Chapter 3

  • 3.1 The five techniques for misleading with graphs are the biased scale lie, the sneaky sample lie, the interpolation lie, the extrapolation lie, and the inaccurate values lie.
  • 3.3 To convert a scatterplot to a range-frame, simply erase the axes below the minimum score and above the maximum score.
  • 3.5 With scale data, a scatterplot allows for a helpful visual analysis of the relation between two variables. If the data points appear to fall approximately along a straight line, the variables may have a linear relation. If the data form a line that changes direction along its path, the variables may have a nonlinear relation. If the data points show no particular relation, it is possible that the two variables are not related.
  • 3.7 A bar graph is a visual depiction of data in which the independent variable is nominal or ordinal and the dependent variable is scale. Each bar typically represents the mean value of the dependent variable for each category. A Pareto chart is a specific type of bar graph in which the categories along the x-axis are ordered from highest bar on the left to lowest bar on the right.
  • 3.9 A pictorial graph is a visual depiction of data typically used for a nominal independent variable with very few levels (categories) and a scale dependent variable. Each level uses a picture or symbol to represent its value on the scale dependent variable. A pie chart is a graph in the shape of a circle, with a slice for every level. The size of each slice represents the proportion (or percentage) of each category. In most cases, a bar graph is preferable to a pictorial graph or a pie chart.
  • 3.11 The independent variable typically goes on the horizontal x-axis and the dependent variable goes on the vertical y-axis.
  • 3.13 Moiré vibrations are any visual patterns that create a distracting impression of vibration and movement. A grid is a background pattern, almost like graph paper, on which the data representations, such as bars, are superimposed. Ducks are features of the data that have been dressed up to be something other than merely data.
  • 3.15 Like a traditional scatterplot, the locations of the points on the bubble graph simultaneously represent the values that a single case (or country) has on two scale variables. The graph as a whole depicts the relation between these two variables.
  • 3.17 Total dollars donated per year is scale data. A time plot would nicely show how donations varied across years.
  • 3.19
    • a. The independent variable is gender and the dependent variable is video game score.
    • b. Nominal
    • c. Scale
    • d. The best graph for these data would be a bar graph because there is a nominal independent variable and a scale dependent variable.
  • 3.21 Linear, because the data could be fit with a line drawn from the upper-left to the lower-right corner of the graph.
  • 3.23
    • a. Bar graph
    • b. Line graph; more specifically, a time plot
    • c. The y-axis should go down to 0.
    • d. The lines in the background are grids, and the three-dimensional effect is a type of duck.
    • e. 3.20%, 3.22%, 2.80%
    • f. If the y-axis started at 0, all of the bars would appear to be about the same height. The differences would be minimized.
  • 3.25 The minimum value is 0.04 and the maximum is 0.36, so the axis could be labeled from 0.00 to 0.40. We might choose to mark every 0.05 value:
  • 3.27 The relation between physical health and positive emotions seems to be positive, with the data fitting a line moving from the lower-left to the upper-right corner of the graph. As positive emotions increase, self-reported physical health also tends to increase.
  • 3.29
    • a. The independent variable is height and the dependent variable is attractiveness. Both are scale variables.
    • b. The best graph for these data would be a scatterplot (which also might include a line of best fit if the relation is linear) because there are two scale variables.
    • c. It would not be practical to start the axis at 0. With the data clustered from 58 to 71 inches, a 0 start to the axis would mean that a large portion of the graph would be empty. We would use cut marks to indicate that the axis did not include all values from 0 to 58. (However, we would include the full range of data0 to 71if omitting some of these numbers would be misleading.)
  • 3.31
    • a. The independent variable is country and the dependent variable is male suicide rate.
    • b. Country is a nominal variable and suicide rate is a scale variable.
    • c. The best graph for these data would be a bar graph or a Pareto chart. Because there are six categories or countries to list along the x-axis, it may be best to arrange them in order from highest to lowest using a Pareto chart.

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    • d. A time series plot could show year on the x-axis and suicide rate on the y-axis. Each country would be represented by a different color line.
  • 3.33
    • a.
    • b. The percentage of residents with a university degree appears to be related to GDP. As the percentage with a university degree increases, so does GDP.
    • c. It is possible that an educated populace has the skills to make that country productive and profitable. Conversely, it is possible that a productive and profitable country has the money needed for the populace to be educated.
  • 3.35
    • a. The independent variable is the academic institution. It is nominal; the levels are the 10 colleges.
    • b. The dependent variable is alumni donation rate. It is a scale variable; the units are percentages, and the range of values is from 50.2 to 62.6.
    • c. The defaults will differ, depending on which software is used. Here is one example.
    • d. The redesigns will differ, depending on which software is used. In this example, we added a clear title and labeled the y-axis (being sure that it reads from left to right). We also eliminated the unnecessary lines in the background and the decimal places of each number on the y-axis.
    • e. There are many possible answers to this question. One might want to identify characteristics of alumni who donate, methods of soliciting donations that result in the best outcomes, or characteristics of universities that have the highest rates.
    • f. Pictures could be used instead of bars. For example, dollar signs might be used to represent the donation rate for each college.
    • g. If the dollar signs become wider as they get taller, as often happens with pictorial graphs, the overall size would be proportionally larger than the increase in donation rate it is meant to represent. A bar graph is not subject to this problem because graphmakers are not likely to make bars wider as they get taller.
  • 3.37
    • a. One independent variable is time frame; it has two levels: 1945–1950 and 1996–1998. The other independent variable is type of graduate program; it also has two levels: clinical psychology and experimental psychology.
    • b. The dependent variable is percentage of graduates who had a mentor while in graduate school.
    • c.
    • d. These data suggest that clinical psychology graduate students were more likely to have been mentored if they were in school in the 1996–1998 time frame than if they were in school during the 1945–1950 time frame. There does not appear to be such a difference among experimental psychology students.
    • e. This was not a true experiment. Students were not randomly assigned to time period or type of graduate program.

