  Null Hypothesis Significance Testing (NHST) has long been of central
importance to psychology as a science, guiding theory development and
underlying the application of evidence-based intervention and decision-making.
Recent years, however, have seen growing awareness of serious problems with
NHST as it is typically used; this awareness has led 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 arise as a
consequence of an historically contingent, essentially unmotivated, and
fundamentally incorrect, choice: that of NHST testing against point-form null
hypotheses. Using simple counting experiments we give a detailed presentation
of an alternative, more general approach: that of testing against
distributional nulls. We show that this distributional approach is
well-motivated mathematically, practically and experimentally, and that the use
of distributional nulls addresses various problems with the standard point-form
NHST approach, avoiding issues to do with sample size and allowing a coherent
estimation of the probability of replication of a given experimental result.
Rather than abandoning NHST, we should use the NHST approach in its most
general form, with distributional rather than point-form null hypotheses.
