Such
a frequentist hypothesis test for this problem would not reject the hypothesis that the parameter had a particular value that turns out to have close to the largest likelihood, at any reasonable significance threshold.
However that is a statistical non-sequitur, based on a poor understanding of
frequentist hypothesis testing, unless the test can be shown to have adequate statistical power (which seems never to be mentioned by those claiming a pause in warming).
This is one of the known problems with
frequentist hypothesis testing.
Not exact matches
But we do not need to know that much more: in a
frequentist setting the explanatory power of
hypothesis testing is quite minimal, for the null
hypothesis merely orients the burden of proof, or refutation if we are to take seriously the myth of falsification.
Standard
frequentist tests of a null
hypothesis based on a Gaussian observation are also unaffected by such a monotonic transformation.
RA Fisher (essentially the inventor of null
hypothesis statistical
tests) wrote that the significance level should depend on the nature of the
hypothesis and the experiment (most particularly your prior beliefs about the plausibility of the two
hypotheses under consideration — ironically something that
frequentist statistics can not quantify directly).
A
frequentist statistical
test can not tell you the probability that a particular
hypothesis is wrong because the
frequentist framework defines probabilities in terms of long - run frequencies (hence the name) and the correctness of a particular
hypothesis does not have a long run frequency, it is either true or it isn't.