RESEARCH METHOD COHEN ok

536 QUANTITATIVE DATA ANALYSIS
First, a coefficient is a simple number and must not
be interpreted as a percentage. A correlation of
0.50, for instance, does not mean 50 per cent
relationship between the variables. Further, a
correlation of 0.50 does not indicate twice as much
relationship as that shown by a correlation of 0.25.
A correlation of 0.50 actually indicates more than
twice the relationship shown by a correlation of
0.25. In fact, as coefficients approach +1 or−1, a
difference in the absolute values of the coefficients
becomes more important than the same numerical
difference between lower correlations would be.
Second, a correlation does not necessarily imply
acause-and-effectrelationshipbetweentwofactors,
as we have previously indicated. It should not
therefore be interpreted as meaning that one factor
is causing the scores on the other to be as they
are. There are invariably other factors influencing
both variables under consideration. Suspected
cause-and-effect relationships would have to be
confirmed by subsequent experimental study.
Third, a correlation coefficient is not to be
interpreted in any absolute sense. A correlational
value for a given sample of a population may
not necessarily be the same as that found in
another sample from the same population. Many
factors influence the value of a given correlation
coefficient and if researchers wish to extrapolate
to the populations from which they drew their
samples they will then have to test the significance
of the correlation.
We now offer some general guidelines for
interpreting correlation coefficients. They are
based on Borg’s (1963) analysis and assume that
the correlations relate to 100 or more subjects.
Correlations ranging from 0.20 to 0.35
Correlations within this range show only very
slight relationship between variables although
they may be statistically significant. A correlation
of 0.20 shows that only 4 per cent ({0.20 ×
0.20}×100) of the variance is common to the two
measures. Whereas correlations at this level may
have limited meaning in exploratory relationship
research, they are of no value in either individual
or group prediction studies.
Correlations ranging from 0.35 to 0.65
Within this range, correlations are statistically
significant beyond the 1 per cent level. When
correlations are around 0.40, crude group
prediction may be possible. As Borg (1963) notes,
correlations within this range are useful, however,
when combined with other correlations in a
multiple regression equation. Combining several
correlations in this range can in some cases yield
individual predictions that are correct within an
acceptable margin of error. Correlations at this
level used singly are of little use for individual
prediction because they yield only a few more
correct predictions than could be accomplished
by guessing or by using some chance selection
procedure.
Correlations ranging from 0.65 to 0.85
Correlations within this range make possible group
predictions that are accurate enough for most
purposes. Nearer the top of the range, group
predictions can be made very accurately, usually
predicting the proportion of successful candidates
in selection problems within a very small margin
of error. Near the top of this correlation range
individual predictions can be made that are
considerably more accurate than would occur if
no such selection procedures were used.
Correlations over 0.85
Correlations as high as this indicate a close
relationship between the two variables correlated.
A correlation of 0.85 indicates that the measure
used for prediction has about 72 per cent variance
in common with the performance being predicted.
Prediction studies in education very rarely yield
correlations this high. When correlations at this
level are obtained, however, they are very useful
for either individual or group prediction.
Regression analysis
Regression analysis enables the researcher to predict
‘the specific value of one variable when