Since to answer the question “Are low likelihood ratios reliable?” requires both a definition of reliable and then a test of whether low likelihood ratios (LRs) meet that definition, the current article offers, from a purely statistical standpoint, that reliability can be determined by assessing whether the rate of inclusionary support for non-donors over many cases is not larger than expected from the LR value.
Thus, it is not the magnitude of the LR alone that determines reliability. Turing’s rule is used to inform the expected rate of non-donor inclusionary support, where the rate of non-donor inclusionary support is at most the reciprocal of the LR, i.e. Pr(LR > x|Ha) ≤1/x. There are parallel concerns about whether the value of the evidence can be communicated. This article does not discuss this in depth; however, it is an important consideration to be addressed with training. The current project used a mixture of real and simulated data to show that the rate of non-donor inclusionary support for these data is significantly lower than the upper bound given by Turing’s rule. This is strong evidence that low LRs are reliable. (publisher abstract modified)