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

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

      Line Graphs

      Similar to scatterplots, line graphs are used to depict how two scale variables are related. Typically in psychology, many line graphs are used to predict the variable on the y-axis from the variable on the x-axis. In fact, this type of line graph starts with a scatterplot such as the one in Figure 3.7. However, we use the scatterplot to draw a line of best fit through the data points, as observed in Figure 3.11. We will learn more about the line of best fit in Chapter 13. For now, if you understand that the line of best fit allows us to predict the variable on the y-axis from a value of the variable on the x-axis, you’re in great shape.

      Line graph: graph used to depict the relationship between two scales variables.

      One type of line graph we encounter in psychological research is called a time plot, or sometimes a time series plot. An example of a time plot appears in Figure 3.12. This figure displays the value of one of the major U.S. stock market gauges, the Dow Jones Industrial Average (DJIA), from 1989 through 2015. On a time plot, time is plotted on the x-axis, and the value of interest is plotted on the y-axis. As you can see, the DJIA has generally increased in value since 1989, with some notable exceptions along the way (e.g., 2000 and 2008).

      Figure 3.11 “Line of Best Fit” That Allows Us to Predict Burnout (on the y-axis) from Role Overload (on the x-axis)

      Figure 3.12 Time Plot of The Dow Jones Industrial Average Since 1989

      Time plot: type of line graph that plots the value of a variable on the y-axis as it changes over time, which is displayed on the x-axis.

      How might a time plot be useful in making decisions? Let’s discuss an example. There is a local pizza place in the small town in which my college is located. They asked me to help predict how much pizza people order so that they can have enough fresh ingredients on hand to meet customers’ demands. To start this process, we plotted how many pizzas the restaurant sold each day for two months. These data are displayed in Figure 3.13. As we can see in this time plot, we know a lot of pizza is ordered on Sundays, with not many ordered on Mondays, Tuesdays, or Wednesdays, but then sales progressively pick up again Thursday, Friday, and Saturday. Armed with this time plot, the restaurant is now in a better position to predict when it will need to have fresh ingredients on hand to meet customer orders.²

      Let’s consider another use of line graphs. In their research, Caroline Campbell and Katherine White (2015) had undergraduate students complete a mood scale (Mayer & Gaschke, 1988) before and after engaging in moderately strenuous exercise. Half of the students listened to music while exercising, whereas the other half of the students did not listen to music while exercising. Their results are presented in a line graph in Figure 3.14. Along the x-axis is time, which was preexercise and postexercise. Along the y-axis is the average mood rating. There are two lines, one for the group of students who listened to music and one for the group of students who did not listen to music (the control group). As you can see in this line graph, both groups of students were in a better mood after exercising than before exercising. However, the mood of the group of students who listened to music while exercising improved even more than did the mood of the control group, who did not listen to music while exercising.

      Figure 3.13 How Can This Time Plot Help a Restaurant Manage Its Pizza Business?

      Figure 3.14 Results of Campbell and White’s (2015) Experiment

      Source: Campbell, C. R., & White, K. R. G. (2015). Working it out: Examining the psychological effects of music on moderate-intensity exercise. Psi Chi Journal of Psychological Research, 20, 73–79.

      Learning Check

      1 Look back at Figure 3.6. Interpret what information this visual display is communicating by using as simple language as possible.A: The Union Program Council was awarded more money (more than $30/respondent) than any other student organization was awarded, followed by the Agricultural Student Council (slightly less than $30/respondent). The History Club and the Math Club were awarded the least amounts of money of any student organization.

      2 Interpret the bar graph in Figure 3.15 by using as simple language as possible:Figure 3.15A: Satisfaction with college tends to be particularly high among first-years and seniors, with sophomores having the lowest level of satisfaction with college.

      3 Look back at Figure 3.7. Interpret what information this visual display is communicating by using as simple language as possible.A: As scores on the measure of role overload increase in value, scores on the burnout measure tend to increase in value as well. Stated differently, as scores on the measure of role overload decrease in value, scores on the burnout measure tend to decrease in value.

      4 Interpret the scatterplot in Figure 3.16 by using as simple language as possible.Figure 3.16A: As scores on the measure of impulsiveness increase in value, scores on the measure of achievement striving tend to decrease in value. Stated differently, as scores on the measure of impulsiveness decrease in value, scores on the measure of achievement striving tend to increase in value.

      5 Interpret the time plot in Figure 3.17 by using as simple language as possible.Figure 3.17A: In 1992, there were close to 300 robberies per 100,000 people. That rate declined steadily until 2000, to about 150 robberies per 100,000 people. It remained at about that level until 2008 when it began to decline again.

      Using SPSS to Make Visual Displays of Data

      In addition to being able to make sense of these