The merit of linear projections as a way to improve the resolution in damage detection under changing environmental conditions is examined. It is contended that if the data from the reference condition is balanced, in the sense that the number of feature vectors available for the various temperatures is similar, then projections, such as those in Principal Component Analysis and Factor Analysis, will not improve performance. Projections, however, help to control the false positive rate when the reference data set is not balanced. Analysis and simulation results suggest that previous claims on the merit of projection as a way to improve damage detection resolution under environmental variability may be too optimistic.