Likelihood Ratio (LR)
Definition
The ratio of two conditional probabilities: the probability of the observed evidence given the prosecution's hypothesis (same source), divided by the probability of the observed evidence given the defence's hypothesis (different source). An LR greater than 1 supports the prosecution hypothesis; an LR less than 1 supports the defence hypothesis. The LR is not a probability of guilt.
- Type
- Bayesian statistical metric
- Field
- Forensic science (cross-disciplinary)
- Governs
- Evaluative reporting of evidence strength
- Direction
- LR > 1 supports prosecution; LR < 1 supports defence; LR = 1 is neutral
- Key promoters
- ENFSI, UK Forensic Science Regulator
Common questions
What is a likelihood ratio in forensic science?+
A likelihood ratio (LR) is the probability of the observed evidence under the prosecution's hypothesis divided by the probability of the same evidence under the defence's hypothesis. An LR greater than 1 means the evidence supports the prosecution. An LR less than 1 means it supports the defence. An LR of exactly 1 means the evidence is neutral.
Why does it matter that the LR is not a probability of guilt?+
The LR only measures the relative strength of the evidence. It tells the court how much more probable the evidence is under one hypothesis compared to the other. Deciding guilt requires combining that with everything else in the case, which is the jury's job, not the forensic expert's.
Where is the likelihood ratio used in forensic practice?+
It is used across many disciplines: DNA profiling, fingerprints, speaker comparison, document examination, tool marks, soil, paint, and forensic botany. Bodies like ENFSI and the UK Forensic Science Regulator promote LR-based reporting as a more principled alternative to older categorical conclusions like 'match' or 'no match'.
Related terms
- Prosecutor's Fallacy
- The error of treating the RMP (or its reciprocal) as the probability that the defendant is innocent, or as the probability that...
- Random Match Probability (RMP)
- The probability that a randomly chosen unrelated person from the relevant population would match the evidence profile by chance. A very small...
- Daubert Standard
- The US federal evidentiary standard (Daubert v. Merrell Dow Pharmaceuticals, 1993) requiring that expert testimony be based on scientifically valid methods with...
- Defence Fallacy
- The converse error of inflating the importance of the RMP by arguing that, because many people in the population share the profile,...
- Evaluative Reporting
- A framework for expressing forensic conclusions in terms of the probability of the evidence given the prosecution hypothesis versus the defence hypothesis...
- Frye Standard
- The US legal test for admissibility of scientific evidence, originating from Frye v. United States (1923), which required that a technique be...
- Prior Odds
- The ratio of the probability of the prosecution hypothesis to the probability of the defence hypothesis before the forensic evidence in question...
- Bayes' Theorem
- The mathematical rule that relates prior odds, the likelihood ratio, and posterior odds. In the odds form: O(Hp|E) = O(Hp) x LR....
- Posterior Odds
- The ratio of the probability of the prosecution hypothesis to the probability of the defence hypothesis after the forensic evidence is taken...
- Product Rule
- The rule that, under independence, the joint probability of a multi-locus genotype equals the product of the individual locus genotype frequencies. Used...
- Theta (FST) Correction
- A correction factor applied to allele frequency estimates to account for population sub-structure (the tendency for allele frequencies to differ between sub-populations)....
- Verbal Scale
- The ENFSI translation of numerical likelihood ratios into courtroom language: very strong support (LR over 10,000), strong support (LR 1,000-10,000), moderate support...
Explained in these topics
- Ante-mortem Data Collection and Victim IdentificationThe statistical measure used to express the strength of a DNA identification: the probability of the observed DNA evidence given the identification hypothesis...
- Bayes Theorem in Evidence EvaluationThe probability of the observed evidence given the prosecution hypothesis divided by the probability of the same evidence given the defence hypothesis. The LR...
- Cognitive Bias, Expert Testimony and the 2009 NAS CritiqueThe ratio of the probability of the evidence under the prosecution's proposition to the probability of the evidence under the defence's proposition. The Bayesi...
- Common Distributions in Forensic ScienceThe ratio of the probability of the observed evidence under two competing hypotheses. The distributional model chosen determines the probability calculations,...
- Computing Likelihood Ratios: Worked ExamplesThe ratio of P(evidence | Hp) to P(evidence | Hd). It measures how much more probable the observed evidence is under the prosecution proposition than under the...
- Conclusion Scales: SWGDOC, ENFSI and Courtroom LanguageThe ratio of the probability of the observed evidence given one hypothesis (typically prosecution hypothesis) to the probability of the same evidence given the...
- DNA Match Probability CalculationThe ratio of the probability of the evidence given the prosecution hypothesis to the probability of the evidence given the defence hypothesis. An LR greater th...
- Error, Uncertainty and the Statistics of Forensic ScienceThe ratio of the probability of the evidence given the prosecution hypothesis to the probability of the evidence given the defence hypothesis. An LR greater th...
- Expert Evidence and Statistical Interpretation in CourtThe ratio of the probability of the evidence under the prosecution hypothesis to the probability under the defence hypothesis. An LR greater than 1 supports th...
