## The pointlessness of the point null hypothesis test##

**Thesis**: Point null hypothesis tests (PNHT) are probably not worth conducting. They do not seem to tell us much about whether there is a causal relationship between variables of interest and it is hard to see why else a researcher would use this test.

**Subheadings**

*Intro*

*What PNHT is*

- Definition of a point null and why I’m focusing on it

- Definition of
*p*-values

- Summary of similar procedures (e.g. Bayes’ factors, your group sequential testing procedure for controlled trials)

- Why PNHT is suspect

*What it is not (and what it shouldn’t be)*

- Tests of point nulls probably aren’t equivalent to tests of small-interval nulls (reply to Meehl 1997 and Rindskopf 1997)

- The point null isn’t the ‘probability that the samples were drawn from different populations’ (reply to Hagen 1997)

- It doesn’t matter that failing to reject point null means shortest confidence interval contains null value in common cases (reply to various authors)

*The ‘superpopulation argument’ for PNHT*

- The point nil (not null) hypothesis might be interpreted as the prediction that there is no causal relationship between variables of interest

- Summary of superpopulation modelling

- PNHT may be a test of proposition that the sampling distribution of the superpopulation follows the point null distribution

- Even Bayesians
*might*like this solution (Berger and Sellke, Casella and Berger)

*Why the argument probably doesn’t work*

- Issues with superpopulation modelling (large, unknown variance)

- The most common class of PNHT (tests generating p-values) would overestimate the evidence against the superpopulation point null

- The prior probability of the superpopulation point null isn’t in the right range enough of the time to justify the use of point p-values (returning to Berger and Sellke, Casella and Berger)

- And why PNHT procedures other than those involving p-values might face similar problems

*Conclusion*

- What (if anything) should replace PNHT?

- What this means for results based on PNHT