  It is suggested that some shortcomings of Null Hypothesis Significance
Testing (NHST), viewed from the perspective of Bayesian statistics, turn benign
once the traditional threshold p value of .05 is substituted by a sufficiently
smaller value. To illustrate, the posterior probability of H0 stating P=.5,
given data that just render it rejected by NHST with a p value of .05 (and a
uniform prior), is shown here to be not much smaller than .50 for most values
of N below 100 (and even exceeds .50 for N>=100); in contrast, with a p value
of .001 posterior probability does not exceed .06 for N<=100 (neither .25 for
N<9000). Yet more interesting, posterior probability becomes quite independent
of N with a p value of .0001, hence practically satisfying the alpha postulate
- set by Cornfield (1966) as the condition for p value being a measure of
evidence in itself. In view of the low prospect that most researchers will soon
convert to use Bayesian statistics in any form, we thus suggest that
researchers who elect the conservative option of resorting to NHST be
encouraged to avoid as much as possible using a p value of .05 as a threshold
for rejecting H0. The analysis presented here may be used to discuss afresh
which level of threshold p value seems to be a reasonable, practical
substitute.
