Читать книгу Interpreting and Using Statistics in Psychological Research - Andrew N. Christopher - Страница 63

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 likely familiar with. Have you ever been so excited or nervous about a test or some sort of performance (e.g., sports or music) that you couldn’t concentrate on doing what you needed to do to succeed at the task? Conversely, have you ever been so unmotivated in a situation that you simply did not care that your performance would be bad? According to Yerkes–Dodson’s Law (1908), our performance on a task is at its best not when we are highly motivated or lacking motivation but at some optimal (midlevel) point of arousal. This nonlinear relationship is displayed in Figure 3.9. As you can see, too much motivation can lead to a decrement in performance because at those overly motivated levels, it becomes difficult to focus on the task itself.

Figure 3.8 Using a Scatterplot to Display a Negative Linear Relationship Between Sleep Quality and Depression

The final type of relationship that a scatterplot can reveal is no relationship between the two variables. That is, the dots on the scatterplot look like they were randomly thrown onto it with no linear or nonlinear relationship. I know of no research suggesting any sort of relationship between shoe size and intelligence. You can see such this relationship in Figure 3.10.

Nonlinear relationship: relationship between two variables that is displayed by a curved line.

Figure 3.9 Yerkes–Dodson’s Law: A Nonlinear Relationship

Figure 3.10 Scatterplot That Displays What “No Relationship” Between Shoe Size and Intelligence Would Look Like