Let a real or complex sequence be given. We say that it converges statistically to some limit if for all
Let denote the -transform of the sequence. Now, consider a sequence such that is statistically convergent. The main results in this paper give necessary and sufficient one- and two-sided ‘statistical’ oscillation conditions which imply statistical convergence of the sequence. The results immediately show that ‘statistical’ slow oscillation or ‘statistical’ slow decrease are Tauberian conditions from statistical -convergence to statistical convergence. These Tauberian conditions hold under ordinary slow oscillation or slow decrease, which in turn are Tauberian conditions from statistical convergence to ordinary convergence; see J. A. Fridy and M. K. Khan [Proc. Am. Math. Soc. 128, 2347-2355 (2000; Zbl 0939.40002)].