**
Graziano & Raulin**

**Research Methods (8th edition)**

To compute the Pearson product-moment correlation between age and
income, we select the Analyze menu, the Correlate submenu, and the
*Bivariate* option (which literally means two variables). These
selections will give us this screen.

We select the variables age and income and move them to the right
box. The default options in this procedure are to compute a Pearson
product-moment correlation and a two-tail *p*-value. Since
these are the options we want, we only need to click on OK to run
the correlations. The resulting output is shown in
this screen.

Note that SPSS for Windows actually gives us four correlations.
The program is set up to compute an intercorrelation matrix (i.e.,
the correlation of each variable with every other variable that was
selected) for as many variables as you select. If you select 10
variables, there would be a 10 by 10 matrix of intercorrelations.
The diagonal (from the upper left to the lower right) of that matrix
will list the correlation of each variable with itself, which will
always be equal to 1.00 (a perfect correlation). The correlational
matrix above and below this diagonal will be mirror images of one
another, because the correlation of variable *X* with
variable *Y* is the same as the correlation of variable *Y*
with variable *X*.

In our simplified example of only two variables, the correlation
between age and income is .883 and the probability of getting that
correlation or a larger correlation by chance if the population
correlation were actually zero (the *p*-value) is listed as
.000. Actually, no correlation will give you a *p*-value of
zero; but since only three digits are printed, a value listed as
.000 actually means that the probability is less than .001. If we
assume the traditional decision criteria (termed alpha level) of
.05, we would conclude that these two variables are significantly
correlated with one another, because our *p*-value is less than
the alpha level of .05 (see Chapter 5 for a more detailed
explanation of this terminology).

Remember that a Pearson product-moment correlation is an index of
the degree of __linear__ relationship between two variables. That
is, the correlation gives an indication of how closely the points in
a scatter plot cluster around a straight line. But the relationship
between two variables is not always linear. For example, if we
correlated a measure of general health with weight, we would likely
find that people who are either excessively heavy or light would
have generally poor health and that people in the middle range of
weight would likely be the healthiest.

To see what the shape of a relationship is like, you would
prepare a scatter plot. SPSS for Windows will prepare a scatter plot
with just a few mouse clicks. Click on the Graphs menu, Interactive
submenu, and select the *Scatterplot* option. These actions
will produce this screen. To prepare a
scatter plot of age by income, move the income variable to *X*
axis and then move the age variable to the *Y* axis of the
graph shown. Clicking on the OK button will produce the
scatter plot. As you can see, the
relationship between age and income does appear to be linear in our
data set.

We have prepared a series of animations that will walk you through the procedures discussed on this page. To run an animation, simply click on the title of the animation in the table below.

Note that we do not recommend that you try to run the animations if you have a slow connection, such as a dial-up connection. You will find that the animations take forever to load with a slow connection.