  Some time-reversal symmetric topological orders are anomalous in that they
cannot be realized in strictly two-dimensions without breaking time reversal
symmetry; instead, they can only be realized on the surface of certain
three-dimensional systems. We propose two quantities, which we call {\it
anomaly indicators}, that can detect if a time-reversal symmetric topological
order is anomalous in this sense. Both anomaly indicators are expressed in
terms of the quantum dimensions, topological spins, and time-reversal
properties of the anyons in the given topological order. The first indicator,
$\eta_2$, applies to bosonic systems while the second indicator, $\eta_f$,
applies to fermionic systems in the DIII class. We conjecture that $\eta_2$,
together with a previously known indicator $\eta_1$, can detect the two known
$\mathbb Z_2$ anomalies in the bosonic case, while $\eta_f$ can detect the
$\mathbb Z_{16}$ anomaly in the fermionic case.
