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.''

Peter Dobcsanyi 2003-12-15