CHAPTER THREE
Visual Displays of Data
NOTE TO INSTRUCTORS
In this chapter, students learn how to create and interpret graphs. Aside from demonstrating the actual mechanics of making graphs, emphasize the use of graphs in the world around them. The class activities have been designed to help you do this. Show students examples of good and poor graphs in newspapers and research articles and demonstrate how to interpret them. Another great resource for interpreting graphs is the Web site, http://www.math.yorku.ca/SCS/Gallery/, described in the textbook, which has some excellent examples of different kinds of graphs and different kinds of lies that can be hidden in graphs. Use these graphs from the Web site in class to help teach students how to interpret graphs and identify graphing errors.
OUTLINE OF RESOURCES
I. How to Mislead with Graphs
Discussion Question 3-1 (p. 22)
Discussion Question 3-2 (p. 23)
Classroom Activity 3-1: Demonstrate How to Mislead with Graphs (p. 23)
Classroom Activity 3-2: Challenge Your Students to Mislead with Graphs (p. 23)
Additional Readings (page 23)
II. Common Types of Graphs
Discussion Question 3-3 (p. 24)
Discussion Question 3-4 (p. 25)
Discussion Question 3-5 (p. 25)
Discussion Question 3-6 (p. 26)
III. How to Build a Graph
Discussion Question 3-7 (p. 27)
Classroom Activity 3-3: Graph Design (p. 27)
Classroom Activity 3-4: Positive Media Example (p. 27)
Classroom Activity 3-5: Negative Media Example (p. 27)
IV. Next Steps: Multivariable Graphs
V. Handouts
Handout 3-1: Graph Design (p. 28)
Handout 3-2: Positive Media Example (p. 29)
Handout 3-3: Negative Media Example (p. 30)
Chapter Guide
I. How to Mislead with Graphs
1.Learning about graphs is an important skill because graphs can reveal previously hidden information, persuade others to change their attitudes or behavior, and lead others to ask better questions.
2.Graphs often tell us information about their creators because they can be used either to deceive or to clarify information.
3.The False Face Validity Lie is when data seem to represent what the graph says they represent. To do this, researchers will label the graph as one thing but supply data for something else.
4.The Biased Scale Lie refers to a biased scale that slants information in a particular way.
5.The Sneaky Sample Lie is when participants are preselected so that the data will turn out in a particular way.
6.The Interpolation Lie is when you assert that some value between the data points lies on a straight line between those data points.
7.The Extrapolation Lie refers to a lie that goes beyond the available data points.
8.The Inaccurate Values Lie tells the truth in one part of the data but visually distorts it in another.
9.The Outright Lie refers to simply making up the data.
Discussion Question 3-1
Why should we spend time learning about graphs and how to interpret them?
Your students’ answers should include:
For those who learn how to create graphs, graphs can reveal previously hidden information, persuade people to change their beliefs or behavior, provoke questions, and communicate new discoveries and ideas.
Learning to interpret graphs gives the student the ability to spot lies and clarify mistaken beliefs.
Discussion Question 3-2
Of the seven types of lies discussed in the chapter, which do you think is the most dangerous and why?
Your students’ answers may include:
Answers will vary. This exercise is meant to promote original, provocative, and creative thinking.
One way to minimize the possibility of such lies would be to use sparklines, or datawords that are data-intense, design-simple, word-sized graphics.
Classroom Activity 3-1
Demonstrate How to Mislead with Graphs
For a simple yet effective demonstration that shows how easy it can be to mislead with graphs, collect height and weight data from each student. Enter the data in Microsoft Excel—use the scatterplot function in the graphs option. Once your graph is complete, simply expand the x-axis and watch what happens; then do the same with the y-axis. Ask your students to describe and interpret the graph when the axes are elongated.
Classroom Activity 3-2
Challenge Your Students to Mislead with Graphs
Have your students work in groups to create a misleading graph to present to the class. Then have the class try to identify which technique each group used to mislead with their graphs. See pages 50–52 of the text for the seven sophisticated techniques used to lie with statistics and graphs.
Additional Readings
Friendly, M., & Denis, D. A. Milestones in the History of Thematic Cartography, Statistical Graphics, and Data Visualization: An illustrated chronology of innovations. http://www.math.yorku.ca/SCS/Gallery/milestone/.
This online book is a comprehensive historical overview of how to visually present and interpret data.
Huff, D., & Geis, I. (reissue 1993). How to Lie with Statistics. New York: W. W. Norton and Company.
This book, originally published in 1954, is a straightforward and often humorous look at how visually misleading presentations allow people to lie with statistics. How to Lie with Statistics is a very readable book (142 pages) that is appropriate for undergraduate students.
Watkins, A., & Landwehr, J. M. (1986). Exploring Data. Palo Alto, CA: Dale Seymour Publications.
This book provides background information on the basics of data exploration.
II. Common Types of Graphs
1.In the previous chapter, we learned how histograms are useful for displaying information about one variable. However, as researchers, we often need to display information about the relationship between variables. As a result, different types of graphs are necessary.
2.A scatterplot is a graph that displays the relationship between two scale variables. The values of each variable are marked along the two axes and a mark is made to indicate the intersection of the two scores for each participant.
3.A range-frame is a scatterplot or related graph that indicates the range of the data on each axis; the lines extend only from the minimum to the maximum scores.
