Clarifying the Concepts
What are the five techniques discussed in this chapter for misleading with graphs?
What are the steps to create a scatterplot?
How can you convert a scatterplot into a range-
What does it mean for two variables to be linearly related?
How can we tell whether two variables are linearly or nonlinearly related?
What is the difference between a line graph and a time plot?
What is the difference between a bar graph and a Pareto chart?
Bar graphs and histograms look very similar. In your own words, what is the difference between the two?
What are pictorial graphs and pie charts?
Why are bar graphs preferred over pictorial graphs and pie charts?
Why is it important to identify the independent variable and the dependent variable before creating a visual display?
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Under what circumstances would the x-axis and y-axis not start at 0?
Chartjunk comes in many forms. What specifically are moiré vibrations, grids, and ducks?
Geographic information systems (GIS), such as those provided by computerized graphing technologies, are particularly powerful tools for answering what kinds of research questions?
How is the bubble graph depicted in the Next Steps section similar to a traditional scatterplot?
How does the bubble graph depicted in the Next Steps section differ from a traditional scatterplot?
Calculating the Statistics
Alumni giving rates, calculated as the total dollars donated per year from 2003 to 2013, represent which kind of variable—
Alumni giving rates for a number of universities, calculated as the number of alumni who donated and the number who did not donate in a given year, represent which kind of variable—
You are exploring the relation between gender and video game performance, as measured by final scores on a game.
In this study, what are the independent and dependent variables?
Is gender a nominal, ordinal, or scale variable?
Is final score a nominal, ordinal, or scale variable?
Which graph or graphs would be appropriate to depict the data? Explain why.
Do the data in the graph below show a linear relation, a nonlinear relation, or no relation? Explain.
Do the data in the graph below show a linear relation, a nonlinear relation, or no relation? Explain.
What elements are missing from the graphs in Exercises 3.20 and 3.21?
The following figure presents the enrollment of graduate students at a university, across six fall terms, as a percentage of the total student population.
What kind of visual display is this?
What other type of visual display could have been used?
What is missing from the axes?
What chartjunk is present?
Using this graph, estimate graduate student enrollment, as a percentage of the total student population, in the fall terms of 2007, 2008, and 2010.
How would the comparisons between bars change if the y-axis started at 0?
When creating a graph, we need to make a decision about the numbering of the axes. If you had the following range of data for one variable, how might you label the relevant axis?
337 280 279 311 294 301 342 273
If you had the following range of data for one variable, how might you label the relevant axis?
0.10 0.31 0.27 0.04 0.09 0.22 0.36 0.18
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The scatterplot in How It Works 3.1 depicts the relation between fertility and life expectancy. Each dot represents a country (or, as in the case of Hong Kong, a special administrative region).
Approximately, what is the highest life expectancy in years? Approximately, what fertility rate (children per woman) is associated with the highest life expectancy?
Does this seem to be a linear relation? Explain why or why not, and explain the relation in plain English.
Based on the data in the bubble graph (Figure 3-
The colors and sizes of the bubbles in the bubble graph (Figure 3-
Applying the Concepts
Type of graph for the relation between height and attractiveness: A social psychologist studied the effect of height on perceived overall attractiveness. Students were recruited to come to a research laboratory in pairs. The pairs sat together in the waiting room for several minutes and then were brought to separate rooms, where their heights were measured. They also filled out a questionnaire that asked, among other things, that they rate the attractiveness of the person who had been sitting with them in the waiting room on a scale of 1 to 10.
In this study, are the independent and dependent variables nominal, ordinal, or scale?
Which graph or graphs would be most appropriate to depict the data? Explain why.
If height ranged from 58 inches to 71 inches in this study, would the axis start at 0? Explain.
Type of graph for the effects of cognitive-
What are the independent and dependent variables in this study?
Are the variables nominal, ordinal, or scale?
Which graph or graphs would be most appropriate to depict the data? Explain why.
Type of graph for comparative suicide rates: The World Health Organization tracks suicide rates by gender across countries (http:/
What are the variables in this study?
Are the variables nominal, ordinal, or scale?
Which graph would be most appropriate to depict the data? Explain why.
If you wanted to track the suicide rates for three of these countries over 50 years, what type of graph might you use to show these data?
