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Concomitant Variable
It is not uncommon in designing research for an investigator to collect an array of variables representing characteristics on each observational unit. Some of these variables are central to the investigation, whereas others reflect preexisting differences in observational units and are not of interest per se. The latter are called concomitant variables, also referred to as covariates. Frequently in practice, these incidental variables represent undesired sources of variation influencing the dependent variable and are extraneous to the effects of manipulated (independent) variables, which are of primary interest. For designed experiments in which observational units are randomized to treatment conditions, failure to account for concomitant variables can exert a systematic influence (or bias) on the different treatment conditions. Alternatively, concomitant variables can increase the error variance, thereby reducing the likelihood of detecting real differences among the groups. Given these potential disadvantages, an ideal design strategy is one that would minimize the effect of the unwanted sources of variation corresponding to these concomitant variables. In practice, two general approaches are used to control the effects of concomitant variables: (1) experimental control and (2) statistical control. An expected benefit of controlling the effects of concomitant variables by either or both of these approaches is a substantial reduction in error variance, resulting in greater precision for estimating the magnitude of treatment effects and increased statistical power.
Experimental Control
Controlling the effects of concomitant variables is generally desirable. In addition to random assignment of subjects to experimental conditions, methods can be applied to control these variables in the design phase of a study. One approach is to use a small number of concomitant variables as the inclusion criteria for selecting subjects to participate in the study (e.g., only eighth graders whose parents have at least a high school education). A second approach is to match subjects on a small number of concomitant variables and then randomly assign each matched subject to one of the treatment conditions. This requires that the concomitant variables are available prior to the formation of the treatment groups. Blocking, or stratification, as it is sometimes referred to, is another method of controlling concomitant variables in the design stage of a study. The basic premise is that subjects are sorted into relatively homogeneous blocks on the basis of levels of one or two concomitant variables. The experimental conditions are subsequently randomized within each stratum. Exerting experimental control through case selection, matching, and blocking can reduce experimental error, often resulting in improved statistical power to detect differences among the treatment groups. As an exclusive design strategy, the usefulness of any one of these three methods to control the effects of concomitant variables is limited, however. It is necessary to recognize that countless covariates, in addition to those used to block or match subjects, may be affecting the dependent variable and thus posing potential threats to drawing appropriate inferences regarding treatment veracity. In contrast, randomization to experimental conditions ensures that any idiosyncratic differences among the groups are not systematic at the outset of the experiment. Random assignment does not guarantee that the groups are equivalent but rather that any observed differences are due only to chance.
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