RESEARCH METHOD COHEN ok

530 QUANTITATIVE DATA ANALYSIS
persons are members rather than non-members.
The data suggest, do they not, an association
between the social class status of individuals and
their membership of public libraries.
Asecondwayofmakinguseofthedatain
Box 24.24 involves the computing of a percentage
ratio (%R). Look, for example, at the data in the
second row of Box 24.24. By dividing 63 by 14
(%R = 4.5) we can say that four and a half times
as many working-class persons are not members of
public libraries as are middle-class persons.
The percentage difference ranges from 0 per cent
when there is complete independence between
two phenomena to 100 per cent when there
is complete association in the direction being
examined. It is straightforward to calculate and
simple to understand. Notice, however, that the
percentage difference as we have defined it can be
employed only when there are only two categories
in the variable along which we percentage and
only two categories in the variable in which
we compare. In SPSS, using the ‘Crosstabs’
command can yield percentages, and we indicate
this in the web site manual that accompanies this
volume.
In connection with this issue, on the accompanying
web site we discuss the phi coefficient,
the correlation coefficient tetrachoric r
(r t ), the contingency coefficient C, and combining
independent significance tests of partial relations,
see http://www.routledge.com/textbooks/
9780415368780 – Chapter 24, file 24.4.doc.
Explaining correlations
In our discussion of the principal correlational
techniques shown in Box 24.23, three are of special
interest to us and these form the basis of much
of the rest of the chapter. They are the Pearson
product moment correlation coefficient, multiple
correlation and partial correlation.
Correlational techniques are generally intended
to answer three questions about two variables or
two sets of data. First, ‘Is there a relationship
between the two variables (or sets of data)’ If the
answer to this question is ‘Yes’, then two other
questions follow: ‘What is the direction of the
relationship’ and ‘What is the magnitude’
Relationship in this context refers to any
tendency for the two variables (or sets of data)
to vary consistently. Pearson’s product moment
coefficient of correlation, one of the best known
measures of association, is a statistical value
ranging from −1.0to+ 1.0 and expresses this
relationship in quantitative form. The coefficient
is represented by the symbol r.
Where the two variables (or sets of data)
fluctuate in the same direction, i.e. as one increases
so does the other, or as one decreases so does
the other, a positive relationship is said to exist.
Correlations reflecting this pattern are prefaced
with a plus sign to indicate the positive nature
of the relationship. Thus, +1.0 would indicate
perfect positive correlation between two factors, as
with the radius and diameter of a circle, and +0.80
ahighpositivecorrelation,asbetweenacademic
achievement and intelligence, for example. Where
the sign has been omitted, a plus sign is assumed.
Anegativecorrelationorrelationship,onthe
other hand, is to be found when an increase
in one variable is accompanied by a decrease
in the other variable. Negative correlations are
prefaced with a minus sign. Thus, −1.0 would
represent perfect negative correlation, as between
the number of errors children make on a spelling
test and their score on the test, and −0.30 a low
negative correlation, as between absenteeism and
intelligence, say. There is no other meaning to
the signs used; they indicate nothing more than
which pattern holds for any two variables (or sets
of data).
Generally speaking, researchers tend to be more
interested in the magnitude of an obtained correlation
than they are in its direction. Correlational
procedures have been developed so that
no relationship whatever between two variables
is represented by zero (or 0.00), as between body
weight and intelligence, possibly. This means that
people’s performance on one variable is totally
unrelated to their performance on a second variable.
If they are high on one, for example, they
are just as likely to be high or low on the other.
Perfect correlations of +1.00 or −1.00 are rarely