It is not the odds the headline is true, nor the odds the study is correct, but only the odds the study supports the headline. For that, I don’t find his rule of thumb inappropriate.
No. The odds that the study supports the headline in the second example are 1⁄16. The formula he gives is
(final opinion on headline) = (initial gut feeling) * (study support for headline)
where the latter two are odds ratios. From context, “final opinion on headline” is pretty clearly supposed to be “opinion on whether the headline is true.”
It is not the odds the headline is true, nor the odds the study is correct, but only the odds the study supports the headline. For that, I don’t find his rule of thumb inappropriate.
No. The odds that the study supports the headline in the second example are 1⁄16. The formula he gives is
(final opinion on headline) = (initial gut feeling) * (study support for headline)
where the latter two are odds ratios. From context, “final opinion on headline” is pretty clearly supposed to be “opinion on whether the headline is true.”