Essential Mathematics and Statistics for Forensic ScienceISBN: 978-0-470-74253-2
Paperback
368 pages
May 2010
 This is a Print-on-Demand title. It will be printed specifically to fill your order. Please allow an additional 10-15 days delivery time. The book is not returnable.
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1 Getting the basics right.
Introduction: Why forensic science is a quantitative science.
1.1 Numbers, their representation and meaning.
Self-assessment exercises and problems.
1.2 Units of measurement and their conversion.
Self-assessment problems.
1.3 Uncertainties in measurement and how to deal with them.
Self-assessment problems.
1.4 Basic chemical calculations.
Self-assessment exercises and problems.
Chapter summary.
2 Functions, formulae and equations.
Introduction: Understanding and using functions, formulae and equations.
2.1 Algebraic manipulation of equations.
Self-assessment exercises.
2.2 Applications involving the manipulation of formulae.
Self-assessment exercises and problems.
2.3 Polynomial functions.
Self-assessment exercises and problems.
2.4 The solution of linear simultaneous equations.
Self-assessment exercises and problems.
2.5 Quadratic functions.
Self-assessment problems.
2.6 Powers and indices.
Self-assessment 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.
Self-assessment exercises.
3.2 Origin and definition of the logarithmic function.
Self-assessment exercises and problems.
Self-assessment exercises.
3.3 Application: the pH scale.
Self-assessment exercises.
3.4 The "decaying" exponential.
Self-assessment problems.
3.5 Application: post-mortem body cooling.
Self-assessment problems.
3.6 Application: forensic pharmacokinetics.
Self-assessment problems.
Chapter summary.
4 Trigonometric methods in forensic science.
Introduction: Why trigonometry is needed in forensic science.
4.1 Pythagoras’s theorem.
Self-assessment exercises and problems.
4.2 The trigonometric functions.
Self-assessment exercises and problems.
4.3 Trigonometric rules.
Self-assessment exercises.
4.4 Application: heights and distances.
Self-assessment problems.
4.5 Application: ricochet analysis.
Self-assessment problems.
4.6 Application: aspects of ballistics.
Self-assessment problems.
4.7 Suicide, accident or murder?
Self-assessment problems.
4.8 Application: bloodstain shape.
Self-assessment problems.
4.9 Bloodstain pattern analysis.
Self-assessment 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.
Self-assessment exercises.
5.3 Linear regression.
Self-assessment exercises.
5.4 Application: shotgun pellet patterns in firearms incidents.
Self-assessment problem.
5.5 Application: bloodstain formation.
Self-assessment problem.
5.6 Application: the persistence of hair, fibres and flints on clothing.
Self-assessment problem.
5.7 Application: determining the time since death by fly egg hatching.
5.8 Application: determining age from bone or tooth material
Self-assessment problem.
5.9 Application: kinetics of chemical reactions.
Self-assessment problems.
5.10 Graphs for calibration.
Self-assessment 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.
Self-assessment problems.
6.2 Frequency statistics.
Self-assessment problems.
6.3 Probability density functions.
Self-assessment problems.
6.4 Excel and basic statistics.
Chapter summary.
7 Probability in forensic science.
Introduction: Theoretical and empirical probabilities.
7.1 Calculating probabilities.
Self-assessment problems.
7.2 Application: the matching of hair evidence.
Self-assessment problems.
7.3 Conditional probability.
Self-assessment problems.
7.4 Probability tree diagrams.
Self-assessment problems.
7.5 Permutations and combinations.
Self-assessment problems.
7.6 The binomial probability distribution.
Self-assessment problems.
Chapter summary.
8 Probability and infrequent events.
Introduction: Dealing with infrequent events.
8.1 The Poisson probability distribution.
Self-assessment exercises.
8.2 Probability and the uniqueness of fingerprints.
Self-assessment problems.
8.3 Probability and human teeth marks.
Self-assessment problems.
8.4 Probability and forensic genetics.
8.5 Worked problems of genotype and allele calculations.
Self-assessment problems.
8.6 Genotype frequencies and subpopulations.
Self-assessment 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.
Self-assessment problems.
9.2 The normal distribution and frequency histograms.
9.3 The standard error in the mean.
Self-assessment problems.
9.4 The t-distribution.
Self-assessment exercises and problems.
9.5 Hypothesis testing.
Self-assessment problems.
9.6 Comparing two datasets using the t-test.
Self-assessment problems.
9.7 The t -test applied to paired measurements.
Self-assessment problems.
9.8 Pearson's χ2 test.
Self-assessment 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.
Self-assessment exercises and problems.
Self-assessment exercises and problems.
10.2 Application: physicochemical measurements.
Self-assessment problems.
10.3 Measurement of density by Archimedes' upthrust.
Self-assessment problems.
10.4 Application: bloodstain impact angle.
Self-assessment problems.
10.5 Application: bloodstain formation.
Self-assessment problems.
10.6 Statistical approaches to outliers.
Self-assessment problems.
10.7 Introduction to robust statistics.
Self-assessment problems.
10.8 Statistics and linear regression.
Self-assessment problems.
10.9 Using linear calibration graphs and the calculation of standard error.
Self-assessment 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.
Self-assessment problems.
11.3 Likelihood ratio, Bayes' rule and weight of evidence.
Self-assessment problems.
11.4 Population data and interpretive databases.
Self-assessment problems.
11.5 The probability of accepting the prosecution case - given the evidence.
Self-assessment problems.
11.6 Likelihood ratios from continuous data.
Self-assessment problems.
11.7 Likelihood ratio and transfer evidence.
Self-assessment problems.
11.8 Application: double cot-death or double murder?
Self-assessment problems.
Chapter summary.
References.
Bibliography.
Answers to self-assessment exercises and problems.
Appendix I: The definitions of non-SI 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 Qcrit for Dixon's Q test.
Some values for Gcrit for Grubbs’ two-tailed test.
Index.
Related Titles
Forensics
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