ForensicSpot10 modules
Forensic Statistics
The statistics of evidence evaluation: probability, match probabilities, the likelihood ratio, Bayesian reasoning, fallacies, and how strength of evidence is reported.
- 60hours
- 30topics
- 10modules
Module 16 hrs3 topics
Why statistics in forensic science
How numbers enter forensic conclusions and why courts increasingly demand them.
Start module- How Numbers Enter Forensic ConclusionsThis topic explains why forensic science moved from categorical assertions to quantified statements of evidential weight. It traces the legal and scientific pressures that made numerical reasoning a courtroom expectation rather than an optional extra.13 min
- The Role of Statistics in Evidence EvaluationThis topic surveys the main tasks where statistics enters forensic practice: comparison, classification, source attribution, and evaluative reporting. It clarifies what statistics can and cannot contribute to an investigation or a trial.13 min
- History of Statistical Evidence in CourtsThis topic reviews landmark cases from multiple jurisdictions, including People v. Collins and R v. Sally Clark, where statistical arguments shaped or distorted verdicts. It draws lessons about the responsibilities of expert witnesses who use numbers in court.13 min
Module 26 hrs3 topics
Probability foundations
Probability rules, conditional probability, independence, and the meaning of "random match".
Start module- Basic Probability RulesThis topic introduces the axioms of probability, the addition rule, the multiplication rule, and complementary events using forensic examples such as trace evidence and database searches. It builds the vocabulary needed for every subsequent module.13 min
- Conditional Probability and IndependenceThis topic explains what it means for one event to depend on another and why independence is a critical assumption that must be justified, not assumed. It shows how incorrect independence assumptions have led to catastrophic courtroom errors.13 min
- The Concept of Random Match ProbabilityThis topic defines the random match probability as the chance that a randomly selected unrelated individual would share the observed evidence characteristics. It situates this probability within a broader probabilistic framework and warns against treating it as the probability of innocence.13 min
Module 36 hrs3 topics
Describing data
Descriptive statistics, variability, and presenting forensic data honestly.
Start module- Descriptive Statistics for Forensic DataThis topic covers measures of central tendency and spread, including mean, median, mode, variance, and standard deviation, applied to physical measurement data such as glass refractive indices and fibre diameters. It emphasises honest presentation and the dangers of cherry-picking summary statistics.13 min
- Visualising Forensic DataThis topic covers histograms, box plots, scatter plots, and kernel density estimates as tools for exploring and communicating forensic datasets. It discusses how graphical choices can clarify or mislead and what peer-reviewed reporting standards expect.13 min
- Variability and Measurement ErrorThis topic distinguishes between natural within-class and between-class variability and instrument measurement error, explaining why both must be characterised before evidence can be interpreted. It introduces precision, accuracy, and repeatability as distinct concepts.13 min
Module 46 hrs3 topics
Distributions and sampling
Common distributions, sampling, confidence intervals, and what a sample can support.
Start module- Common Distributions in Forensic ScienceThis topic introduces the normal, binomial, Poisson, and gamma distributions and shows where each arises in forensic contexts such as particle counts, event frequencies, and chemical concentration data. It explains how choosing the wrong distributional model affects inference.13 min
- Sampling Strategies and Representative DataThis topic covers random, stratified, and cluster sampling and explains why the quality of inference depends critically on how a sample was drawn. It addresses practical constraints in forensic sampling, such as limited exhibit material or biased case selection.13 min
- Confidence Intervals and What a Sample Can SupportThis topic explains the construction and correct interpretation of confidence intervals, including the common misreading that a 95% interval contains the true value with 95% probability. It shows how interval width depends on sample size and variance and how to communicate uncertainty honestly.13 min
Module 56 hrs3 topics
Match probabilities
Random match probability, population databases, and the statistics behind a "match".
Start module- Population Databases for Forensic StatisticsThis topic examines how reference population databases are constructed, stratified, and validated for use in forensic match probability calculations, drawing on examples from DNA, fingerprint, and glass databases across multiple countries. It addresses database size, population substructure, and the consequences of a mismatched reference population.13 min
- DNA Match Probability CalculationThis topic explains the product rule for calculating multi-locus DNA match probabilities and the corrections applied for population substructure using the NRC-II theta correction. It focuses on the statistical inference layer and cross-links to forensic biotechnology and forensic biology for laboratory context.13 min
- Match Probabilities Beyond DNAThis topic extends match probability reasoning to non-DNA evidence types including fingerprint minutiae, glass fragments, fibres, and footwear impressions, highlighting how rarity estimates are derived when hard population data are scarce. It discusses the challenges of validating match probability claims in evidence categories that lack the statistical infrastructure of DNA.13 min
Module 66 hrs3 topics
The likelihood ratio framework
The likelihood ratio as the logically correct way to weigh evidence, with worked cases.
