  Null Hypothesis Significance Testing (NHST) has long been central to the
scientific project, guiding theory development and supporting evidence-based
intervention and decision-making. Recent years, however, have seen growing
awareness of serious problems with NHST as it is typically used, and hence to
proposals to limit the use of NHST techniques, to abandon these techniques and
move to alternative statistical approaches, or even to ban the use of NHST
entirely. These proposals are premature, because the observed problems with
NHST all arise as a consequence of a contingent and in many cases incorrect
choice: that of NHST testing against point-form nulls. We show that testing
against distributional, rather than point-form, nulls is better motivated
mathematically and experimentally, and that the use of distributional nulls
addresses many problems with the standard point-form NHST approach. We also
show that use of distributional nulls allows a form of null hypothesis testing
that takes into account both the statistical significance of a given result and
the probability of replication of that result in a new experiment. Rather than
abandoning NHST, we should use the NHST approach in its more general form, with
distributional rather than point-form nulls.
