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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