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    • f. A time series plot would be inappropriate with so few data points. It would suggest that we could interpolate between these data points. It would suggest a continual increase in the likelihood of being mentored among clinical psychology students, as well as a stable trend, albeit at a high level, among experimental psychology students.
    • g. The story based on two time points might be falsely interpreted as a continual increase of mentoring rates for the clinical psychology students and a plateau for the experimental psychology students. The expanded data set suggests that the rates of mentoring have fluctuated over the years. Without the four time points, we might be seduced by interpolation into thinking that the two scores represent the end points of a linear trend. We cannot draw conclusions about time points for which we have no data—especially when we have only two points, but even when we have more points.
  • 3.39
    • a. The details will differ, depending on the software used. Here is one example.
    • b. The default options that students choose to override will differ. For the bar graph on the next page, we (1) added a title, (2) labeled the x-axis, (3) labeled the y-axis, (4) rotated the y-axis label so that it reads from left to right, and (5) eliminated the unnecessary key.
  • 3.41
    • a. The graph is a scatterplot: individual points are identified for two scale variables—academic standing and “hotness.”
    • b. The variables are academic standing and “hotness.”
    • c. The graph could be redesigned to get rid of moiré vibrations, such as the colored background; and the grid (the background pattern of graph paper) and duck (the woman in the background image) could be eliminated.
  • 3.43 Each student’s advice will differ. The following are examples of advice.
    • a. Business and women: Eliminate all the pictures, including the woman, piggy banks, the dollar signs in the background, and the icons to the right (e.g., house). The two bars near the top could mislead us into thinking they indicated quantity, even though they are the same length for two different median wages. Either eliminate the bars or size them so that they are appropriate to the dollars they represent. Ideally, the two median wages would be presented in a bar graph. Eliminate unnecessary words (e.g., “The Mothers of Business Invention”).
    • b. Workforce participation: Eliminate all the pictures. A falling line in the art shown indicates an increase in percentage; notice that 40% is at the top and 80% is at the bottom. Make the y-axis go from highest to lowest, starting from 0. Make the lines easier to compare by eliminating the three- dimensional effect. Make it clear where the data point for each year falls by including a tick mark for each number on the x-axis.
  • 3.45
    • a. The graph proposes that Type I regrets of action are initially intense but decline over the years, while Type II regrets of inaction are initially mild but become more intense over the years.
    • b. There are two independent variables: type of regret (a nominal variable) and age (a scale variable). There is one dependent variable: intensity of regrets (also a scale variable).
    • c. This is a graph of a theory. No data have been collected, so there are no statistics of any kind.
    • d. The story that this theoretical relation suggests is that regrets over things a person has done are intense shortly after the actual behavior but decline over the years. In contrast, regrets over things a person has not done but wishes they had are initially low in intensity but become more intense as the years go by.
  • 3.47
    • a. When first starting therapy, the client showed a decline, as measured by the Mental Health Index (MHI). After 8 weeks of therapy, this trajectory reversed and there was a week-to- week improvement in the client’s MHI.
    • b. There are many possible answers. For example, the initial decline in the client’s MHI may have been due to difficulties in adapting to therapy that the client overcame while working with the therapist. Alternatively, it may be that the client initially entered therapy because of difficult life circumstances that continued through the first weeks of therapy but resolved after several weeks.
    • c. Because the client is not beneath the failure boundary, and because the client experienced improvement over the last few weeks of therapy, it may be beneficial for the client to continue in therapy.
  • 3.49
    • a. Data can almost always be presented more clearly in a bar graph or table than in a pie chart.

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    • b. Answers to this question should include revising the data to add up to 100%, removing chartjunk (e.g., colors, shading, background images, etc.), and more clearly labeling categories with candidate names only. The graph also should not have 3-D features.
  • 3.51
    • a. The independent variable is song type, with two levels: romantic song and nonromantic song.
    • b. The dependent variable is dating behavior.
    • c. This is a between-groups study because each participant is exposed to only one level or condition of the independent variable.
    • d. Dating behavior was operationalized by giving one’s phone number to an attractive person of the opposite sex. This may not be a valid measure of dating behavior, as we do not know if the participant actually intended to go on a date with the researcher. Giving one’s phone number might not necessarily indicate an intention to date.
    • e. We would use a bar graph because there is one nominal independent variable and one scale dependent variable.
    • f. The default graph will differ, depending on which software is used. Here is one example:
    • g. The default options that students choose to override will differ. Here is one example.