4.To create a scatterplot, organize the data by participant so that each participant has two scores—one for each interval variable. Label the x-axis with the independent variable and the y-axis with the dependent variable and each axis with the possible values that apply. For each participant, place a mark on the graph at the score on each axis.
5.Graphs also allow us to observe what kind of relationship exists between our two variables. A linear relation means that the relation between the two variables is best described using a straight line.
6.With a positive relationship, the pattern of data points flows up and to the right. With a negative relationship, the pattern of data points flows down and to the right.
7.In a nonlinear relation, the relationship between the two variables is best described using a line that breaks or curves.
Discussion Question 3-3
What would be a real-life example of a linear relation? A nonlinear relation?
Your students’ answers may include:
Linear relation: As a person exercises more, he loses more weight; as a person studies more, his grade goes up.
Nonlinear relation: As a person spends up to 50 hours working at his business, his profit rises. But as a person works more than 50 hours, his profit starts to drop.
8.Another type of graph, a line graph, can be used in two situations. It can be used as a line of best fit that describes the trend of the data in the scatterplot. Alternatively, it can be used to describe change over time in a time plot or time series plot.
9.A best fit line allows us to predict the y-value from the x-value.
10.To create a best fit line, label the x-axis and y-axis with the name of the independent and dependent variable, respectively. For each participant, make a mark above the score on the x-axis and y-axis. Draw the line of best fit through the points on the scatterplot using a regression equation (to be covered in Chapter 16).
11.A time plot or time series plot plots an interval variable on the y-axis as it changes over an increment of time on the x-axis.
12.To create a time plot, the x-axis is labeled with the independent variable as the appropriate increment of time and the dependent variable is marked on the y-axis. A mark is placed at the intersecting points for the x- and y-values for each participant. Then the dots in the plot are connected.
Discussion Question 3-4
What would we need to do to create a time plot from a line graph?
Your students’ answers should include:
Label the x-axis with the name of the independent variable and its possible values;
Label the y-axis with the name of the dependent variable and its possible values, starting with 0 if practical;
Make a mark above every score on the x-axis and next to every score on the y-axis;
Connect the dots; and
Convert to a range-frame by erasing the y-axis below the minimum
y-value and above the maximum y-value.
13.Bar graphs are visual depictions of data when the independent variable is nominal and the dependent variable is interval. Each bar represents the mean value of the dependent variable for each category.
Discussion Question 3-5
What is a bar graph?
Your students’ answers should include:
A bar graph describes the relation between two or more variables.
The x-axis of a bar graph displays a nominal variable score.
The y-axis of a bar graph can display many other variables, including interval measures of dependent variables.
14.To create a bar graph, the x-axis is labeled with the name and levels of the nominal independent variable. The y-axis is labeled with the name of the dependent variable and its possible values. For each category, draw a bar with the height of the category’s mean on the dependent variable axis.
15.When there are many categories along the x-axis, it is useful to create a Pareto chart, where the categories are ordered from the highest bar on the left to the lowest on the right.
16.When very few differences need to be depicted, a pictorial graph can be used, which uses a picture or symbol to represent its value on the interval dependent variable. Pictorial graphs use pictures rather than bars in the graphs.
17.Although pictorial graphs are often eye-catching, researchers typically do not use them because they are often misleading and hard to interpret. As a result, it is best to avoid using them when possible.
18.Data can also be depicted in the form of a pie chart or a graph in the shape of a circle with a slice representing the proportion or percentage of each category.
19.Pie charts should also be avoided because it is difficult to perceive the magnitude of a pie slice correctly or compare two or more pie slices. Bar graphs are much easier to read and are preferred.
Discussion Question 3-6
Why do researchers prefer not to use pictorial graphs and pie charts?
Your students’ answers should include:
Pictorial graphs: The pictures can distract the reader from seeing critical information; if not sized to proportionate scaling, the mis-sized pictures can be misleading to the reader; even if pictures are presented to scale, the human eye can still too easily misperceive the information intended to be shown.
Pie charts: It is difficult to perceive accurately the magnitude of a pie slice; bar graphs are much easier to interpret and compare with one another than pie charts.
III. How to Build a Graph
1.It can often be difficult to determine what kind of graph to use. Keep in mind that when we are presenting one scale variable it is best to use a histogram or frequency polygon. With one scale independent variable and one scale dependent variable, use a scatterplot or line graph. With one scale dependent variable and one nominal independent variable, use a bar graph or pareto chart. With one scale independent variable and two or more nominal independent variables, use a bar graph.
2.When creating a graph make sure that you use the same terms used in the body of the paper. In addition, the graph should provide all of the necessary information; in other words, it should not be necessary to go back to the main text to understand the graph.
3.Also, be aware of using chartjunk, or unnecessary information that detracts from our ability to understand the data.
4.In particular, avoid the use of Moiré vibrations, or patterns that computers provide as options to fill in bars. Instead, use shades of gray.
5.Also avoid using background patterns on which the data representations are superimposed, known as grids.
6.Lastly, avoid using ducks, or features of the data that have been dressed up to be something other than merely data. These include three-dimension effects, cutesy pictures, and fancy fonts.
7.When using a computer to create a graph, do not rely on defaults or the options that the software designer has preselected; these are the built-in decisions that the software will implement if we do not instruct it otherwise.
Discussion Question 3-7
What are three examples of chartjunk? Why should they be avoided?
Your students’ answers should include: