  Alternating sign trapezoids have recently been introduced as a generalisation
of alternating sign triangles. Fischer established a threefold refined
enumeration of alternating sign trapezoids and provided three statistics on
column strict shifted plane partitions with the same joint distribution. In
this paper, we are able to add a new pair of statistics to these results. More
precisely, we consider the number of $-1$s on alternating sign trapezoids and
introduce a corresponding statistic on column strict shifted plane partitions
that has the same distribution. More generally, we show that the joint
distributions of the two quadruples of statistics on alternating sign
trapezoids and column strict shifted plane partitions, respectively, coincide.
In addition, we provide a closed-form expression for the $2$-enumeration of
alternating sign trapezoids.
