I was reading this paper by Dennis Lindley ("Analysis of a Wine Tasting", J. Wine Econ. 2006). Statistically, the paper is a straightforward analysis of a $10\times 11$ two-way table. To test whether a certain effect is significant, Lindley computes both a p-value using the F-test and a Bayes factor.
However, I don't understand the final paragraph in the paper, of which the last few sentences are:
It will readily be seen that the Bayes factor is more conservative than the F-test. For example, take the one degree of freedom for France versus the States in the Cabernet table (13). The F-test is significant at 0.1%, or 0.001. The Bayes factor is only 0.020, 20 times greater.
(Emphasis mine.) This suggests that the Bayes factor and the p-value can be compared on the same scale. How can this be?