Scatterplot of daily cycling distances and type of climb: Every summer, the touring company America by Bicycle conducts its Cross-
Mileage | Climb | Mileage | Climb | Mileage | Climb |
---|---|---|---|---|---|
83 | 600 | 69 | 2500 | 102 | 2600 |
57 | 600 | 63 | 5100 | 103 | 1000 |
51 | 2000 | 66 | 4200 | 80 | 1000 |
76 | 8500 | 96 | 900 | 72 | 900 |
51 | 4600 | 124 | 600 | 68 | 900 |
91 | 800 | 104 | 600 | 107 | 1900 |
73 | 1000 | 52 | 1300 | 105 | 4000 |
55 | 2000 | 85 | 600 | 90 | 1600 |
72 | 2500 | 64 | 300 | 87 | 1100 |
108 | 3900 | 65 | 300 | 94 | 4000 |
118 | 300 | 108 | 4200 | 64 | 1500 |
65 | 1800 | 97 | 3500 | 84 | 1500 |
76 | 4100 | 91 | 3500 | 70 | 1500 |
66 | 1200 | 82 | 4500 | 80 | 5200 |
97 | 3200 | 77 | 1000 | 63 | 5200 |
92 | 3900 | 53 | 2500 |
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Construct a scatterplot of the cycling data, putting mileage on the x-axis. Be sure to label everything and include a title.
We haven’t yet learned to calculate inferential statistics on these data, so we can’t really know what’s going on, but do you think that the amount of vertical climb is related to a day’s mileage? If yes, explain the relation in your own words. If no, explain why you think there is no relation.
It turns out that inferential statistics do not support the existence of a relation between these variables and that the staff seems to be the most accurate in their appraisal. Why do you think the cyclists and organizers are wrong in opposite directions? What does this say about people’s biases and the need for data?
Scatterplot of gross domestic product and education levels: The Group of Eight (G8) consists of many of the major world economic powers. It meets annually to discuss pressing world problems. In 2013, for example, the G8 met in the United Kingdom with an agenda that included international security. Decisions made by G8 nations can have a global impact; in fact, the eight nations that make up the membership reportedly account for almost two-
Country | GDP (in trillions of $US) | Percentage with University Degree |
---|---|---|
Canada | 0.98 | 19 |
France | 2.00 | 11 |
Germany | 2.71 | 13 |
Italy | 1.67 | 9 |
Japan | 4.62 | 18 |
United Kingdom | 2.14 | 17 |
United States | 11.67 | 27 |
Create a scatterplot of these data, with university degree on the x-axis. Be sure to label everything and to give it a title. Later, we’ll use statistical tools to determine the equation for the line of best fit. For now, draw a line of best fit that represents your best guess as to where it would go.
In your own words, describe the relation between the variables that you see in the scatterplot.
Education is on the x-axis, indicating that education is the independent variable. Explain why it is possible that education predicts GDP. Now reverse your explanation of the direction of prediction, explaining why it is possible that GDP predicts education.
Time series plot of organ donations: The Canadian Institute for Health Information (CIHI) is a nonprofit organization that compiles data from a range of institutions—
Year | Donor Rate per Million Population | Year | Donor Rate per Million Population |
---|---|---|---|
2001 | 13.4 | 2006 | 14.1 |
2002 | 12.9 | 2007 | 14.7 |
2003 | 13.3 | 2008 | 14.4 |
2004 | 12.9 | 2009 | 14.4 |
2005 | 12.7 | 2010 | 13.6 |
Construct a time series plot from these data. Be sure to label and title your graph.
What story are these data telling?
If you worked in public health and were studying the likelihood that families would agree to donate after a loved one’s death, what research question might you ask about the possible reasons for the trend suggested by these data?
Bar graph of alumni donation rates at different kinds of universities: U.S. universities are concerned with increasing the percentage of alumni who donate to the school because alumni donation rate is a factor in the U.S. News & World Report’s university rankings. What role might type of university play in alumni donation rates? U.S. News & World Report ranks private national universities, public national universities, and private liberal arts colleges (http:/
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Top 10 Colleges and Universities in Terms of Alumni Donation | Alumni Donation Rates (%) |
---|---|
Princeton University (NJ) | 62.6% |
Thomas Aquinas College (CA) | 58.9 |
Carleton College (MN) | 58.2 |
Williams College (MA) | 57.5 |
Amherst College (MA) | 57.3 |
Centre College (KY) | 54.9 |
Middlebury College (VT) | 54.7 |
Davidson College (NC) | 53.4 |
College of the Holy Cross (MA) | 51.1 |
Bowdoin College (ME) | 50.2 |
What is the independent variable in this example? Is it nominal or scale? If nominal, what are the levels? If scale, what are the units and what are the minimum and maximum values?
