Abnormal Psychology

Researching Abnormality 161

Professors who teach statistics are fond

of having their students memorize a simple

statement:Correlation does not imply cau-

sation. To determine causation, a researcher

must manipulate an independent variable

while holding everything else constant.

Only then can the results demonstrate that

changes in the independent variable actually

caused changes in the dependent variable.

Measuring a Correlation

The strength of the correlation between any

two variables is quantified by a number

called a correlation coefficient (most typi-

cally symbolized by r). When this number is

positive, it signifi es that the variables change

in the same direction; both variables either

increase or decrease in the same general pat-

tern. A positive relationship is indicated by

any correlation coeffi cient between 0 and +1.

When the correlation coeffi cient is negative, it

signifi es that the variables change in opposite

directions in the same general pattern; one

goes up while the other goes down. A nega-

tive relationship is indicated by a correlation

coeffi cient between 0 and –1. In either case,

positive or negative, the stronger the relation-

ship, the closer the coeffi cient is to +1 or –1.

If the variables do not have any relationship

at all, the correlation coeffi cient is 0.

If you plot two variables on a graph,

putting one variable on each axis, you can

see whether or not the variables change to-

gether. The closer the data points are to a

straight line, the stronger the correlation.

Figure 5.2 illustrates five possible correla-

tions. When you draw a line through the

data points as in the fi gure, you can measure

the distance (parallel to the vertical axis) be-

tween each point and the line. The shorter

these distances, on average, the stronger the

correlation (leaning toward +1 or –1). Com-

puter programs that perform statistical tests

use a mathematical formula to calculate the

correlation coeffi cient.

Statistical Signifi cance

Even when variables are completely inde-

pendent, they might vary in the same pattern

simply by chance. In fact, the correlation co-

effi cient between any two randomly selected

sets of data is very seldom exactly 0. A cor-

relation coeffi cient is statistically signifi cant when it is greater than what would be

expected by chance alone. Statistical signifi cance is not the same thing as “impor-

tance.” It simply means that the observed result is unlikely to be a quirk of random

variation in the data. Suppose, for your participants, you calculated the correlation

between age when experiencing a loss during childhood and symptoms of depres-

sion after an adult breakup, and the result was r = –0.11. This means the younger

5.2 • Five Values of Correlation

Figure 5.2

hii h h ldb 52•Fi Vl fC lti

x

y

Perfect positive correlation (1.0)

Moderate positive correlation(.5)

x

y

x

y

No correlation (0.0)

Moderate negative correlation(–.5)

x

y

Perfect negative correlation (–1.0)

x

y