All test items are perfectly reliable. The unreliability of test scores results solely from person fluctuations. The theory implies that: (1) test length effects are a sampling phenomenon; (2) person reliabilities can be compared from person characteristic curves; (3) all ICC for a unidimensional test have the same slope; (4) ICC are not necessarily invariant from one group to another; and (5) reliabilities of groups can be compared from ICC.A reliability coefficient of the theory is defined as the proportion of variance in obtained scores attributable to variance in average attribute level for subjects. Lower bounds for the classical reliability coefficient are also lower bounds for the new coefficient. Statistics calculated from this coefficient have no useful application.