In statistical practice, some experiments focus on comparing the effect of each treatment to each other treatment; these are the elementary contrasts . The variances of the elementary contrasts for a connected design , aside from the constant , are
for , where is the general element of . Several optimality criteria are based on the numbers , called pairwise variances. Moreover, partial balance properties are reflected in the . For these reasons, pairwise_variances is also an element in the external representation. For disconnected designs some elementary contrasts are not estimable; in the external representation, the corresponding values are recorded as ``not_applicable.''