Statistical Analysis in Forensic Science

Evidential Value of Multivariate Physicochemical Data

Grzegorz Zadora, Agnieszka Martyna, Daniel Ramos, Colin Aitken

• Publisher: Wiley
• Year: 2013
• ISBN:
  9781118763186
• Edition: 1
• Topic: Matematica
• Subtopic: Probabilità e statistica

A practical guide for determining the evidential value of physicochemical data

Microtraces of various materials (e.g. glass, paint, fibres, and petroleum products) are routinely subjected to physicochemical examination by forensic experts, whose role is to evaluate such physicochemical data in the context of the prosecution and defence propositions. Such examinations return various kinds of information, including quantitative data. From the forensic point of view, the most suitable way to evaluate evidence is the likelihood ratio. This book provides a collection of recent approaches to the determination of likelihood ratios and describes suitable software, with documentation and examples of their use in practice. The statistical computing and graphics software environment R, pre-computed Bayesian networks using Hugin Researcher and a new package, calcuLatoR, for the computation of likelihood ratios are all explored.

Statistical Analysis in Forensic Science will provide an invaluable practical guide for forensic experts and practitioners, forensic statisticians, analytical chemists, and chemometricians.

Key features include:

• Description of the physicochemical analysis of forensic trace evidence.
• Detailed description of likelihood ratio models for determining the evidential value of multivariate physicochemical data.
• Detailed description of methods, such as empirical cross-entropy plots, for assessing the performance of likelihood ratio-based methods for evidence evaluation.
• Routines written using the open-source R software, as well as Hugin Researcher and calcuLatoR.
• Practical examples and recommendations for the use of all these methods in practice.

1

Physicochemical data obtained in forensic science laboratories

1.1 Introduction

Various materials can be subjected to physicochemical examination by forensic experts. Such materials include illegal substances, blood and other body fluids, and transfer evidence (e.g. small fragments of glass, paint, fibres, plastics, organic and inorganic gunshot residues, fire debris). The size of samples subjected to analysis is very small, for example, fragments of glass with a linear dimension below 0.5 mm. Therefore, the analysis of morphological features, such as thickness and colour, is of no value for solving a comparison (Chapter 4) or classification problem (Chapter 5). Thus, it is necessary to employ the physicochemical features of the analysed fragments. When choosing an analytical method for analysis of microtraces for forensic purposes an expert should take into account not only the fact that the amount of material is very small but also that the method chosen should be non-destructive, leaving the material available for reuse. Examinations performed by the application of various analytical methods return several kinds of information including:

• qualitative data, for example, information on compounds detected in fire debris samples based on a chromatogram, information obtained from the spectrum of an unknown sample, and morphological information such as the number and thicknesses of layers in a cross-section of car paints;
• quantitative data, for example, the concentration of elements or value of the refractive index in a glass fragment, peak areas of a drug profile chromatogram or gasoline detected in fire debris, and the concentration of ethanol in blood samples.

In general, the fact finders (i.e. judges, prosecutors, policemen) are not interested in the physicochemical composition of a particular material (e.g. the elemental composition of glass) except in situations where such information could have a direct influence on the legal situation of a suspect (e.g. information on the level of ethyl alcohol in a blood sample). Questions raised by the police, prosecutors and the courts relate to the association between two or more items (which is known in the forensic sphere as a comparison problem; Chapter 4) and/or identification and classification of objects into certain categories (known in the forensic sphere as a classification problem; Chapter 5). These problems can be solved by the application of various statistical methods.

There are two main roles of statistics in forensic science. The first is during the investigation stage of a crime before a suspect has been identified, where statistics can be used to assist in the investigation (Aitken 2006a). The second is during the trial stage (Aitken 2006b), where statistics can be used to assist in the evaluation of the evidence. This last role of statistics is described in detail in this book.

When the evaluation of evidence is based on analytical data obtained from physicochemical analysis, careful attention to the following considerations is required:

• possible sources of uncertainty (sources of error), which should at least include variations in the measurements of characteristics within the recovered and/or control items, and variations in the measurements of characteristics between various objects in the relevant population (e.g. the population of glass objects);
• information about the rarity of the determined physicochemical characteristics (e.g. elemental and/or chemical composition of compared samples) for recovered and/or control samples in the relevant population;
• the level of association (correlation) between different characteristics when more than one characteristic has been measured;
• in the case of the comparison problem, the similarity of the recovered material and the control sample.

