To all my colleagues in the academic discipline of mathematical statistics
We all know about the fallacy of the transposed conditional: to confuse P(A|B) with P(B|A), for instance by mistaking the probability of the obtained data given the null hypothesis for the probability of the null hypothesis given the data. And of course we know better than to fall for that fallacy. But not all of our colleagues who represent other academic disciplines, and who need to do statistics in their daily dealings with empirical data, are as sophisticated statistical thinkers as we are. Many of them are prone to slip into that very fallacy. So can we please please agree to avoid language that encourages them to do so? In particular, can we agree to never ever use ``θ is likely to be 0.7´´ as shorthand for ``the likelihood function L(θ) takes a relatively large value for θ=0.7´´? Please?
See Item (b) in Section 2 of my latest paper The need for nuance in the null hypothesis significance testing debate, to appear in Educational and Psychological Measurement.