Comment by ivan_ah
6 years ago
Agree that NHST using simple null hypothesis of the form
H0: μ = 0
doesn't provide much value. H0 is never true, and the conclusion of "rejecting H0" based on a p-value is therefore not super profound. Also "rejecting H0" conclusion doesn't really tells anything about the alternative hypothesis HA (not even considered when computing p-value, since p-value is under H0). Dichotomies in general are bad, but NHST with point H0 is useless!
However a composite hypothesis setup of the form
H0: μ ≤ 0
HA: μ > 0
is probabilistically sound (in as much as some journal requires you to report a p-values). Much better to report effect size estimate and/or CI.
That still gives 50-50 odds with sufficient sample size, not much of a test of the research hypothesis (since many alternatives will predict the same direction). It is better than 100% chance of rejection though.
Couldn't you make an argument that the point H0 has use when you are testing whether two populations are identical? i.e. it's probably true that \mu is very close to 0 if it is the difference in heights of men from Nebraska vs men from Iowa.
You've kind of hit the point with the second half of your comment. Two populations are virtually never identical, so you don't need any statistics to answer the question. A more reasonable question is whether or not you have the statistical power (i.e. measurement precision) to see the difference, and whether the difference is big enough to matter.