Interpreting and Using Statistics in Psychological Research. Andrew N. Christopher

With each frequency plotted, we place a dot centered above each category score. We then connect the dots to form a polygon, such as the one in Figure 3.3. Frequency polygons are particularly helpful in displaying frequencies for continuous data, which, as you’ll recall from the previous chapter, can take on any fractional value along the x-axis (such as time, which can be measured in seconds or fractions of seconds). Histograms are better to use with discrete data, such as the burnout scores, which could take on only a whole-number value in Wendt’s (2013) research.

      Figure 3.3 Displaying Frequency Scale Data With a Frequency Polygon

      Frequency polygon: line graph that displays frequency of occurrence of scores; used for continuous data.

      Learning Check

      1 Table 3.5 is a frequency distribution table for the ages of participants in Wendt’s (2013) research.Use it to answer the following questions:What was the range of participant ages in this research?A: 15 years old to 23 years oldHow many 20-year-olds were there in this research?A: 6What percentage of the participants were 18 years old?A: 30.6% Table 3.5

      2 What is the difference between a histogram and a frequency polygon?A: A histogram is more appropriate for discrete data, whereas a frequency polygon is more appropriate for continuous data.

      3 Why might frequency distribution graphs be preferable to tables as a way to display data?A: Visual information is typically easier for people to understand quickly. Tables convey the same information, but it is often more difficult for people to digest information in tabular format than in pictorial format.

      4 Figure 3.4 contains a histogram that displays the frequency of occurrence for scores on a class midterm exam (these data are for illustrative purposes only). Use this histogram to answer the following questions:How many students took this midterm exam?A: To get this number, add the frequency for each exam score. Doing so reveals that 40 students took the midterm exam.What was the most frequently occurring score on the midterm?A: Look for the highest point on the histogram; then see what score along the x-axis it corresponds to. Here, the most frequently occurring score is 85.How many students scored 91% on the midterm?A: 3Figure 3.4 Histogram of Class Scores on a Midterm Exam

      5 In Wendt’s (2013) research, she recorded respondent’s sex. What sort of frequency distribution graph would be used for these data? Explain your response.A: A bar graph is the best choice because a person’s sex, similar to a person’s year in college, is measured on a nominal scale.

      Common Visual Displays of Data in Research

      Frequency tables and graphs are helpful in understanding large quantities of data. To get a sense of how variables are related to each other, researchers often present visual displays of relationships. In this section, we will discuss three types of visual displays that are frequently used in psychological research. In doing so, we will highlight the appropriate uses for each one and how to interpret them. In the next section of this chapter, we will learn how to make each of these types of displays using SPSS.

      Bar Graphs

      As we discussed in the previous section, bar graphs are used to display categorical (i.e., nominal) data. For example, suppose we want to know which group of students, first-years or seniors, scored higher on the measure of burnout. To find out, we can make a bar graph with the variable of year in school on the x-axis and average burnout score on the y-axis. As you can see in Figure 3.5, seniors did have a higher score on the burnout measure than did first-year students. In Chapters 7 and 8, we will learn to use tools that will allow us to determine whether in fact this is a meaningful difference between the two groups of students.

      Figure 3.5 Using a Bar Graph to Display Average Burnout Scores for First-Year and Senior College Students in Wendt’s (2013) Research

      Let’s examine another example of a bar graph. In a research study that we will detail in more depth in Chapter 10, Donte Bernard and his colleagues (Bernard, McManus, & Saucier, 2014) asked students to allocate a fixed amount of money to various campus student organizations. Some of their results are displayed in a bar graph that you can see in Figure 3.6. Along the x-axis is the name of each student organization. The y-axis contains the average amount of money that participants allocated to each organization. Again, notice that there is a space between each bar because student organization is a nominal variable.

      Scatterplots

      Scatterplots are used to display the relationship between two variables operationalized using a scale measurement. For example, in Wendt’s (2013) research, she constructed a scatterplot between two of her variables, specifically, a scatterplot of the relationship between role overload and burnout. This scatterplot appears in Figure 3.7. Each dot in the scatterplot represents the score of one respondent on the role overload measure (along the x-axis) and the burnout measure (along the y-axis). We examine the trend that these dots display and see that, in general, as people score toward the high end of the role overload measure, they tend to score toward the high end of the burnout measure. Of course, there are exceptions to this general trend, but that’s the overall picture that is painted in this scatterplot.

      Figure 3.6 Using a Bar Graph to Display Average Dollar Allocations for Student Organizations in Bernard et al.’s (2014) Research

      Scatterplot: graph that visually displays the relationship between two scale variables.

      In Chapters 12 and 13, we will learn statistical tools that quantify the strength of the relationship between two scale variables displayed in a scatterplot. For now, understand that there are three types of relationships between scale variables that a scatterplot can reveal. First, there is a linear relationship; that is, the relationship can be displayed with a straight line. The relationship between role overload and burnout in Wendt’s (2013) research is an example of a linear relationship because the general pattern of data points flows from the lower left to the upper right (what is called a “positive” linear relationship, which we touched on quickly in Chapter 1 and will discuss in detail in Chapter 12). Another example of a linear relationship would be the relationship between sleep quality and depression (Davidson, Babson, Bonn-Miller, Soutter, & Vannoy, 2013). You can see an example of this linear relationship in Figure 3.8. Here, the data points flow from the upper left corner to the lower right corner (what is called a “negative” linear relationship).

      Figure 3.7 Using a Scatterplot to Display a Positive Linear Relationship Between Role Overload and Burnout in Wendt’s (2013) Research

      Linear relationship: relationship between two variables that is displayed with a straight line.

      If one type of relationship is called linear, it will come as no surprise that another type of relationship between scale variables is called a nonlinear relationship. That is, the relationship is displayed by a curve rather than by a straight line. Let’s take an example that you are