# Can the Bayes factor be negative?

This is what I saw in a source I am referring to:

Since both the numerator and the denominator are probabilities (so they can only take any value between 0 and 1), how can the result of division be negative?

• This isn't saying Negative in the sense of a negative number < 0 -- indeed, the Range column just says < 1. It means negative in the more logical sense of being evidence against a hypothesis rather than for -- Positive/Negative evidence, For/Against, Pro/Contra, etc. Apr 13 at 14:19

Not sure what your source is, but whoever it is seems to have botched Harold Jeffreys' cutoffs. The items in the table do match his recommendations, but with two problems. The first is that the cutoffs are intended to be for $$\log \text{BF}$$ rather than for the Bayes factor itself (EDIT: slightly misspoke, the unit is "decihartleys" which corresponds to $$10 \log_{10}(\text{BF})$$). The second is that, probably because the person who put the table together didn't realize the scale was suppose to be $$\log$$, they "corrected" the first row to be $$< 1$$ instead of $$< 0$$ because they assumed $$< 0$$ must be a typo (since Bayes factors can't be negative).