Statistical significance, by itself, is not a sufficient condition for claiming that a hypothesis has been supported. Constructive replications are considerably more important. Unfortunately, classical (Fisherian) statistics are not easily adapted to sequential research strategies; their focus is the single experiment. For this reason, statistically significant results may be meaningless while a particular sequence of nonsignificant results may be quite important. Advice on how to overcome some limitations of classical statistical procedures is given, along with a compendium of "do's and don't's.".