A sequence $(x_n)$ of points in a 2-normed space $X$ is statistically quasi-Cauchy if the sequence of difference between successive terms statistically converges to 0. In this paper we mainly study statistical ward continuity, where a function $f$ defined on a subset $E$ of $X$ is statistically ward continuous if it preserves statistically quasi-Cauchy sequences of points in $E$. Some other types of continuity are also discussed, and interesting results related to these kinds of continuity are obtained in 2-normed space setting.