Data Representation

1
Data Representation
2
Overview

• To frame our discussion, consider

3
Outline

• Activities
• Types of Data
• Representations
• Guidelines

4
Research Activities

• Data Gathering
• Data Summarization
• Data Interpretation

5
Types of Data

• Nominal
• Ordinal
• Discrete
• Continuous

6
Representations

• Pie Charts
• Bar Charts
• Pareto Diagrams
• Frequency Distributions
• Stem-and-Leaf Plots
• Scatter Plots
• Box Plots
• Time Series

7
Pie Charts

• The pie chart is appropriate for displaying
  nominal and ordinal data. The pie chart shows the
  percentage of the total measurements that fall in
  a certain category.

8
Example
9
Bar/Column Charts

• Bar/Column charts are also useful in displaying
  nominal and ordinal data. The bar chart can
  display either percentages, as the pie chart did,
  or the number of measurements in a category.

10
Example (1)
11
Example (2)
12
Example (3)
13
Pareto Diagrams

• Pareto diagrams are named after Vilfredo Pareto,
  an Italian sociologist and economist, who
  invented this method of information presentation
  toward the end of the 19th century.
• The chart is similar to the histogram or bar
  chart, except that the bars are arranged in
  decreasing magnitude from left to right along the
  abscissa.

14
Pareto Diagrams

• The fundamental idea behind the use of Pareto
  diagrams for quality improvement is that the
  first few (as presented on the diagram)
  contributing causes to a problem usually account
  for the majority of the result.   Thus,
  targeting these "major causes" for elimination
  results in the most cost-effective improvement
  scheme.

15
Example
From Harnessing the Power of the Pareto
Principle, www.shawresources.com
16
Frequency Distributions

• Frequency histograms are used representing
  discrete or continuous data.
• The range of measures, max minus min, is used to
  construct class intervals. Class intervals all
  have the same range.
• To avoid assignment problems, choose endpoints
  for the class intervals that have one more digit
  of precision than the data.
• The number of classes is chosen based on the size
  of the data set, and the granularity you wish to
  portray.

17
Example
18
Stem-and-Leaf Plots

• For small data sets, a stem-and-leaf plot
  presents the distribution quickly without loss of
  information.
• Separate each observation into two parts, a stem,
  consisting of the leftmost digit(s), and a leaf,
  the rightmost digit(s).
• Beginning with the smallest stem write the stems
  in a vertical column.
• Write each leaf in the row to right of its stem,
  in increasing order.

19
Stem-and- Leaf Displays

• Select one or more leading digits for the stem
  values. The trailing digits become the leaves.
• List stem values in a vertical column.
• Record the leaf for every observation.
• Indicate the units for the stem and leaf on the
  disply.

20
Stem-and-Leaf Example
Observed values
9, 10, 15, 22, 9, 15, 16, 24,11

• 0 9 9
• 1 0 5 5 6
• 2 4

Stem tens digit
Leaf units digit
21
Example
22
Relating Variables

• Most studies involve more than one variable. We
  need a way to represent data so we can look for
  relationships.

23
Scatterplot

• A scatterplot shows the relationship between two
  quantitative variables measured on the same
  individual.

24
Example
25
Interpreting the Scatterplot

• Look at
• Form
• Do the data points form a shape?
• Direction
• Does the shape formed indicate a direction?
• Strength
• Is there little scatter about the shape?

26
Associations

• Two variables can be either
• Positively associated
• Or
• Negatively associated

27
Positively Associated

• Two variables are positively associated when
  above average values in one variable results in
  above average values in the other.

28
Example (2)
29
Choosing a Representation

• Set priorities.
• Who is the audience?
• What is the message?
• Choose the graph type.
• Set the title to inform the reader of the
  purpose.
• Use color to convey tone (warm tones are dramatic
  whereas pastels are conservative).