The definition of strong Cesaro summability with respect to a modulus is extended to a definition of strong A-summability with respect to a modulus when A is a nonnegative regular matrix summability method. It is shown that if a sequence is strongly A-summable with respect to an arbitrary modulus then it is A-statistically convergent and that A- statistical convergence and strong A-summability with respect to a modulus are equivalent on the bounded sequences.