Oxford Handbook of Human Resource Management

(Steven Felgate) #1

the sample size and R^2 for the performance equation increases and as the
collinearity of HR with other independent variables decreases (e.g. Cohen and
Cohen 1983 : 109 ).^4
When eVect sizes are expressed in unstandardized regression coeYcient terms
and the variables are in ratio scale form (e.g. dollars), it changes the discussion of
researchWndings and the discussion of implications from what it is when a binary
test of statistical signiWcance is the focus (Becker and Gerhart 1996 ). Indeed, many
of the issues I discuss below may not matter a great deal if the inference goal is to
simply make a binary statistical signiWcance decision. In contrast, when one begins
to estimate and report policy-relevant eVect sizes (for instance,Wrms using HR
system A have 20 percent higher proWts thanWrms using HR system B, e.g. Huselid
1995 —see below), oneWnds that conclusions can change signiWcantly, depending
on methodological issues such as the level of reliability (which, in turn, depends on
estimating reliability correctly). Therefore, once one interprets point-estimate
eVects of HR-related variables on natural metric outcomes like proWts and total
shareholder return, one is forced to a much greater degree to think about whether
the eVect sizes are plausible or not.
There are other advantages as well to using unstandardized regression coeY-
cients rather than standardized regression coeYcients. First, whereas unreliability
in the dependent variable biases the standardized regression coeYcient, it does not
bias the unstandardized regression coeYcient. (Unreliability in the independent
variable biases both types of regression coeYcients and unreliability in either the
independent or dependent variable also leads to downward bias in R^2 .) Second,
range restriction in the independent variable (variance in the sample is less than its
variance in the population) biases the standardized regression coeYcient toward
zero, but does not bias the unstandardized regression coeYcient (Cain and Watts
1970 ; Cohen and Cohen 1983 ; Darlington 1990 ).^5 This bias in the standardized
coeYcient is a major drawback, and, as Cain and Watts observe, stems from this
eVect size estimate being ‘dependent upon the particular policies pursued when the
data were collected’; and if these policies have restricted variance, using the
standardized coeYcient ‘runs the risk of declaring a policy feeble simply because
historically it was not vigorously applied’ ( 199 : 236 ). (Range restriction in the
independent variable does lead to downward bias in R^2. Range restriction in y
biases both standardized and unstandardized regression coeYcients. See discussion
of sample selection bias.)


(^4) Sometimes an author claims that when a regression coeYcient is not statistically signiWcant, ‘if we
had used a larger sample size, the coeYcient would have reached statistical signiWcance.’ This is not
necessarily correct because the regression coeYcient varies across samples, meaning it could be smaller
in a diVerent sample. So, while it is correct that the conWdence interval around the coeYcient would
be smaller in a larger sample,ceteris paribus, it is unlikely that the conWdence interval would be
centered around the same coe 5 Ycient estimate in that larger sample.
Range enhancement, by contrast, leads to an upward bias in the standardized coeYcient.
modeling hrm and performance linkages 555

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