  This chapter demystifies P-values, hypothesis tests and significance tests,
and introduces the concepts of local evidence and global error rates. The local
evidence is embodied in \textit{this} data and concerns the hypotheses of
interest for \textit{this} experiment, whereas the global error rate is a
property of the statistical analysis and sampling procedure. It is shown using
simple examples that local evidence and global error rates can be, and should
be, considered together when making inferences. Power analysis for experimental
design for hypothesis testing are explained, along with the more locally
focussed expected P-values. Issues relating to multiple testing, HARKing, and
P-hacking are explained, and it is shown that, in many situation, their effects
on local evidence and global error rates are in conflict, a conflict that can
always be overcome by a fresh dataset from replication of key experiments.
Statistics is complicated, and so is science. There is no singular right way to
do either, and universally acceptable compromises may not exist. Statistics
offers a wide array of tools for assisting with scientific inference by
calibrating uncertainty, but statistical inference is not a substitute for
scientific inference. P-values are useful indices of evidence and deserve their
place in the statistical toolbox of basic pharmacologists.
