Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics

A criterion is evolved for testing the nonclassical character of the field even if it does not exhibit squeezing and sub-Poissonian statistics. An explicit example of a state of the field is given to demonstrate the utility of this criterion. The production of such a state by state-reduction methods is also shown. This criterion also enables us to study the nonclassical character of the Schrödinger cat state in regions where it does not exhibit sub-Poissonian statistics.