- Expert Reporting and Court Testimony in Forensic BotanyA numerical expression of how much more probable the evidence is under one hypothesis than another. An LR greater than 1 supports the prosecution hypothesis; e...
- History of Statistical Evidence in CourtsThe ratio of the probability of the observed evidence given the prosecution hypothesis to the probability of the same evidence given the defence hypothesis. An...
- Interpreting Biological Evidence in CourtA number expressing how much more probable the observed evidence is under one hypothesis (typically the prosecution's) than under an alternative (typically the...
- The Likelihood Ratio: Definition and LogicThe probability of the evidence given the prosecution hypothesis divided by the probability of the evidence given the defence hypothesis. Written as LR = P(E |...
- Match Probabilities Beyond DNAThe ratio of the probability of the evidence under the prosecution hypothesis to the probability of the evidence under the defence hypothesis. An LR greater th...
- How Numbers Enter Forensic ConclusionsThe probability of the observed evidence given the prosecution hypothesis, divided by the probability of the same evidence given the defence hypothesis. It mea...
- Paint Databases (PDQ, EUCAP) and Comparison CaseworkA Bayesian metric expressing the probability of the observed comparison data given a common source versus a different source; values above 1 support common sou...
- Prior and Posterior Odds in CourtThe scientist's numerical contribution: the probability of the observed evidence if Hp is true, divided by the probability of the same evidence if Hd is true....
- Probative Value and the Weight of EvidenceThe probability of the observed evidence under the prosecution hypothesis divided by the probability of the same evidence under the defence hypothesis. An LR g...
- Allele Frequencies, Random Match Probability and the Likelihood RatioThe ratio of the probability of the evidence under the prosecution hypothesis to the probability under the defence hypothesis. For a full single-source profile...
- The Concept of Random Match ProbabilityThe ratio of the probability of the observed evidence under the prosecution hypothesis to the probability of the same evidence under the defence hypothesis. Un...
- Reconstruction and Probabilistic ReasoningThe ratio of the probability of the evidence under one hypothesis to the probability of the same evidence under an alternative hypothesis. Values above 1 suppo...
- The Role of Statistics in Evidence EvaluationThe probability of the observed evidence under hypothesis H1 divided by its probability under hypothesis H2. In forensic reporting, H1 is usually the prosecuti...
- Soil Comparison Casework and Statistical InferenceThe ratio of the probability of the observed forensic data given the prosecution's proposition to the probability of the same data given the defence's proposit...
- Speaker Comparison: Methods and the Expert's RoleThe ratio of the probability of the observed evidence given the same-speaker hypothesis to the probability given the different-speaker hypothesis. An LR of 10...
- Spectrographic Voiceprint History and Its Modern RejectionIn forensic speaker comparison, the ratio of the probability of the observed acoustic evidence given that the two recordings came from the same speaker to the...
- Standards, Accreditation and Admissibility in Fingerprint EvidenceA numerical expression of the relative probability of the observed evidence under two competing propositions (e.g., same source vs. different source); used in...
- Standards, Accreditation and Admissibility in QDEIn evaluative forensic reporting, the ratio of the probability of the observed evidence given the prosecution hypothesis to the probability given the defence h...
- Statistical Comparison and the Reference Population ProblemThe ratio of the probability of the observed data given a prosecution hypothesis (same source) to the probability given a defence hypothesis (different source)...
- FRStat, Likelihood Ratios and the Post-2009 NAS DebateThe ratio of two conditional probabilities: the probability of the observed evidence given the prosecution's hypothesis (same source), divided by the probabili...
- Strength of Evidence and Likelihood Ratio ScalesThe ratio of the probability of the evidence given one hypothesis to the probability of the evidence given an alternative hypothesis. In forensic evaluative re...
- The Defence FallacyThe ratio of the probability of the evidence given one hypothesis to the probability of the evidence given an alternative hypothesis. In forensic matching, LR...
- The Expert Report: Structure and DutiesA numerical expression of how much more probable the observed evidence is under one proposition than under another. An LR greater than 1 supports the prosecuti...
- The Prosecutor's FallacyThe ratio P(evidence | prosecution hypothesis) divided by P(evidence | defence hypothesis). A LR greater than 1 supports the prosecution hypothesis; a LR less...
- Tool-Mark Comparison Microscopy and 3D ImagingThe probability of the observed evidence under the prosecution hypothesis (same source) divided by its probability under the defence hypothesis (different sour...
- Verbal Equivalents of the Likelihood RatioThe ratio of the probability of the observed evidence given the prosecution hypothesis to the probability of the same evidence given the defence hypothesis. An...
- Voice Analysis: Spectrography, Speaker Identification and Legal AspectsBayesian measure of how much more probable the evidence is under the same-speaker hypothesis than under the different-speaker hypothesis, reported with verbal...
- Writing Evaluative Statements in Forensic ReportsThe ratio of the probability of the evidence given the prosecution proposition to the probability of the evidence given the defence proposition. An LR greater...