RESEARCH METHOD COHEN ok

MEASURING ASSOCIATION 535
Many useful studies have been based on this
simple design. Those involving more complex
relationships, however, utilize multiple and partial
correlations in order to provide a clearer picture of
the relationships being investigated.
One final point: it is important to stress again
that correlations refer to measures of association
and do not necessarily indicate causal relationships
between variables. Correlation does not imply
cause.
Interpreting the correlation coefficient
Once a correlation coefficient has been computed,
there remains the problem of interpreting it.
A question often asked in this connection is
how large should the coefficient be for it to be
meaningful. The question may be approached
in three ways: by examining the strength of
the relationship, by examining the statistical
significance of the relationship and by examining
the square of the correlation coefficient.
Inspection of the numerical value of a
correlation coefficient will yield clear indication
of the strength of the relationship between the
variables in question. Low or near zero values
indicate weak relationships, while those nearer to
+1 or−1 suggeststrongerrelationships.Imagine,
for instance, that a measure of a teacher’s success
in the classroom after five years in the profession is
correlated with his or her final school experience
grade as a student and that it was found that
r =+0.19. Suppose now that the teacher’s score
on classroom success is correlated with a measure
of need for professional achievement and that this
yielded a correlation of 0.65. It could be concluded
that there is a stronger relationship between
success and professional achievement scores than
between success and final student grade.
Where a correlation coefficient has been derived
from a sample and one wishes to use it as a basis
for inference about the parent population, the
statistical significance of the obtained correlation
must be considered. Statistical significance, when
applied to a correlation coefficient, indicates
whether or not the correlation is different from
zero at a given level of confidence. As we have
seen earlier, a statistically significant correlation
is indicative of an actual relationship rather than
one due entirely to chance. The level of statistical
significance of a correlation is determined to a
great extent by the number of cases upon which
the correlation is based. Thus, the greater the
number of cases, the smaller the correlation need
be to be significant at a given level of confidence.
Exploratory relationship studies are generally
interpreted with reference to their statistical
significance, whereas prediction studies depend
for their efficacy on the strength of the correlation
coefficients. These need to be considerably higher
than those found in exploratory relationship
studies and for this reason rarely invoke the
concept of significance.
The third approach to interpreting a coefficient
is provided by examining the square of the
coefficient of correlation, r 2 . This shows the
proportion of variance in one variable that can be
attributed to its linear relationship with the second
variable. In other words, it indicates the amount
the two variables have in common. If, for example,
two variables A and B have a correlation of 0.50,
then (0.50) 2 or 0.25 of the variation shown by the
BscorescanbeattributedtothetendencyofBto
vary linearly with A. Box 24.28 shows graphically
the common variance between reading grade and
arithmetic grade having a correlation of 0.65.
There are three cautions to be borne in mind
when one is interpreting a correlation coefficient.
Box 24.28
Visualization of correlation of 0.65 between
reading grade and arithmetic grade
Source:Fox1969
57.75% 42.25% 57.75%
Chapter 24