have occurred in a category. Normally, this numbershould be zero.
shows the iMac data with
a baseline of 50. Once again, the difference in areas suggestsa different story than the true differences in
percentages. The number of Windows-switchers seems minusculecompared to its true value of 12%.
A redrawing of
with a baseline of
50. Finally, we note that it is a serious mistake to use a line
graph when the X-axis contains merely qualitative variables. Aline graph is essentially a bar graph with the tops of the bars
represented by points joined by lines (the rest of the bar issuppressed).
inappropriately shows a line
graph of the card game data from Yahoo. The drawback to
is that it gives the false impression that the
games are naturally ordered in a numerical way.
A line graph of the number of people playing
different card games on Sunday and Wednesday.
Summary
Pie charts and bar charts can both be effective methods of
portraying qualitative data. Bar charts are better when thereare more than just a few categories and for comparing two or
more distributions. Be careful to avoid creating misleadinggraphs.
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Source:
OpenStax, Collaborative statistics (custom online version modified by t. short). OpenStax CNX. Jul 15, 2013 Download for free at http://cnx.org/content/col11476/1.5
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