Ebook
Essential Mathematics and Statistics for Forensic ScienceISBN: 9781119964186
366 pages
September 2011

From a basis of high school mathematics, the book develops essential quantitative analysis techniques within the context of a broad range of forensic applications. This clearly structured text focuses on developing core mathematical skills together with an understanding of the calculations associated with the analysis of experimental work, including an emphasis on the use of graphs and the evaluation of uncertainties. Through a broad study of probability and statistics, the reader is led ultimately to the use of Bayesian approaches to the evaluation of evidence within the court. In every section, forensic applications such as ballistics trajectories, postmortem cooling, aspects of forensic pharmacokinetics, the matching of glass evidence, the formation of bloodstains and the interpretation of DNA profiles are discussed and examples of calculations are worked through. In every chapter there are numerous selfassessment problems to aid student learning.
Its broad scope and forensically focused coverage make this book an essential text for students embarking on any degree course in forensic science or forensic analysis, as well as an invaluable reference for postgraduate students and forensic professionals.
Key features:
 Offers a unique mix of mathematics and statistics topics, specifically tailored to a forensic science undergraduate degree.
 All topics illustrated with examples from the forensic science discipline.
 Written in an accessible, studentfriendly way to engage interest and enhance learning and confidence.
 Assumes only a basic highschool level prior mathematical knowledge.
1 Getting the basics right.
Introduction: Why forensic science is a quantitative science.
1.1 Numbers, their representation and meaning.
Selfassessment exercises and problems.
1.2 Units of measurement and their conversion.
Selfassessment problems.
1.3 Uncertainties in measurement and how to deal with them.
Selfassessment problems.
1.4 Basic chemical calculations.
Selfassessment exercises and problems.
Chapter summary.
2 Functions, formulae and equations.
Introduction: Understanding and using functions, formulae and equations.
2.1 Algebraic manipulation of equations.
Selfassessment exercises.
2.2 Applications involving the manipulation of formulae.
Selfassessment exercises and problems.
2.3 Polynomial functions.
Selfassessment exercises and problems.
2.4 The solution of linear simultaneous equations.
Selfassessment exercises and problems.
2.5 Quadratic functions.
Selfassessment problems.
2.6 Powers and indices.
Selfassessment problems.
Chapter summary.
3 The exponential and logarithmic functions and their applications.
Introduction: Two special functions in forensic science.
3.1 Origin and definition of the exponential function.
Selfassessment exercises.
3.2 Origin and definition of the logarithmic function.
Selfassessment exercises and problems.
Selfassessment exercises.
3.3 Application: the pH scale.
Selfassessment exercises.
3.4 The "decaying" exponential.
Selfassessment problems.
3.5 Application: postmortem body cooling.
Selfassessment problems.
3.6 Application: forensic pharmacokinetics.
Selfassessment problems.
Chapter summary.
4 Trigonometric methods in forensic science.
Introduction: Why trigonometry is needed in forensic science.
4.1 Pythagoras’s theorem.
Selfassessment exercises and problems.
4.2 The trigonometric functions.
Selfassessment exercises and problems.
4.3 Trigonometric rules.
Selfassessment exercises.
4.4 Application: heights and distances.
Selfassessment problems.
4.5 Application: ricochet analysis.
Selfassessment problems.
4.6 Application: aspects of ballistics.
Selfassessment problems.
4.7 Suicide, accident or murder?
Selfassessment problems.
4.8 Application: bloodstain shape.
Selfassessment problems.
4.9 Bloodstain pattern analysis.
Selfassessment problems.
Chapter summary.
5 Graphs  their construction and interpretation.
Introduction: Why graphs are important in forensic science.
5.1 Representing data using graphs.
5.2 Linearizing equations.
Selfassessment exercises.
5.3 Linear regression.
Selfassessment exercises.
5.4 Application: shotgun pellet patterns in firearms incidents.
Selfassessment problem.
5.5 Application: bloodstain formation.
Selfassessment problem.
5.6 Application: the persistence of hair, fibres and flints on clothing.
Selfassessment problem.
5.7 Application: determining the time since death by fly egg hatching.
5.8 Application: determining age from bone or tooth material
Selfassessment problem.
5.9 Application: kinetics of chemical reactions.
Selfassessment problems.
5.10 Graphs for calibration.
Selfassessment problems.
5.11 Excel and the construction of graphs.
Chapter summary.
