The paper contains a proof that the Guttman additive quasi‐simplex model is invariant under selection of examinees when a set of continuous variables each having different error of measurement is ordered on the simplex continuum in terms of either increasing or decreasing magnitudes of ‘complexity’ provided that selection is based on those measures which are less variable than each of the measures of the remaining set. When variables with highest ‘complexity’ ranks constitute the basis of selection, then such an invariance breaks down. The significance of the problem is discussed in the context of personnel selection. In addition, many implications of the results are stated which hold good for various multivariate statistical t