5.2 Quantifying probative value
The magnitude of the LR conveys the strength of the support that \(E\) provides for \(H_p\) compared to \(H_d\). LRs of 1,000,000 and 10 both provide support in favour of proposition \(H_p\) compared to \(H_d\), but the LR of 1,000,000 provides much stronger support than the LR of 10 does. Similarly, LRs of 0.0000001 and 0.1 provide support in favour of proposition \(H_d\) compared to \(H_p\), but the LR of 0.0000001 provides much stronger support than the LR of 0.1 does. As the value of the LR gets further away from 1, the stronger the support is in favour of proposition \(H_p\) or \(H_d\) (depending on whether the LR is greater or less than 1) when compared to its competitor.
Since the LR provides a numerical value for the relative support that a piece of evidence provides for \(H_p\) against \(H_d\), it can be seen as quantifying the probative value of a piece of evidence for those propositions. This interpretation of the LR is one of the reasons why it is advocated as a tool to quantify expert evidence. It is the role of the expert witness to present the probative value of scientific evidence within their domain of expertise to the court. The LR provides a logical means to achieve this. The fact finder can then use the probative value of evidence given by the LR to reason about the truth of \(H_p\) and \(H_d\).
LRs are often categorised verbally instead of quoting the numerical value, using categories such as ‘strong support for \(H_p\) compared to \(H_d\).’ Table 5.3 shows an example set of categories, but others, some with fewer categories, are also in common use.
| LR | verbal category |
|---|---|
| less than 0.000001 | extremely strong support for \(H_d\) compared to \(H_p\) |
| at least 0.000001 but less than 0.0001 | very strong support for \(H_d\) compared to \(H_p\) |
| at least 0.0001 but less than 0.001 | strong support for \(H_d\) compared to \(H_p\) |
| at least 0.001 but less than 0.01 | moderately strong support for \(H_d\) compared to \(H_p\) |
| at least 0.01 but less than 0.1 | moderate support for \(H_d\) compared to \(H_p\) |
| at least 0.1 but less than 1 | weak support for \(H_d\) compared to \(H_p\) |
| 1 | equal support for \(H_p\) and \(H_d\) |
| at least 1 but less than 10 | weak support for \(H_p\) compared to \(H_d\) |
| at least 10 but less than 100 | moderate support for \(H_p\) compared to \(H_d\) |
| at least 100 but less than 1000 | moderately strong support for \(H_p\) compared to \(H_d\) |
| at least 1000 but less than 10,000 | strong support for \(H_p\) compared to \(H_d\) |
| at least 10,000 but less than 1,000,000 | very strong support for \(H_p\) compared to \(H_d\) |
| at least 1,000,000 | extremely strong support for \(H_p\) compared to \(H_d\) |