  Our basic concept is the set $\mathcal{E}(H)$ of effects on a finite
dimensional complex Hilbert space $H$. If $a,b\in\mathcal{E}(H)$, we define the
sequential product $a[\mathcal{I}]b$ of $a$ then $b$. The sequential product
depends on the operation $\mathcal{I}$ used to measure $a$. We begin by
studying the properties of this sequential product. It is observed that
$b\mapsto a[\mathcal{I}]b$ is an additive, convex morphism and we show by
examples that $a\mapsto a[\mathcal{I}]b$ enjoys very few conditions. This is
because a measurement of $a$ can interfere with a later measurement of $b$. We
study sequential products relative to Kraus, L\"uders and Holevo operations and
find properties that characterize these operations. We consider repeatable
effects and conditions on $a[\mathcal{I}]b$ that imply commutativity. We
introduce the concept of an effect $b$ given an effect $a$ and study its
properties. We next extend the sequential product to observables and
instruments and develop statistical properties of real-valued observables. This
is accomplished by employing corresponding stochastic operators. Finally, we
introduce an uncertainty principle for conditioned observables.
