  We examine the role of trustworthiness and trust in statistical inference,
arguing that it is the extent of trustworthiness in inferential statistical
tools which enables trust in the conclusions. Certain tools, such as the
p-value and significance test, have recently come under renewed criticism, with
some arguing that they damage trust in statistics. We argue the contrary,
beginning from the position that the central role of these methods is to form
the basis for trusted conclusions in the face of uncertainty in the data, and
noting that it is the misuse and misunderstanding of these tools which damages
trustworthiness and hence trust. We go on to argue that recent calls to ban
these tools would tackle the symptom, not the cause, and themselves risk
damaging the capability of science to advance, and feeding into public
suspicion of the discipline of statistics. The consequence could be aggravated
mistrust of our discipline and of science more generally. In short, the very
proposals could work in quite the contrary direction from that intended. We
make some alternative proposals for tackling the misuse and misunderstanding of
these methods, and for how trust in our discipline might be promoted.
