Graphing relationships between variables was discussed briefly in Chapter 4. A common way to graph relationships between variables is to use a bar graph or a line graph. Figure 12.5 is a bar graph depicting the means for the model and no-model groups. The levels of the independent variable (no-model and model) are represented on the horizontal x axis, and the dependent variable values are shown on the vertical y axis. For each group, a point is placed along the y axis that represents the mean for the groups, and a bar is drawn to visually represent the mean value. Bar graphs are used when the values on the x axis are nominal categories (e.g., a no-model and a model condition). Line graphs are used when the values on the x axis are numeric (e.g., marijuana use over time, as shown in Figure 7.1). In line graphs, a line is drawn to connect the data points to represent the relationship between the variables.
Graph of the results of the modeling experiment showing mean aggression scores
Choosing the scale for a bar graph allows a common manipulation that is sometimes used by scientists and all too commonly used by advertisers. The trick is to exaggerate the distance between points on the measurement scale to make the results appear more dramatic than they really are. Suppose, for example, that a cola company (cola A) conducts a taste test that shows 52% of the participants prefer cola A and 48% prefer cola B. How should the cola company present these results? The two bar graphs in Figure 12.6 show the most honest method, as well as one that is considerably more dramatic. It is always wise to look carefully at the numbers on the scales depicted in graphs.
Two ways to graph the same data
It is important to know whether a relationship between variables is relatively weak or strong. A correlation coefficient is a statistic that describes how strongly variables are related to one another. You are probably most familiar with the Pearson product-moment correlation coefficient, which is used when both variables have interval or ratio scale properties. The Pearson product-moment correlation coefficient is called the Pearson r. Values of a Pearson r can range from 0.00 to ±1.00. Thus, the Pearson r provides information about the strength of the relationship and the direction of the relationship. A correlation of 0.00 indicates that there is no relationship between the variables. The nearer a correlation is to 1.00 (plus or minus), the stronger is the relationship. Indeed, a 1.00 correlation is sometimes called a perfect relationship because the two variables go together in a perfect fashion. The sign of the Pearson r tells us about the direction of the relationship; that is, whether there is a positive relationship or a negative relationship between the variables.
Data from studies examining similarities of intelligence test scores among siblings illustrate the connection between the magnitude of a correlation coefficient and the strength of a relationship. The relationship between scores of monozygotic (identical) twins reared together is .86 and the correlation for monozygotic twins reared apart is .74, demonstrating a strong similarity of test scores in these pairs of individuals. The correlation for dizygotic (fraternal) twins reared together is less strong, with a correlation of .59. The correlation among non-twin siblings raised together is .46, and the correlation among non-twin siblings reared apart is .24. Data such as these are important in ongoing research on the relative influence of heredity and environment on intelligence (Devlin, Daniels, & Roeder, 1997; Kaplan, 2012).
There are several different types of correlation coefficients. Each coefficient is calculated somewhat differently depending on the measurement scale that applies to the two variables. As noted, the Pearson r correlation coefficient is appropriate when the values of both variables are on an interval or ratio scale. We will now focus on the details of the Pearson product-moment correlation coefficient.