Statistical Control

The control of nuisance variables via an experimental design or statistical technique is rooted in causal inference. To infer causality in a study, a researcher must be able to infer that the results are a result of the treatment and not unchecked nuisance variables. For example, in comparing different drugs to determine which one is most effective in reducing diastolic blood pressure, changes in diastolic blood pressure must be attributable to the drugs. Clearly, if one is not careful in the assignment of individuals to the different drug treatment conditions, then one could end up making the wrong causal inference because of group idiosyncrasies. To make a fair comparison of the drugs, one must have “an equal playing field.” The researcher must control those variables that are known to affect diastolic blood pressure like age, health, physical activity, and diet. Because there is also a possibility of unknown variables affecting blood pressure, the researcher must be very careful. In most experimental situations, individuals are assigned at random to the treatment conditions to control for unknown as well as known nuisance variables that could upset the playing field. Ideally, participants in all the treatment conditions should be identical except for the drug being taken. Only under these conditions can one unmistakably infer causality. Using statistical procedures to adjust the result of a study for nuisance variable differences is the primary purpose of statistical control.

Using statistical procedures to adjust treatment comparisons for individual differences that could bias the comparison is especially important when randomization is not possible. Consider the following example, a researcher studying different methods of teaching math assigns a method to each classroom/teacher. In this situation, for many [Page 1445]reasons one cannot assign students to classrooms at random; that is, randomization is not possible. This situation is known as a field study. When randomization is not possible, one must seek other means of control. A way to try to assert control of nuisance variables is to use statistical techniques that equalize the playing field. Statistical techniques equalize the playing field by using the principle of conditionality. Consider age: If age plays a factor in blood pressure, it would be advantageous to use participants of the same age, say 40. Although possible, it is very unlikely to happen because it is very difficult to find only 40-year-old individuals to participate in the study. One can achieve a similar effect, however, with statistical control.

A plethora of statistical techniques can be used to attempt to achieve this “conditionalization” of nuisance variables. This entry discusses only the most fundamental ones: the analysis of variance with a blocked (subdivided) variable, the analysis of covariance, propensity scores, multiple regression, and the statistical control charts.