  The light curve of an eclipsing system shows anomalies whenever the eclipsing
body passes in front of active regions on the eclipsed star. In some cases, the
pattern of anomalies can be used to determine the obliquity $\Psi$ of the
eclipsed star. Here we present a method for detecting and analyzing these
patterns, based on a statistical test for correlations between the anomalies
observed in a sequence of eclipses. Compared to previous methods, ours makes
fewer assumptions and is easier to automate. We apply it to a sample of 64
stars with transiting planets and 24 eclipsing binaries for which precise
space-based data are available, and for which there was either some indication
of flux anomalies or a previously reported obliquity measurement. We were able
to determine obliquities for ten stars with hot Jupiters. In particular we
found $\Psi \lesssim$10$^\circ$ for Kepler-45, which is only the second M dwarf
with a measured obliquity. The other 8 cases are G and K stars with low
obliquities. Among the eclipsing binaries, we were able to determine
obliquities in 8 cases, all of which are consistent with zero. Our results also
reveal some common patterns of stellar activity for magnetically active G and K
stars, including persistently active longitudes.
