In this article we recall a remarkable result stated as " For a fixed α, 0 < α ≤ 1, the set of all bounded statistically convergent sequences of order α is a closed linear subspace of m (m is the set of all bounded real sequences endowed with the sup norm) " by Bhunia et al. (Acta Math. Hungar. 130 (1-2) (2012), 153–161) and to develop the objective of this perception we demonstrate that the set of all bounded statistically convergent sequences of order α may not form a closed subspace in other sequence spaces. Also we determine two different sequence spaces in which the set of all statistically convergent sequences of order α (irrespective of boundedness) forms a closed set