What is the dependent variable in this example? Is it nominal or scale? If nominal, what are the levels? If scale, what are the units and what are the minimum and maximum values?
Construct a bar graph of these data, with one bar for each of the top 10 schools, using the default options in your computer software.
Construct a second bar graph of these data, but change the defaults to satisfy the guidelines for graphs discussed in this chapter. Aim for simplicity and clarity.
Cite at least one research question that you might want to explore next if you worked for one of these universities. Your research question should grow out of these data.
Explain how these data could be presented as a pictorial graph. (Note that you do not have to construct such a graph.) What kind of picture could you use? What would it look like?
What are the potential pitfalls of a pictorial graph? Why is a bar chart usually a better choice?
Bar graph versus Pareto chart of countries’ gross domestic product: In How It Works 3.2, we created a bar graph for the 2012 GDP, in U.S. dollars per capita, of each of the G8 nations. In How It Works 3.3, we created a Pareto chart for these same data.
Explain the difference between a Pareto chart and a standard bar graph in which the countries are in alphabetical order along the x-axis.
What is the benefit of the Pareto chart over the standard bar graph?
Bar graph versus time series plot of graduate school mentoring: Johnson, Koch, Fallow, and Huwe (2000) conducted a study of mentoring in two types of psychology doctoral programs: experimental and clinical. Students who graduated from the two types of programs were asked whether they had a faculty mentor while in graduate school. In response, 48.00% of clinical psychology students who graduated between 1945 and 1950 and 62.31% who graduated between 1996 and 1998 reported having had a mentor; 78.26% of experimental psychology students who graduated between 1945 and 1950 and 78.79% who graduated between 1996 and 1998 reported having had a mentor.
What are the two independent variables in this study, and what are their levels?
What is the dependent variable?
Create a bar graph that depicts the percentages for the two independent variables simultaneously.
What story is this graph telling us?
Was this a true experiment? Explain your answer.
Why would a time series plot be inappropriate for these data? What would a time series plot suggest about the mentoring trend for clinical psychology graduate students and for experimental psychology graduate students?
For four time points—
Bar graph versus pie chart of student participation in community activities: The National Survey on Student Engagement (NSSE) has surveyed more than 400,000 students—
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Software defaults of graphing programs that portray satisfaction with graduate advisors: The 2000 National Doctoral Program Survey asked 32,000 current and recent Ph.D. students in the United States, across all disciplines, to respond to the statement “I am satisfied with my advisor.” The researchers calculated the percentage of students who responded “agree” or “strongly agree”: current students, 87%; recent graduates, 86%; former students who left without completing the Ph.D., 48%.
Use a software program that produces graphs (e.g., Excel, SPSS, Minitab) to create a bar graph for these data.
Play with the options available to you. List aspects of the bar graph that you are able to change to make your graph meet the guidelines listed in this chapter. Be specific, and include the revised graph.
Software defaults of graphing programs for depicting the “world’s deepest” trash bin: The car company Volkswagen has sponsored a “fun theory” campaign in recent years in which ordinary behaviors are given game-
Use a software program that produces graphs (e.g., Excel, SPSS, Minitab) to create a bar graph for these data.
Play with the options available to you. List aspects of the bar graph that you are able to change to make your graph meet the guidelines listed in this chapter. Be specific, and include the revised graph.
Multivariable graphs and college rankings by academics and sexiness: Buzzfeed.com published a multivariable graph that purported to rank colleges by academics and sexiness. The data from this graph are represented here.
What kind of graph is this? Explain.
List the variables that are included in this graph.
List at least three ways in which this graph could be redesigned in light of the guidelines in this chapter.
Types of graph appropriate for behavioral science research: Give an example of a study—
Frequency polygon
Line graph (line of best fit)
Bar graph (one independent variable)
Scatterplot
Time series plot
Pie chart
Bar graph (two independent variables)
Creating the perfect graph: What advice would you give to the creators of each of the following graphs? Consider the basic guidelines for a clear graph, for avoiding chartjunk, and regarding the ways to mislead through statistics. Give three pieces of advice for each graph. Be specific—
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Business and women:
Workforce participation:
Graphs in the popular media: Find an article in the popular media (newspaper, magazine, Web site) that includes a graph in addition to the text.
Briefly summarize the main point of the article and graph.
What are the independent and dependent variables depicted in the graph? What kind of variables are they? If nominal, what are the levels?
What descriptive statistics are included in the article or on the graph?
In one or two sentences, what story is the graph (rather than the article) trying to tell?
How well do the text and graph match up? Are they telling the same story? Are they using the same terms? Explain.
