RESEARCH METHOD COHEN ok

MEASURING ASSOCIATION 529
Box 24.23
Common measures of relationship
Measure Nature of variables Comment
Spearman’s rho Two ordinal variables Relationship linear
Pearson product moment r
Two continuous variables; interval or Relationship linear
ratio scale
Rank order or Kendall’s tau
Two continuous variables; ordinal
scale
Correlation ratio η (eta)
One variable continuous; other either Relationship nonlinear
continuous or discrete
Intraclass
One variable continuous other
discrete; interval or ratio scale
Purpose: to determine within-group
similarity
Biserial r bis
Point biserial r pt bis
One variable continuous; other
continuous but dichotomized, r bis
Index of item discrimination (used in
item analysis)
or true dichotomy r pt bis
Phi coefficient ϕ
Two true dichotomies; nominal or
ordinal series
Partial correlation r 12.3 Three or more continuous variables Purpose: to determine relationship
between two variables, with effect of
third held constant
Multiple correlation r 1.234 Three or more continuous variables Purpose: to predict one variable from
alinearweightedcombinationoftwo
or more independent variables
Kendall’s coefficient of concordance
(W)
Three or more continuous variables;
ordinal series
Purpose: to determine the degree of
(say, inter-rater) agreement
Chapter 24
Source:Mouly1978
can take on only numerals or values that are
specific points on a scale. The number of players
in a football team is a discrete variable. It is usually
11; it could be fewer than 11, but it could never
be 7 1 4 !
The percentage difference
The percentage difference is a simple asymmetric
measure of association. An asymmetric measure
is a measure of one-way association. That is
to say, it estimates the extent to which one
phenomenon implies the other but not vice
versa. Gender, as we shall see shortly, may imply
driving test success or failure. The association
could never be the other way round! Measures
that are concerned with the extent to which
two phenomena imply each other are referred
to as symmetric measures. Box 24.24 reports the
percentage of public library members by their social
class origin.
Box 24.24
Percentage of public library members by their
social class origin
Public library
membership
Middle class
Social class status
Working class
Member 86 37
Non-member 14 63
Total 100 100
What can we discover from the data set out in
Box 24.24
By comparing percentages in different columns
of the same row, we can see that 49 per cent
more middle-class persons are members of public
libraries than working-class persons. By comparing
percentages in different rows of the same columns
we can see that 72 per cent more middle-class