I agree with this comment, but I want to point out that there may be a problem with equating the natural language concept “strength of evidence” with the likelihood ratio.
You can compare two probabilities on either an additive or multiplicative scale. When applying a likelihood ratio of 1000, your prior changes by a multiplicative factor of 1000 (this actually applies to odds rather than probabilities, but for low probability events, the two approximate each other). However, on an additive scale, a change from 10^{-18} to 10^{-15} is really just a change of less than 10^{-15} , which is negligible.
The multiplicative scale is great for several reasons: The likelihood ratio is suggested by Bayes’ theorem, it is easy to reason with, it does not depend on the priors, several likelihood ratios can easily be applied sequentially, and it is suitable for comparing the strength of different pieces of evidence for the same hypothesis.
The additive scale does not have those nice properties, but it may still correspond more closely to the natural language concept of “strength of evidence”
I agree with this comment, but I want to point out that there may be a problem with equating the natural language concept “strength of evidence” with the likelihood ratio.
You can compare two probabilities on either an additive or multiplicative scale. When applying a likelihood ratio of 1000, your prior changes by a multiplicative factor of 1000 (this actually applies to odds rather than probabilities, but for low probability events, the two approximate each other). However, on an additive scale, a change from 10^{-18} to 10^{-15} is really just a change of less than 10^{-15} , which is negligible.
The multiplicative scale is great for several reasons: The likelihood ratio is suggested by Bayes’ theorem, it is easy to reason with, it does not depend on the priors, several likelihood ratios can easily be applied sequentially, and it is suitable for comparing the strength of different pieces of evidence for the same hypothesis.
The additive scale does not have those nice properties, but it may still correspond more closely to the natural language concept of “strength of evidence”
I have not said that it’s strong evidence. I said it’s evidence.