Summary: It is shown that if a sequence is strongly p-Cesàro summable or \(w_ p\) convergent for \(0<p<\infty\) then the sequence must be statistically convergent and that a bounded statistically convergent sequence must be \(w_ p\) convergent for any p, \(0<p<\infty\). It is also shown that the statistically convergent sequences do not form a locally convex FK space. A characterization of conservative matrices which map the bounded statistically convergent sequences into convergent sequences is given and applied to Nörlund and Nörlund-type means.