RESEARCH METHOD COHEN ok

534 QUANTITATIVE DATA ANALYSIS
assume linearity (e.g. the Pearson productmoment
correlation). However, rather than using
correlational statistics arbitrarily or blindly, the
researcher will need to consider whether, in fact,
linearity is a reasonable assumption to make,
or whether a curvilinear relationship is more
appropriate (in which case more sophisticated
statistics will be needed, e.g. η (‘eta’) (Cohen
and Holliday 1996: 84; Glass and Hopkins
1996, section 8.7; Fowler et al. 2000: 81–89) or
mathematical procedures will need to be applied
to transform non-linear relations into linear
relations. Examples of curvilinear relationships
might include:
pressure from the principal and teacher
performance
pressure from the teacher and student
achievement
degree of challenge and student achievement
assertiveness and success
age and muscular strength
age and physical control
age and concentration
age and sociability
age and cognitive abilities.
Hopkins et al. (1996)suggestthatthevariable
‘age’ frequently has a curvilinear relationship with
other variables, and also point out that poorly
constructed tests can give the appearance of
curvilinearity if the test is too easy (a ‘ceiling
effect’ where most students score highly) or if it is
too difficult, but that this curvilinearity is, in fact,
spurious, as the test does not demonstrate sufficient
item difficulty or discriminability (Hopkins et al.
1996: 92).
In planning correlational research, then,
attention will need to be given to whether linearity
or curvilinearity is to be assumed.
Coefficients of correlation
The coefficient of correlation, then, tells us
something about the relations between two
variables. Other measures exist, however, which
allow us to specify relationships when more than
two variables are involved. These are known
as measures of ‘multiple correlation’ and ‘partial
correlation’.
Multiple correlation measures indicate the
degree of association between three or more
variables simultaneously. We may want to know,
for example, the degree of association between
delinquency, social class background and leisure
facilities. Or we may be interested in finding out
the relationship between academic achievement,
intelligence and neuroticism. Multiple correlation,
or ‘regression’ as it is sometimes called, indicates
the degree of association between n variables.
It is related not only to the correlations of
the independent variable with the dependent
variables, but also to the intercorrelations between
the dependent variables.
Partial correlation aims at establishing the
degree of association between two variables after
the influence of a third has been controlled or
partialled out. Guilford and Fruchter (1973) define
apartialcorrelationbetweentwovariablesasone
which nullifies the effects of a third variable (or
a number of variables) on the variables being
correlated. They give the example of correlation
between the height and weight of boys in a group
whose age varies, where the correlation would
be higher than the correlation between height
and weight in a group comprised of boys of only
the same age. Here the reason is clear – because
some boys will be older they will be heavier and
taller. Age, therefore, is a factor that increases the
correlation between height and weight. Of course,
even with age held constant, the correlation would
still be positive and significant because, regardless
of age, taller boys often tend to be heavier.
Consider, too, the relationship between success
in basketball and previous experience in the game.
Suppose, also, that the presence of a third factor,
the height of the players, was known to have
an important influence on the other two factors.
The use of partial correlation techniques would
enable a measure of the two primary variables
to be achieved, freed from the influence of the
secondary variable.
Correlational analysis is simple and involves
collecting two or more scores on the same group of
subjects and computing correlation coefficients.