Transposition Fallacy
Definition
The error of treating the probability of the evidence given a hypothesis as though it were the probability of the hypothesis given the evidence. In the context of LR scales, the transposition fallacy arises when a jury reads 'strong support for the prosecution hypothesis' as meaning the defendant is probably guilty, rather than understanding it as a statement about the relative probability of the evidence.
- Field
- Forensic statistics, evidence interpretation
- Also known as
- Confusion of the inverse
- Confuses
- P(evidence | hypothesis) with P(hypothesis | evidence)
- Common courtroom form
- Prosecutor's fallacy
- Related concept
- Bayes' theorem, likelihood ratio
Common questions
Why does a strong likelihood ratio not equal a high probability of guilt?+
The likelihood ratio only measures how much more likely the evidence is under one hypothesis than another. Converting that into a probability of guilt requires combining it with the prior odds, which depend on the rest of the case, not on the forensic result alone.
How do expert witnesses avoid triggering this fallacy in testimony?+
They are trained to phrase findings as statements about the evidence given a hypothesis, for example 'these results are X times more likely if the samples share a common source,' and to avoid any wording that sounds like a direct statement of guilt or innocence probability.
Is the transposition fallacy unique to DNA and forensic science evidence?+
No, it appears whenever conditional probabilities are reversed, including in medical test interpretation and general legal reasoning. Forensic identification evidence is simply the context where courts and statisticians have written about it most.
Related terms
- Likelihood Ratio (LR)
- A ratio comparing the probability of findings under one stated proposition with their probability under another, conditional on relevant information. Its direction...
- 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....
- ENFSI Guideline
- The European Network of Forensic Science Institutes Guideline for Evaluative Reporting in Forensic Science (2015, updated 2016). It defines the propositions framework,...
- Evaluative Reporting
- Assessment of findings against alternative propositions, sometimes expressed using a supported likelihood ratio. An LR compares probabilities of the findings under those...
- Jeffreys Scale
- A logarithmic scale for Bayes factors proposed by Harold Jeffreys in Theory of Probability (1961). Levels run from 'barely worth mentioning' at...
- Log10(LR)
- The base-10 logarithm of the likelihood ratio, sometimes called the weight of evidence (following I.J. Good). A log10(LR) of 1 corresponds to...
- Posterior Odds
- The ratio of the probability of the prosecution hypothesis to the probability of the defence hypothesis after the forensic evidence is taken...
- Prior Odds
- The ratio of the probability of the prosecution hypothesis to the probability of the defence hypothesis before the forensic evidence in question...
- Verbal Equivalence Scale
- A table that assigns a verbal phrase to a range of LR values or log10(LR) values. The phrase is used in written...
Explained in these topics
- Prior and Posterior Odds in CourtThe error of treating P(E|Hd) as equal to P(Hd|E). The probability of finding this evidence if the defendant is innocent is not the same as the probability of...
- Strength of Evidence and Likelihood Ratio Scales