1.15–1.18: Scientific thinking can help us make wise decisions.

What can you believe? Reading labels is essential to evaluating products and the claims about them.

“Let’s look at the data.” Using points and lines and symbols and a variety of other graphic elements to display measured quantities is a powerful tool commonly used throughout the sciences. Such visual displays of data can serve a range of purposes, which relate to both the presentation of and the exploration of the data.

Whether making a point, illustrating an idea, or facilitating the testing of a hypothesis, visual displays of data typically have one feature in common: they condense large amounts of information into a more easily digested form. In doing so, they can help readers think about and compare data, ultimately helping them to synthesize the information and see useful patterns.

There is an almost infinite variety of ways to display data, including maps, tables, charts, and graphs. Graphs are particularly prevalent in biology, and a few forms are used most frequently. These include bar graphs, line graphs, and pie charts (FIGURE 1-18).

Figure 1.18: Presenting what we have observed, precisely and concisely.

Visual displays of data generally have a few common elements. Most have a title, for example, which usually appears at the top and describes the content of the display. Bar graphs and line graphs include axes, usually a horizontal axis, also called the x-axis, and a vertical axis, called the y-axis. Each axis has a scale, generally labeled with some gradations, indicating one dimension by which the data can be described.

The x-axis of a line graph, for example, might describe the number of hours a student spends studying for a class, in which case it would be labeled “Time spent studying each day (hrs),” while the y-axis might be labeled “Performance on midterm exams (%).” Depending on the size of the data set (the total number of observations collected in the experiment that relate an individual’s performance on a midterm and the number of hours that student spent studying each day), individual data points are included on the graph, with additional information conveyed by the shape, color, or pattern of the data points (FIGURE 1-19). One data point might reflect that one student spent 2 hours studying per day and scored 85% on a midterm exam, while another spent 1 hour per day and scored 94% on the midterm exam. A line or curve may be used to connect data points or to illustrate a relationship between the two variables, and the axes must always be labeled and include the units of measure.

Figure 1.19: Common elements of effective graphical presentations of data. Shown here: an example of a line graph.

Rather than displaying individual data points, a bar graph has rectangular bars, each with a height proportional to the value being represented—maybe hours spent studying in a particular class. In a pie chart, each “slice” is a proportion of the whole—for instance, each slice representing the portion of a student’s total number of study hours spent on each different topic every day. A legend may be included for the graph, identifying which information is represented by which bar or data point or pie slice.

One of the most common functions of visual displays of information is to present the relationship between two variables, such as in a graph. These variables may be described as independent and dependent variables. An independent variable is some entity that can be observed and measured at the start of a process, and whose value can be changed as required. A dependent variable is one that can also be observed and measured, but whose response is created by the process being observed and depends on the independent variable. The dependent variable is generally represented by the y-axis and is expected to change in response to a change in the independent variable, represented on the x-axis. The number of hours of sleep a student gets each night, for example, could be thought of as an independent variable, while some measure of academic performance—maybe grade point average—would be a dependent variable.

Visual displays of data can be simple and straightforward, but they can also have features that reduce their effectiveness, or even cause them to be downright misleading. These difficulties can arise from ambiguity in the axis labels or scales, or incomplete information on how each data point was collected (and how the points might have varied), or biases or hidden assumptions in the presentation or grouping of the data, or unknown or unreliable sources of data, or an insufficient or inappropriate context given for the data presentation.

In each chapter of this book, you will see that one of the visual displays of data is labeled with the “Graphic Content” icon (you’ll have noticed this on Figure 1-17). For each of these figures, in the Check Your Knowledge section at the end of the chapter you’ll find several questions about the figure’s content. These questions will guide you in evaluating aspects of the figure (such as: “What is its main point?”) and in extracting information from it. They will also help you understand when it might be warranted to approach a data display with more than the usual amount of skepticism, and when greater trust is reasonable.