  Previous claims of significant evidence for mirror-parity in the large-scale
cosmic microwave background (CMB) data from the Wilkinson Microwave Anisotropy
Probe (WMAP) experiment have been recently echoed in the first study of
isotropy and statistics of CMB data from Planck. We revisit these claims with a
careful analysis of the latest data available. We construct statistical
estimators in both harmonic and pixel space, test them on simulated data with
and without mirror-parity symmetry, apply different Galactic masks, and study
the dependence of the results on arbitrary choices of free parameters. We
confirm that the data exhibit evidence for odd mirror-parity at a significance
which reaches as high as ~ 99 per cent C.L., under some circumstances. However,
given the inherent biases in the pixel-based statistic and the dependence of
both pixel and harmonic space statistics on the particular form of Galactic
masking and other a-posteriori choices, we conclude that these results are not
in significant tension with the predictions of the concordance cosmological
model.