6 The statistical analysis of data.
Introduction: Statistics and forensic science.
6.1 Describing a set of data.
Selfassessment problems.
6.2 Frequency statistics.
Selfassessment problems.
6.3 Probability density functions.
Selfassessment problems.
6.4 Excel and basic statistics.
Chapter summary.
7 Probability in forensic science.
Introduction: Theoretical and empirical probabilities.
7.1 Calculating probabilities.
Selfassessment problems.
7.2 Application: the matching of hair evidence.
Selfassessment problems.
7.3 Conditional probability.
Selfassessment problems.
7.4 Probability tree diagrams.
Selfassessment problems.
7.5 Permutations and combinations.
Selfassessment problems.
7.6 The binomial probability distribution.
Selfassessment problems.
Chapter summary.
8 Probability and infrequent events.
Introduction: Dealing with infrequent events.
8.1 The Poisson probability distribution.
Selfassessment exercises.
8.2 Probability and the uniqueness of fingerprints.
Selfassessment problems.
8.3 Probability and human teeth marks.
Selfassessment problems.
8.4 Probability and forensic genetics.
8.5 Worked problems of genotype and allele calculations.
Selfassessment problems.
8.6 Genotype frequencies and subpopulations.
Selfassessment problems.
Chapter summary.
9 Statistics in the evaluation of experimental data: comparison and confidence.
How can statistics help in the interpretation of experimental data?
9.1 The normal distribution.
Selfassessment problems.
9.2 The normal distribution and frequency histograms.
9.3 The standard error in the mean.
Selfassessment problems.
9.4 The tdistribution.
Selfassessment exercises and problems.
9.5 Hypothesis testing.
Selfassessment problems.
9.6 Comparing two datasets using the ttest.
Selfassessment problems.
9.7 The t test applied to paired measurements.
Selfassessment problems.
9.8 Pearson's χ2 test.
Selfassessment problems.
Chapter summary.
10 Statistics in the evaluation of experimental data: computation and calibration.
Introduction: What more can we do with statistics and uncertainty?
10.1 The propagation of uncertainty in calculations.
Selfassessment exercises and problems.
Selfassessment exercises and problems.
10.2 Application: physicochemical measurements.
Selfassessment problems.
10.3 Measurement of density by Archimedes' upthrust.
Selfassessment problems.
10.4 Application: bloodstain impact angle.
Selfassessment problems.
10.5 Application: bloodstain formation.
Selfassessment problems.
10.6 Statistical approaches to outliers.
Selfassessment problems.
10.7 Introduction to robust statistics.
Selfassessment problems.
10.8 Statistics and linear regression.
Selfassessment problems.
10.9 Using linear calibration graphs and the calculation of standard error.
Selfassessment problems.
Chapter summary.
11 Statistics and the significance of evidence.
Introduction: Where do we go from here?  Interpretation and significance.
11.1 A case study in the interpretation and significance of forensic evidence.
11.2 A probabilistic basis for interpreting evidence.
Selfassessment problems.
11.3 Likelihood ratio, Bayes' rule and weight of evidence.
Selfassessment problems.
11.4 Population data and interpretive databases.
Selfassessment problems.
11.5 The probability of accepting the prosecution case  given the evidence.
Selfassessment problems.
11.6 Likelihood ratios from continuous data.
Selfassessment problems.
11.7 Likelihood ratio and transfer evidence.
Selfassessment problems.
11.8 Application: double cotdeath or double murder?
Selfassessment problems.
Chapter summary.
References.
Bibliography.
Answers to selfassessment exercises and problems.
Appendix I: The definitions of nonSI units and their relationship to the equivalent SI units.
Appendix II: Constructing graphs using Microsoft Excel.
Appendix III: Using Microsoft Excel for statistics calculations.
Appendix IV: Cumulative z probability table for the standard normal distribution.
Appendix V: Student's t test: tables of critical values for the t statistic.
Appendix VI: Chi squared χ2 test: table of critical values.
Appendix VII: Some values of Q_{crit} for Dixon's Q test.
Some values for G_{crit} for Grubbs’ twotailed test.
Index.
 Offers a unique mix of mathematics and statistics topics, specifically tailored to a forensic science undergraduate degree.
 All topics illustrated with examples from the forensic science discipline.
 Written in an accessible, studentfriendly way to engage interest and enhance learning and confidence.
 Assumes only a basic highschool level prior mathematical knowledge.