  The combination of data from long-baseline and reactor oscillation
experiments leads to a preference of the leptonic CP phase $\delta_{\rm CP}$ in
the range between $\pi$ and $2\pi$. We study the statistical significance of
this hint by performing a Monte Carlo simulation of the relevant data. We find
that the distribution of the standard test statistic used to derive confidence
intervals for $\delta_{\rm CP}$ is highly non-Gaussian and depends on the
unknown true values of $\theta_{23}$ and the neutrino mass ordering. Values of
$\delta_{\rm CP}$ around $\pi/2$ are disfavored at between $2\sigma$ and
$3\sigma$, depending on the unknown true values of $\theta_{23}$ and the mass
ordering. Typically the standard $\chi^2$ approximation leads to over-coverage
of the confidence intervals for $\delta_{\rm CP}$. For the 2-dimensional
confidence region in the ($\delta_{\rm CP},\theta_{23}$) plane the usual
$\chi^2$ approximation is better justified. The 2-dimensional region does not
include the value $\delta_{\rm CP} = \pi/2$ up to the 86.3\% (89.2\%)~CL
assuming a true normal (inverted) mass ordering. Furthermore, we study the
sensitivity to $\delta_{\rm CP}$ and $\theta_{23}$ of an increased exposure of
the T2K experiment, roughly a factor 12 larger than the current exposure and
including also anti-neutrino data. Also in this case deviations from
Gaussianity may be significant, especially if the mass ordering is unknown.
