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Figure 2.2.2
One way of organizing the data from a correlational study with two variables is to graph the
values of each of the measured variables using a scatter plot. As you can see in Figure 2.10
"Examples of Scatter Plots", a scatter plot is a visual image of the relationship between two
variables. A point is plotted for each individual at the intersection of his or her scores for the two
variables. When the association between the variables on the scatter plot can be easily
approximated with a straight line, as in parts (a) and (b) of Figure 2.10 "Examples of Scatter
Plots", the variables are said to have a linear relationship.
When the straight line indicates that individuals who have above-average values for one variable
also tend to have above-average values for the other variable, as in part (a), the relationship is
said to be positive linear. Examples of positive linear relationships include those between height
and weight, between education and income, and between age and mathematical abilities in
children. In each case people who score higher on one of the variables also tend to score higher
on the other variable. Negative linear relationships, in contrast, as shown in part (b), occur when
above-average values for one variable tend to be associated with below-average values for the
other variable. Examples of negative linear relationships include those between the age of a child
and the number of diapers the child uses, and between practice on and errors made on a learning
task. In these cases people who score higher on one of the variables tend to score lower on the
other variable.
Relationships between variables that cannot be described with a straight line are known
as nonlinear relationships. Part (c) of Figure 2.10 "Examples of Scatter Plots" shows a common
pattern in which the distribution of the points is essentially random. In this case there is no
relationship at all between the two variables, and they are said to be independent. Parts (d) and
(e) of Figure 2.10 "Examples of Scatter Plots" show patterns of association in which, although