The Statistical Imagination
• Chapter 3. Charts and Graphs:
A Picture Says a Thousand
Words
© 2008 McGraw-Hill Higher Education
Graphs and Charts: Pictorial
Presentation of Data
• Graphs and charts provide a
direct sense of proportion
• With graphics, visible spatial
features substitute for abstract
numbers
© 2008 McGraw-Hill Higher Education
Types of Graphs and Levels of
Measurement
• For nominal/ordinal variables,
use pie charts and bar charts
• For interval/ratio variables, use
histograms and polygons (line
graphs)
© 2008 McGraw-Hill Higher Education
Graphing and Table Guidelines
• Choose a design based on a variable’s
level of measurement, study objectives,
and targeted audience
• A good graphic simplifies, not complicates
• A good graph is self-explanatory
• Produce rough drafts and seek advice
• Adhere to inclusiveness and exclusiveness
• Provide a descriptive title and indicate the
source of material
• Scrutinize computer generated graphics
© 2008 McGraw-Hill Higher Education
Pie Chart
• A circle that is dissected or sliced
from its center point with each slice
representing the proportional
frequency of a category of a
nominal/ordinal variable
• Pie charts are especially useful for
conveying a sense of fairness,
relative size, or inequality among
categories
© 2008 McGraw-Hill Higher Education
Constructing a Pie Chart
• To determine the correct size of a
“slice,” multiply a category’s
proportional frequency by 360
degrees
• Use a protractor to cut the pie
• Percentages are placed on the pie
chart for the sake of clarity
© 2008 McGraw-Hill Higher Education
Interpreting a Pie Chart
• Focus on the largest pie slice (i.e., the
category with the highest percentage
frequency) and comment on it
• Compare slices and comment on stark
differences in sizes
• Compare the results to other
populations
• Summarize with a main point
© 2008 McGraw-Hill Higher Education
Bar Chart
• A series of vertical or horizontal bars
with the length of a bar representing
the percentage frequency of a
category of a nominal/ordinal variable
• Bar charts are especially useful for
conveying a sense of competition
among categories
© 2008 McGraw-Hill Higher Education
Constructing a Bar Chart
• Construct on two axes, the abscissa (horizontal)
and the ordinate (vertical)
• Categories of a variable are situated on one axis,
and markings for percentages on the other
• To determine the correct bar size for a category,
compute its percentage frequency
• To compare several groups, use clustered bar
charts
© 2008 McGraw-Hill Higher Education
Interpreting a Bar Chart
• Observe the heights of bars and
comment on the tallest (i.e., the
category with the highest frequency)
• Compare and rank heights of bars and
comment on stark differences
• Compare the results to other
populations
• Summarize with a main point
© 2008 McGraw-Hill Higher Education
Frequency Histogram
• A 90-degree plot presenting the
scores of an interval/ratio variable
along the horizontal axis and the
frequency of each score in a column
parallel to the vertical axis
• Similar to bar charts except columns
may touch to account for real limits
and the principle of inclusiveness
© 2008 McGraw-Hill Higher Education
Constructing a Histogram
• Work from a frequency distribution and
calculate the real limits of each score of X.
• Draw the horizontal axis and label for X.
Draw the vertical axis and label for
frequency of cases
• Draw the columns with the height of a
column representing the frequency of
scores for a given real limit span of X
• The width of each column of the histogram
will be the same
© 2008 McGraw-Hill Higher Education
Interpreting Frequency
Histograms
• Observe the heights of columns and
note the tallest (i.e., the score with the
highest frequency)
• Look for clusters of columns and a
“central tendency”
• Look for symmetry (balance) in the
shape of the histogram
• Summarize with a main point
© 2008 McGraw-Hill Higher Education
Frequency Polygon
• A 90-degree plot with interval/ratio scores plotted
on the horizontal axis and score frequencies
depicted by the heights of dots located above
scores and connected by straight lines
• Portrays a sense of trend or movement
• Especially useful for comparing two or more
samples
© 2008 McGraw-Hill Higher Education
Constructing a Polygon
• Work from a frequency distribution
• Draw the horizontal axis and label for the
variable X. Draw the vertical axis and label
for the frequency or percentage of cases
• Place dots above the scores X at the
height of the frequency or percentage
frequency
• Connect the dots with straight lines, closing
the ends to the baseline of the lower and
upper real limits of the distribution
© 2008 McGraw-Hill Higher Education
Interpreting Polygons
• Look for peaks and comment on the tallest
(i.e., the score with the highest frequency)
• Look for expanse of space under the line and
for peaks and valleys
• Look for a “central tendency”
• Look for symmetry (balance) in the shape of
the line graph
• Summarize with a main point
© 2008 McGraw-Hill Higher Education
Polygons with Two
or More Groups
• When two or more groups (populations,
samples, or subsamples) are plotted,
compare their peaks and shapes
• Plot percentage frequencies to adjust for
differing group sizes
• Look for contrasting central tendencies
among the groups
• Note the presence or lack of overlap in the
polygons of any two groups
© 2008 McGraw-Hill Higher Education
Graphs Reveal Outliers
• For a distribution of scores, an
outlier (or deviant) score is one that
stands out as markedly different
from the others
• With a trained eye, outliers may be
noted in a frequency distribution,
but are easily detected with graphs
© 2008 McGraw-Hill Higher Education
Statistical Follies
• Graphs may be intentionally or
mistakenly distorted
• Make sure any claimed differences in
scores is real and not simply a distortion
of the graphic
• Use computer graphics carefully and
edit output. Rely on the computer as
simply a drawing tool
© 2008 McGraw-Hill Higher Education