The Variance-Weighted Comparison

Abstract

The interpretation of data from unplanned experiments is sometimes difficult because of unequal subclass numbers. For instance, when evaluating the impact of sales training courses before a new salesman is given his territory, it is unlikely that there will be equal numbers of trained and untrained salesmen in each area. The problem arises as to how to weight the information from each area. The hypothetical example in Table 1 defines the problem with a specific example. It shows the sales of trained and untrained men in three sales areas, A, B, and C. The data show that in the worst sales area (Area A) all but two of the new salesmen were trained, that half the new men going into Area B, the next best area, were trained, but that only one of the men in the best area (Area C) had been trained. The comparison of the means of all trained and all untrained salesmen reflects the effect of both training and area and (18.8 29.3) is therefore confounded and an unsatisfactory way of answering the question, How much better or worse were the trained salesmen? One common approach is to weight the difference between means in each area by the number of trained salesmen in each area: