Science with or without statistics: Discover-generalize-replicate? Discover-replicate-generalize?

Overstated generalizability (external validity) is common in research. It may coexist with inflation of the magnitude and statistical support for effects and dismissal of internal validity problems. Generalizability may be secured before attempting replication of proposed discoveries or replication may precede efforts to generalize. These opposite approaches may decrease or increase, respectively, the use of inferential statistics with advantages and disadvantages.