MODULE 5
VISUAL DISPLAYS FOR CONTINUOUS VARIABLES
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Visual Displays for Continuous
Variables Introduction
Learning Objectives
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Evaluate visual displays of data for continuous variables.
A researcher conducted a study in which she observed students’ scores on an examination. One of the
first steps in analyzing a sample of data is to examine the distribution of values for variables in the data
set. The distribution of the data tells her about the frequency with which various values are observed.
Distributions can be examined in visual displays such as tables and graphs. A good graph or table is
informative and allows researchers to identify and communicate important characteristics of the data.
Different approaches are taken for visually displaying categorical and continuous variables.
Visual Displays of Categorical
Variables Introduction
Learning Objectives
•
Evaluate visual displays of categorical variables.
A researcher asks students how they perceived their body weight. They might respond
with overweight, underweight, or just about right, in which case each student is a unit of analysis, the
answer options represent categories of responses, each answer option is a value, and all of the students’
responses comprises a data set. One of the first steps in analyzing a sample of data such as this one is
to examine what is referred to as the distribution of values for the data set’s variables.
Visual displays of data help researchers communicate the distribution and other key information (the
story they are telling with their data) both effectively and efficiently, including for their own exploration. Put
another way, visual displays of data allow researchers to quickly identify interesting aspects of their data
(for example, are the study’s participants predominately satisfied with their body weight?), and to do so
more efficiently than merely using words. Researchers take different approaches for visually displaying
categorical and continuous variables. This skill builder focuses on visual displays for the former.
Identifying Categorical Variables
Categorical variables are those that have a small number of possible values. Usually, categorical
variables involve nominal or ordinal levels of measurement. For example, political party affiliation is an
example of a nominal, categorical variable. This variable places individuals into one of just a few
categories (e.g. Democrat, Republican, or Independent). An example of an ordinal, categorical variable is
highest grade completed, with categories of less than high school, high school diploma, and more than
high school. Again, this variable has just a small number of possible values. You will typically use
categorical methods of displaying data, such as a bar chart or a pie chart, when the number of categories
is less than 10 or 12. If there are too many categories, the displays become messy and difficult to read.
Also keep in mind that pie charts and bar charts are not typically used for non-categorical variables. An
example of a non-categorical variable would be students’ percentile ranking on a standardized math test;
this variable has a large range of values and students aren’t simply placed into one of a limited number of
categories.
Learn by Doing
Hints, displayed below
Which of the following variables would (YES) or would not (NO) be considered
a categorical variable amenable to a categorical visual display?
Table of multiple choice questions
Yes
No
Weight
perception
with values
of
underweight,
about right,
and
overweight
An
individual’s
weight
measured in
whole
pounds
Hair color
coded as
black,
brown,
blonde, red,
or other
Getting back to the study of body image, presume that the researcher actually has a random sample of
1,200 U.S. college students who were asked the question of how they perceive their body weight as part
of a larger survey. The following table shows part of the responses collected:
Body Image
Student
Body Image
student 25
overweight
student 26
about right
student 27
underweight
student 28
about right
student 29
about right
Here is some information that would be interesting to get from these data:
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What percentage of the sampled students fall into each category?
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How are students divided across the three body image categories? Are they
equally divided? If not, do the percentages follow some other kind of pattern?
There is no way to answer these questions by looking at the raw data, which are in the form of a
long list of 1,200 responses, and thus not very manageable. However, both of these questions can
be easily answered once the researcher summarizes how often each of the categories occurs and
looks at the frequency distribution of the different values for the variable Body Image.
Creating a table that presents the different values (categories) for the variable Body Image is the first
step to take to summarize the distribution of a categorical variable. For example, the table below
shows how many times the value “About right” occurs (count), and, more importantly, how often this
value occurs (relative frequency) as a percentage. To convert the counts to percentages, divide the
frequency (855) by the total number of observations (1200) to obtain the relative frequency, and
multiply by 100 to convert to a percentage.
Body Image Distribution
Category
Count
Percent
About right
855
(855/1200) * 100 = 71.3%
Overweight
235
(235/1200) * 100 = 19.6%
Underweight
110
(110/1200) * 100 = 9.2%
Total
n = 1200
100%
Did I Get This
What are the correct percentages for each of the two remaining values
(“Overweight” and “Underweight”) for the Body Image variable displayed in the
table below? Drag each percentage to its correct location.
Accessible mode
Screen reader users: use the accessible mode button above and use alt+down arrow to open the combo
boxes.
Category
Count
Percent
About right
855
(855/1200) ? 100=71.3%
Overweight
235
Underweight
110
Total
n=1200
100%
(235/1200) ? 100=19.6%
( 110/1200) ? 100=9.2%
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