  Of the available classes of insulators which have been shown to contain
topologically non-trivial properties one of the most important is class AII,
which contains systems that possess time-reversal symmetry $T$ with $T^2=-1.$
This class has been the subject of significant attention as it encompasses
non-trivial Z$_2$ topological insulators such as the quantum spin Hall (QSH)
state and the 3D strong topological insulator. One of the defining properties
of this system is the robustness of the state under the addition of disorder
that preserves $T.$ In this letter, we explore the phase diagram of the
disordered QSH state as a function of disorder strength and chemical potential
by examining the entanglement spectrum for disordered class AII symplectic
systems. As for the case of the $T$ breaking Chern insulator we show that there
is a correspondence between the level-spacing statistics of the Hamiltonian and
that of the level spacing statistics of the entanglement spectrum. We observe a
feature in the statistics of the entanglement spectrum that aids the
identification of delocalized states and consequently critical energies across
which phase transitions occur.
