# 6.2 Bayes’ Rule in practice: the likelihood ratio

In law, probabilities based on Bayes’ Rule are often presented in a particular form, known as the ‘likelihood ratio’. This is to avoid the legal requirement introduced earlier in the course that prevents experts from providing assistance on any non-expert issues. The likelihood ratio is a way of presenting probabilities in a way that does not depend on the probabilities of the rest of the evidence.

A likelihood ratio is calculated from a probability by dividing the probability by its opposite. For example, if the probability that it is going to rain on a certain day is 0.33, then the opposite is that there is a 0.66 probability that it is not going to rain. The likelihood ratio is, therefore, 0.33/0.66 = 0.5.

Whereas probabilities can take any value from 0 to 1, likelihood ratios can take any value from 0 to infinity. Likelihood ratios are not very intuitive, so you can refer to Table 2, which compares some probabilities with common likelihood ratios.

## Table 2 Likelihood ratios

Probability | Equivalent likelihood ratio | Verbal description
--- | --- | ---
0 | 0 | Impossible
0.25 | 0.33 |
0.5 | 1 | Evenly balanced
0.75 | 3 |
1 | Infinity | Certainty

Table 3 shows likelihood ratios with categories of verbal equivalents used by the Association of Forensic Science Providers (AFSP) and adopted by a large number of forensic practitioners.

## Table 3 Likelihood ratio scale suggested by the AFSP

Value of likelihood ratio | Verbal equivalent
--- | ---
>1–10 | Weak support for proposition
10–100 | Moderate support for proposition
100–1000 | Moderately strong support for proposition
1000–10,000 | Strong support for proposition
10,000–1,000,000 | Very strong support for proposition
>1,000,000 | Extremely strong support for proposition

In the next activity, you will see how different probabilities can be converted to likelihood ratios so that standard evidence and expert evidence can be combined.

## Activity 7 Try your hand at using likelihood ratios

Allow about 20 minutes

OpenLearn - Expert evidence and forensic science in the courtroom
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