Page 213 - The Handbook of Persuasion and Social Marketing

Empirical Generalizations for Social Marketing 205

socially responsible organizational behaviors may improve both corporate
and social well-being, a final section summarizes the effects of corporate so-
cial or environmental performance on financial performance.
Empirical generalizations on these issues are largely presented in terms
of four types of effect sizes: correlation coefficients, elasticities, standard-
ized mean differences, and odds ratios. To facilitate interpretation of the
findings, the next section provides a brief review of the meaning and inter-
pretation of these metrics. Much more detail is available in sources such as
Borenstein (2009) and Cooper and colleagues (2009).

Interpreting Effect Sizes

The correlation coefficient, usually symbolized r, is a measure of the
strength of the linear relationship between two variables. It equals the co-
variance between two variables divided by the product of their standard
deviations, and is therefore constrained to a range between −1 and +1. As
r approaches ±1, a scatterplot of the variables’ values approaches a straight
line (sloping up for r = 1 and down for r = −1). When r = 0, there is no
(linear) relationship between the variables. Values of r equal to .1, .3, and
.5 are often considered to be small, medium, and large effects, respectively
(Cohen, 1992). Dunlap’s (1994) common language effect size indicator, or
CL , helps to clarify the practical implications of these values. For exam-
R
ple, Dunlap notes that the correlation between fathers’ heights and sons’
−1
heights is about .40, giving CL = sin (.40)/π + .5 = .63. This value implies
R
that the taller of two fathers has a 63% likelihood of having the taller son.
CL values for r = .0, .1, .3, and .5 equal .500, .532, .597, and .667, re-
R
spectively. Thus, if two variables, x and y, are uncorrelated (r = 0), then
xy
knowing that one of two people has a higher x value indicates nothing
about which of the two has a higher y value. If r = .3, though, then the
xy
person who has a higher x value has a 60% chance of having a higher y
value, or 3-to-2 odds. If r = .5, the person who has a higher x value has a
xy
67% chance of having a higher y value, or 2-to-1 odds. As a concrete ex-
ample, the correlation between corporate environmental performance and
financial performance is .10 (Margolis, Elfenbein, & Walsh, 2009; see
Table 8.6). Thus, of two companies, the one that performs better environ-
mentally has a 53% chance of also performing better financially.
An elasticity, e, gives the percent change in quantity demanded of one vari-
able given a 1% change in another variable. Unlike correlations, elasticities
can be greater than 1 or less than −1, indicating elastic demand or more-than-
proportional responses to changes in inputs. If e is less than 1 in absolute
value, demand is inelastic. Price elasticities are typically negative, such that