## 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*-valuesSummary 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