Basic
Skills and Principles: Statistics and Graphing
Presenting
Data
Choosing the Values to Graph
Students
can also have difficulty with graphing because they are unsure exactly
what data to graph. Let's examine an example to show you what I
mean.
Let's
assume that a researcher is attempting to determine the effects
of pesticide pollution on the hatching success of fish eggs.
He has noticed that fish eggs in streams near agricultural
fields fare poorly, while those is undisturbed areas hatch
successfully. The researcher sets up a lab experiment in which
ten groups of fish eggs are allowed to develop in unmanipulated
stream water, and ten groups of eggs develop in stream water
with the addition of pesticide. The proportion of eggs hatching
in each group is tallied (Table 3), and descriptive statistics
for the two groups compared.
Statistic

No
Pesticide

Pesticide

Mean
proportion eggs hatching 
0.87

0.59

Standard
deviation 
0.07

0.09


Group

Proportion
eggs hatching

No
Pesticide

Pesticide

1

0.80

0.50

2

0.76

0.45

3

0.81

0.68

4

0.90

0.77

5

0.95

0.64

6

0.84

0.60

7

0.88

0.54

8

0.99

0.57

9

0.86

0.62

10

0.93

0.57

Table
3. Effects of pesticide pollution on
hatching success of fish eggs.

Now
that we have the data, how do we graph it? First, we determine that
a bar graph is most appropriate, as the independent variable is
the two groups, and this is categorical, not continuous. Second,
we must determine what to graph. If we graph all of the values,
we get a graph like the one below.
Figure
12. Effects of pesticide pollution on
hatching success of fish eggs.
But
what does this graph tell you? There are 20 bars, 2 categories,
and lots of different group numbers of mix things up. If we take
a step back and look at the study, what we're really interested
in doing is comparing the hatching success in groups exposed to
pesticide and the groups not exposed to pesticide. So what we really
want to do is to graph the mean of the two groups and compare them
to one another. If we do that, we get a graph that looks like:
Figure
13. Effects of pesticide pollution on
hatching success of fish eggs.
Now
while this graph is useful in that it readily allows us to compare
the means of the two groups, it doesn't provide us with any indication
of the spread of the data in each group. Knowing the spread of the
data can be important in making conclusions, so you need to provide
the reader with this information. This is done by adding "error
bars" to data points or bars on a graph that indicate the standard
deviation of the data. In this example, we would add the standard
deviation error bar to the bar for each group. In bar and line charts,
error bars are drawn both above and below the mean to a distance
equal to their value.
Figure
14. Effects of pesticide pollution on
hatching success of fish eggs.
Realize
that error bars are only appropriate when graphing a group's mean.
If you are graphing individual data points, you cannot add error
bars as there is only one data point per point on the graph (hence,
no mean or standard deviation). Error bars are useful in that they
allow you to see the overlap in the data points from two groups.
Remembering that all of the data points in a distribution are within
two standard deviations of the mean, you can visually estimate the
data's distribution by doubling the height of the error bar (because
it's only drawn to one standard deviation) for each group and seeing
the degree to which their distributions overlap. As shown in the
examples below, including error bars can make a big difference in
your interpretation of a graph. Although the means of the two groups
are identical in each of the graphs, the two groups in the first
figure appear to be more different from one another than the two
in the second figure due to the smaller error bars and lesser degree
of overlap.
Figure
15. The role of error bars in estimating differences in treatment
groups
Creating
Graphs
You may choose to make your graphs by hand or with the assistance
of a computer software application. In either case, you need to
make sure your choice of graphs, the data to graph, and the formatting
are all appropriate. There are several software applications that
enable you to create graphs (e.g., Microsoft Excel) that are available
in the campus computer labs. There are also some web sites that
allow you to create graphs online, and they are listed below. Providing
directions for graph preparation in each would be prohibitively
long, so you will need to become familiar with their operation on
your own if you opt to use them.
StatCrunch:
http://www.statcrunch.com/
National
Center for Education Statistics: http://www.nces.ed.gov/nceskids/graphing/
