Nuisance Variables
C. MITCHELL DAYTON
Volume 3, pp. 1441–1442
Encyclopedia of Statistics in Behavioral Science
ISBN-13: 978-0-470-86080-9 ISBN-10: 0-470-86080-4
Editors: Brian S. Everitt & David C. Howell
John Wiley & Sons, Ltd, Chichester, 2005
Nuisance Variables
Nuisance variables are associated with variation in
an outcome (dependent variable) that is extraneous
to the effects of independent variables that are of
primary interest to the researcher. In experimental
comparisons among randomly formed treatment
groups, the impact of nuisance variables is to
increase experimental error and, thereby, decrease
the likelihood that true differences among groups
will be detected. Procedures that control nuisance
variables, and thereby reduce experimental error,
can be expected to increase the power for detecting
group differences. In addition to randomization,
there are three fundamental approaches to
controlling for the effects of nuisance variables.
First, cases may be selected to be similar for one or
more nuisance variables (e.g., only 6-year-old girls
with no diagnosed learning difficulties are included
in a study). Second, statistical adjustments may be
made using stratification (e.g., cases are stratified
by sex and grade in school). Note that the most
complete stratification occurs when cases are
matched one-to-one prior to application of
experimental treatments. Stratification, or
matching, on more than a small number of
nuisance variables is often not practical. Third,
statistical adjustment can be made using regression
procedures (e.g., academic ability is used as a
covariate in analysis of covariance, ANCOVA). In
the social sciences, randomization is considered a
sine qua non for experimental research. Thus, even
when selection, stratification, and/or covariance
adjustment is used, randomization is still necessary
for controlling unrecognized nuisance variables.
Although randomization to experimental
treatment groups guarantees their equivalence in
expectation, the techniques of selection,
stratification, and/or covariance adjustment are still
desirable in order to increase statistical power. For
example, if cases are stratified by grade level in
school, then differences among grades and the
interaction between grades and experimental
treatments are no longer confounded with
experimental error. In practice, substantial
increases in statistical power can be achieved by
controlling nuisance variances. Similarly, when
ANCOVA is used, the variance due to experimental
error is reduced in proportion to the squared
correlation between the dependent variable and the
covariate. Thus, the greatest benefit from statistical
adjustment occurs when the nuisance variables are
strongly related to the dependent variable. In effect,
controlling nuisance variables can reduce the
sample size required to achieve a desired level of
statistical power when making experimental
comparisons.
While controlling nuisance variables may
enhance statistical power in nonexperimental
studies, the major impetus for this control is that, in
the absence of randomization, comparison groups
cannot be assumed to be equivalent in expectation.
Thus, in nonexperimental studies, the techniques of
matching, stratification, and/or ANCOVA are
utilized in an effort to control preexisting
differences among comparison groups. Of course,
complete control of nuisance variables is not
possible without randomization. Thus,
nonexperimental studies are always subject to
threats to internal validity from unrecognized
nuisance variables. For example, in a case-control
study, controls may be selected to be similar to the
cases and matching, stratification, and/or
ANCOVA may be used, but there is no assurance
that all relevant nuisance variables have been taken
into account. Uncontrolled nuisance variables may
be confounded with the effects of treatment in such
a way that comparisons are biased.
For studies involving the prediction of an
outcome rather than comparisons among groups
(e.g., multiple regression and logistic regression
analysis), the same general concepts that apply to
nonexperimental studies are relevant. In regression
analysis, the independent contribution of a specific
predictor, say X, can be assessed in the context of
other predictors in the model. These other
predictors may include dummy-coded stratification
variables and/or variables acting as covariates (see
Dummy Variables). Then, a significance test for
the regression coefficient corresponding to X will
be adjusted for these other predictors. However, as
in the case of any nonexperimental study, this
assessment may be biased owing to unrecognized
nuisance variables.
C. MITCHELL DAYTON
Hardcover 2352 pages
June 2005 US $1,290.00
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