The Joint Variance: A Reply.

Abstract The article presents the author's reply to Professor R.M. Piper's comments on his paper "A Note on the Joint Variance." Piper raises the question of whether the three-variance method should be taught at all. The value of bringing the joint variance into classroom discussions of variance analysis is twofold. First, there are a number of possible treatments of this variance, and consideration of these alternatives is impossible without its explicit recognition. According to Piper, since the joint variance cannot be controlled by a single manager, it should not be assigned to any single manager. However, such treatment of the joint variance requires its recognition and separation. Thus, Piper himself seems to provide the requested rationalization for the three-variance analysis. The second reason for discussing the joint variance is so that students will recognize that the two-variance method commonly used and taught implicitly treats the joint variance as part of the price variance. This recognition may also help students remember that the multiplier of the price variance is actual quantity while the multiplier of the quantity variance is standard price, as opposed to alternative combinations.