  The Kepler mission discovery of candidate transiting exoplanets (KOIs)
enables a plethora of ensemble analysis of the architecture and properties of
exoplanetary systems. We compare the observed transit durations of KOIs to a
synthetic distribution generated from the known eccentricities of radial
velocity (RV) discovered exoplanets. We find that the Kepler and RV
distributions differ at a statistically significant level. We identify three
related systematic trends that are likely due to errors in stellar radii, which
in turn affect the inferred exoplanet radii and the distribution thereof, and
prevent a valid analysis of the underlying ensemble eccentricity distribution.
First, 15% of KOIs have transit durations >20% longer than the transit duration
expected for an edge-on circular orbit, including 92 KOIs with transit
durations >50% longer, when only a handful of such systems are expected.
Second, the median transit duration is too long by up to ~25%. Random errors of
<50% in the stellar radius are not adequate to account for these two trends,
and they are present for all spectral types in the Kepler sample. We identify
that incorrect estimates of stellar metallicity and extinction could account
for these anomalies, rather than astrophysical effects such as eccentric
exoplanets improbably transiting near apastron. Third, we find that the median
transit duration is correlated with stellar radius, when no such trend is
expected. All three effects are still present, although less pronounced, when
considering only multiple transiting KOI systems which are thought to have a
low false positive rate. Improved stellar parameters for KOIs are necessary for
the validity of future ensemble tests of exoplanetary systems found by Kepler.