Start module- The Likelihood Ratio: Definition and LogicThis topic introduces the likelihood ratio as the ratio of the probability of the evidence under the prosecution hypothesis to its probability under the defence hypothesis, and explains why it is the theoretically correct measure of evidential weight. It distinguishes the LR from the posterior probability of guilt, which is not for the expert to calculate.13 min
- Computing Likelihood Ratios: Worked ExamplesThis topic walks through LR calculations for DNA profiles, glass refractive index measurements, and speaker comparison, showing how numerator and denominator probabilities are estimated from data or models. It demonstrates how LR values above and below 1 support opposite propositions.13 min
- Strength of Evidence and Likelihood Ratio ScalesThis topic reviews numerical scales used to describe evidential strength, including the Jeffreys scale and scales adopted by forensic laboratories and standards bodies, and discusses their strengths and limitations. It connects quantitative LR values to the verbal equivalents used in evaluative reports.13 min
Module 76 hrs3 topics
Bayesian evidence evaluation
Prior and posterior odds, Bayes theorem in court, and the role of the fact-finder.
Start module- Bayes Theorem in Evidence EvaluationThis topic presents Bayes theorem in odds form, showing how prior odds are updated to posterior odds by multiplying by the likelihood ratio. It illustrates the theorem with simple forensic scenarios and explains why the prior odds are for the fact-finder, not the expert.13 min
- Prior and Posterior Odds in CourtThis topic explores how prior odds are formed from non-scientific case information and how the expert's LR shifts those odds toward the posterior. It discusses the proper division of roles between the scientist, the judge, and the jury in Bayesian evidence evaluation.13 min
- Bayesian Networks for Complex EvidenceThis topic introduces directed acyclic graphs as a way to model dependencies among multiple evidence items and intermediate propositions without violating the rules of conditional probability. It shows how Bayesian networks have been applied in cases involving mixed DNA profiles and multi-source trace evidence.13 min
Module 86 hrs3 topics
Statistical fallacies
The prosecutor fallacy, the defence fallacy, and the transposed conditional.
Start module- The Prosecutor's FallacyThis topic defines the prosecutor's fallacy as the erroneous transposition of the conditional, where the probability of the evidence given innocence is misrepresented as the probability of innocence given the evidence. It analyses real cases where the fallacy inflated the apparent weight of forensic evidence and explains how experts and advocates can guard against it.13 min
- The Defence FallacyThis topic defines the defence fallacy as the argument that a one-in-a-million match probability is negligible because millions of people could match, ignoring the rest of the evidence in the case. It shows how this reasoning misuses population size and explains the correct way to contextualise a match probability.13 min
- Other Statistical Fallacies in Forensic ContextsThis topic covers additional reasoning errors including the base rate neglect, the ecological fallacy, the multiple comparisons problem in database searches, and the look-elsewhere effect. It explains how each distorts probabilistic reasoning and how expert witnesses should address them in reports and testimony.13 min
Module 96 hrs3 topics
Evaluative reporting
Verbal equivalents of the likelihood ratio, standards for evaluative opinions, and report language.
Start module- Verbal Equivalents of the Likelihood RatioThis topic presents the verbal probability scales adopted by institutions such as ENFSI, the UK Forensic Science Regulator, and AFSP Australia, mapping numerical LR ranges to phrases such as 'moderate support' or 'very strong support'. It discusses the communication rationale, the risks of misinterpretation, and ongoing debates about which scale to adopt.13 min
- Evaluative Opinion Standards and FrameworksThis topic surveys the standards and guidance documents that govern evaluative reporting, including ENFSI Guideline for Evaluative Reporting, ILAC G19, and ISO 17025 requirements, placing them in the context of accreditation and admissibility. It explains what a compliant evaluative opinion must include and what it must not claim.13 min
- Writing Evaluative Statements in Forensic ReportsThis topic provides practical guidance on drafting propositions at the correct level (source, activity, or offence), selecting the appropriate verbal equivalent, and structuring an evaluative section within a forensic report. It includes annotated examples from casework and highlights common drafting errors that undermine the logical integrity of the opinion.13 min
Module 106 hrs3 topics
Error, validation and uncertainty
Error rates, method validation, measurement uncertainty, and proficiency testing.
Start module- False Positive and False Negative Error RatesThis topic defines false positive and false negative rates in the context of forensic classification decisions, shows how they interact through the ROC curve, and explains why both must be estimated and disclosed rather than assumed to be negligible. It covers how error rates should be reported to courts and how they modify the strength of a forensic opinion.13 min
- Method Validation and Fitness for PurposeThis topic covers the validation studies required before a forensic method can be used operationally, including limit of detection, selectivity, robustness, and reproducibility testing, with reference to ISO 17025 and discipline-specific guidance. It explains what 'fitness for purpose' means statistically and how validation data underpin the LR calculation.13 min
- Measurement Uncertainty and Proficiency TestingThis topic introduces the GUM framework for expressing measurement uncertainty, explains how uncertainty propagates through forensic calculations, and shows how proficiency test results provide an independent check on laboratory performance. It discusses how declared uncertainty should be incorporated into evaluative opinions and disclosed in court reports.13 min