  Yobuko recently introduced the notion of quasi-$F$-splitting and $F$-split
heights, which generalize and quantify the notion of Frobenius-splitting, and
proved that $F$-split heights coincide with Artin-Mazur heights for Calabi-Yau
varieties. In this paper, we prove Fedder type criteria of quasi-$F$-splittings
of complete intersections, and in particular obtain an easy formula to compute
Artin-Mazur heights of Calabi-Yau hypersurfaces. Moreover, as applications, we
give explicit examples of quartic K3 surfaces over $\mathbb{F}_{3}$ realizing
all the possible Artin-Mazur heights, we provide explicit computations of
$F$-split heights for all the rational double points and bielliptic surfaces,
and introduce interesting phenomena concerned with inversion of adjunction,
fiber products, Fano varieties, and general fibers of fibrations.
