Analysis of Covariance: Increasing Precision in Comparison by Controlling Covariate

Abstract

To compare the effectiveness of two or more treatments on certain criterion variable, we use one-way analysis of variance technique. This technique has been discussed in Chap. 7. In testing the comparative effectiveness of different treatments, the subjects are selected in each experimental group by using the principle of randomization. In a situation if the randomization is not possible, groups are equated on the basis of one or more known parameters. The randomization or matching is done in order to have the similar initial conditions so that whatever the difference occurs in the criterion variable in the treatment, groups can be attributed due to treatments only. But in many situations, randomization of subjects or experimental units may not be possible as the experimenter may be forced to take the two or more intact samples from different locations due to administrative or financial constraints. For example, consider an experiment where it is desired to compare the effect of different types of tariff incentives on the increase in mobile recharge. In that situation, an experimenter will not have any choice to select the subject randomly in different experimental groups. Samples will have to be drawn from the predefined clientele sets of the different mobile companies. In such situations, groups are not homogeneous initially. These subjects in intact groups may differ in so many ways which might affect their behavior pattern. Thus, statistical control or indirect procedure is necessary to reduce the experimental error due to such initial differences in the groups.