Write a paragraph to the graph’s creator with advice for improving the graph. Be specific, citing the guidelines from this chapter.
Redo the graph, either by hand or by computer, in line with your suggestions.
Interpreting a graph about two kinds of career regrets: The Yerkes–
Briefly summarize the theoretical relations proposed by the graph.
What are the independent and dependent variables depicted in the graph? What kind of variables are they? If nominal or ordinal, what are the levels?
What descriptive statistics are included in the text or on the graph?
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In one or two sentences, what story is the graph trying to tell?
Critiquing a graph about the frequency of psychology degrees: The American Psychological Association (APA) compiles many statistics about training and careers in the field of psychology. The accompanying graph tracks the number of bachelor’s, master’s, and doctoral degrees conferred between the years 1970 and 2000.
What kind of graph is this? Why did the researchers choose this type of graph?
Briefly summarize the overall story being told by this graph.
What are the independent and dependent variables depicted in the graph? What kind of variables are they? If nominal or ordinal, what are the levels?
List at least three things that the graph creators did well (that is, in line with the guidelines for graph construction).
List at least one thing that the graph creators should have done differently (that is, not in line with the guidelines for graph construction).
Name at least one variable other than number that might be used to track the prevalence of psychology bachelor’s, master’s, and doctoral degrees over time.
The increase in bachelor’s degrees over the years is not matched by an increase in doctoral degrees. List at least one research question that this finding suggests to you.
Interpreting a graph using a mental health index: The gray line in Figure 3-18 depicts the Mental Health Index (MHI) for a fictional client in relation to several benchmarks. Use the information supplied in Figure 3-18 to answer the following questions:
Describe the trajectory of the client’s MHI over the course of the therapy sessions.
Provide a possible explanation for the trajectory described in part (a).
Based on the benchmarks depicted in the graph, would you recommend that the client continue therapy?
Interpreting a graph about traffic flow: Go to http:/
How is the density and flow of traffic represented in this graph?
Describe traffic patterns in different regions of your country.
What are the benefits of this interactive graph?
Interpreting a graph about political support: As we learned in this chapter, pie charts are often not the best choice to present data.
What is the primary flaw in this presentation of data as a pie chart?
How would you redesign this graph? Be specific and cite at least three ways in which you would change it.
Multivariable graphs and shipwrecks: The cliché “women and children first” originated in part because of the Titanic captain’s famous directive as his ship was sinking. Yet, the cliché is not grounded in reality. See the multivariable graph below.
What kind of graph is this?
List the variables that are included in this graph.
Are the data on the top and the bottom necessary to tell this story? Explain. Why do you think both sides are included?
In your own words, tell the story that this graph is visualizing.
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Putting It All Together
Type of graph describing the effect of romantic songs on ratings of attractiveness: Guéguen, Jacob, and Lamy (2010) wondered if listening to romantic songs would affect the dating behavior of the French heterosexual women who participated in their study. The women were randomly assigned to listen to either a romantic song (“Je l’aime à Mourir,” or “I Love Her to Death”) or a nonromantic song (“L’heure du Thé,” or “Tea Time”) while waiting for the study to begin. Later in the study, an attractive male researcher asked each participant for her phone number. Of the women who listened to the romantic song, 52.2% gave their phone number to the researcher, whereas only 27.9% of the women who listened to the nonromantic song gave their phone number to the researcher.
What is the independent variable in this study?
What is the dependent variable?
Is this a between-
Think back to our discussion of variables in Chapter 1. How did the researcher operationalize “dating behavior” in this study? Do you think this is a valid measure of dating behavior? Explain your answer.
What is the best type of graph to depict these results? Explain your answer.
Create the graph you described in part (e) using software without changing any of the defaults.
Create the graph you described in part (e) a second time, changing the defaults to meet the criteria in the checklist introduced in this chapter.
Developing research questions from graphs: Graphs not only answer research questions, but can spur new ones. Figure 3-9 on page 55 depicts the pattern of changing attitudes, as expressed through Twitter.
On what day and at what time is the highest average positive attitude expressed?
On what day and at what time is the lowest average negative attitude expressed?
What research question(s) do these observations suggest to you with respect to weekdays versus weekends? (Remember, 0 on Sunday is midnight—
How are the researchers operationalizing mood? Do you think this is a valid measure of mood? Explain your answer.
One of the highest average negative attitudes occurs at midnight on Sunday. How does this fit with the research hypothesis you developed in part (c)? Does this suggest a new research hypothesis?