Not surprisingly then, guidelines for statistical methods (even) in psychology
journals now admonish researchers that ‘if the units of measurement are meaningful
on a practical level... then we usually prefer an unstandardized measure (regres-
sion coeYcient or mean diVerence) to a standardized measure (r or d)’ and that ‘it
helps to add brief comments that place these eVect sizes in a practical and theoretical
context’ (Wilkinson and the Task Force on Statistical Inference 1999 : 599 ). Likewise,
a recent article on meta-analysis (Bond et al. 2003 ) calls for cumulating eVect sizes in
terms of ‘raw mean diVerences’ whenever meaningful, rather than using standard
deviation units or other standardized eVect sizes (e.g., d, r).
27.4 Challenges in Inferring Causality
and Potential Solutions
.........................................................................................................................................................................................
Cook and Campbell, drawing on John Stuart Mill, give three necessary conditions
for inferring causality: (a) covariance between cause and eVect (i.e. a non-zero
eVect size), (b) time precedence (cause occurs in time before the eVect), and (c) ‘rule
out alternative interpretations for a possible cause and eVect connection’ ( 1979 : 31 ).
It is useful to keep in mind, however, the following points. First, eVect size
estimation and ruling out alternative causal models is often not separable. The
wrong causal model (e.g. omitting variables, ignoring reciprocal causation) often
results in biased eVect size estimates. As another example, a statistically signiWcant
and credible causal relationship may be of trivial magnitude. Second, the require-
ment to ‘rule out’ alternative models may have the unfortunate eVect of leading
researchers to believe that they must choose between two models, rather than
combining elements of both. This is especially a problem with reciprocal causation,
where researchers sometimes seem determined to show that causation runs one
way or another, but not in both directions. I return to this point later.
The three speciWc issues I have chosen to address below arise from the violation
of one assumption of the earlier described classical regression/OLS model (Duncan
1975 ; Wooldridge 2002 : 50 – 1 ): that the independent variable (HR here) and e are
independent, or cov(HR,e)¼ 0.^6 These three issues are: measurement error (‘errors
in variables’), speciWcation error (usually referring to omitted variables), and
simultaneity (i.e. reciprocal or non-recursive causation).^7 Sample selection bias
(^6) There are other important assumptions (e.g. homoskedasticity, lack of autocorrelation).
(^7) Wooldridge ( 2002 : 50 ) observes that in applied econometrics, the term ‘endogenous’ is used to
refer to any right hand side variable that that is correlated with the disturbance term. He also notes,
however, that the term endogenous has a more traditional meaning (Alwin and Hauser 1975 ): any
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