When determining the generalizedT2statistics for a sample ofnobservations using principal components, the occasion may arise where one is interested not in the average of the deviations of a particular component from its aim or standard, but the average of the absolute values of these deviations because it is the magnitude, not the direction. which is of interest. A largesample approximation suitable for quality control applications is proposed to still enable one to include this component in the computation ofTM2. The adequacy of this approximation is examined and a numerical example is included.