  We find that the observed pressure-mode rotational splittings of
slowly/moderately rotating Delta Scuti stars and Beta Cephei stars mostly have
a positive asymmetry. That is, the left frequency spacing is larger than the
right spacing in the dipole mode splitting triplets and the $l=2$ mode
splitting multiplets (considering $m=1, 0, -1$ modes only). This is in
agreement with the second-order perturbative effect of the rotational
non-spherical distortion: both the prograde and retrograde modes have their
frequencies shifted towards lower values relative to the $m=0$ modes. We thus
study the rotational perturbation both in the first and second order, as well
as the near-degeneracy mode coupling effect in MESA models representing Delta
Scuti stars. For faster rotators, the near-degeneracy mode coupling between the
nearest radial and quadrupole modes can significantly shift the $m=0$ modes,
reduce the splitting asymmetry, and even change its sign. We find the
theoretical splitting asymmetry from the second-order non-spherical distortion
is larger than observed asymmetry. To facilitate future detections, we predict
correlations between splitting asymmetry, splitting amplitude, and pulsation
frequency. We also discuss additional factors that can influence splitting
asymmetry, including embedded magnetic fields, resonant mode coupling, and
binarity.