In this book it is advocated that the best way to include all these factors in the evidence evaluation process is by the application of likelihood ratio (LR) approach (Chapter 2).

It was mentioned that results of physicochemical analysis of various types of forensic evidence can be enhanced using statistical methods. Nevertheless such methods should always be treated as a supportive tool and any results should be subjected to critical analysis. In other words, statistical methods do not deliver the absolute truth as the possibility of obtaining false answers is an integral part of these methods. Therefore, sensitivity analysis (an equivalent of the validation process for analytical methods) should be performed in order to determine the performance of these methods and their influence on the next step, that of making a decision (Chapter 6).

With the aim of fully understanding the processes of the evaluation of the evidential value of physicochemical data it is necessary to first understand the origin of these data. Therefore, some details concerning the analysis of glass, flammable liquids, car paints, inks, and fibres for forensic purposes are presented in this chapter. The data obtained in the course of these analyses are used later in this book.

1.2 Glass

Glass is a material that is used in many areas of human activity. In domestic and commercial construction it appears most frequently as window glass, whereas in automotive transport it can form car windows and windscreens, car headlamps, car mirrors, and light bulbs. It is also used to make bottles, jars, tableware, and decorative items. Fragments of glass with a maximum linear dimension of 0.5 mm or less can be formed during events such as car accidents, burglaries and fights. These fragments may be recovered from the scene of the incident, as well as from the clothes and bodies of participants in any event of forensic interest (Figures 1.1(a), (b)). Such fragments may provide evidence of activity as well as the source of an object (Curran et al. 2000). The glass refractive index measurement (GRIM) method and scanning electron microscopy coupled with an energy dispersive X-ray spectrometer (SEM-EDX) are routinely used in many forensic institutes for the investigation of glass and other trace evidence (Aitken et al. 2007; Evett 1977, 1978; Evett and Lambert 1982; Kirk 1951; Koons et al. 1988; Latkoczy et al. 2005; Lucy and Zadora 2011; Neocleous et al. 2011; Ramos and Zadora 2011; Zadora 2007a, 2009; Zadora et al. 2010; Zadora and Brozek-Mucha 2003; Zadora and Neocleous 2009a; Zadora and Neocleous 2009b; Zadora 2010).

Figure 1.1 Principles of determination of elemental composition of glass fragments by the SEM-EDX technique: (a) debris collected from suspect clothes; (b) glass fragments located on an SEM stub; (c) view of SEM-EDX equipment; (d) SEM image of an analysed glass sample; (e) the spectrum of a glass sample obtained from an EDX detector.

Other methods used to determine the elemental composition of glass include: μ-X-ray fluorescence (μ-XRF) (Hicks et al. 2003) and laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) (Latkoczy et al. 2005; Trejos and Almirall 2005a, b).

1.2.1 SEM-EDX technique

During the production of glass (Caddy 2001), many different elements are incorporated into the molten mixture. Certain elements are crucial for glass production and are always present. These major components are oxides of silica, sodium, calcium, magnesium, and potassium. Sodium is present, usually in the form of sodium carbonate, to reduce the softening point of silica, while calcium oxide and magnesium oxide make glass more chemically resistant. Minor components are also present, such as the oxides of aluminium and iron. Iron oxides are used to impart colour. Trace elements are also included, mostly depending on the required properties of the glass, particularly for any specialist uses.

The elements analysed using SEM-EDX are the major and minor elements found in glass. SEM-EDX does not allow for determination of the trace elements. The presence of the major and minor elements does not have great discriminating power as they are commonly present in glass. The trace elements are often regarded as imperative for the discrimination of glass, and suitable techniques are available for analysing the trace elements such as μ-XRF and LA-ICP-MS. However, in the field of forensic science the available equipment must often be used for as many purposes as possible, therefore if the concentrations of the major and minor elements alone can give correct and reliable data to solve a comparison and classification problem (Chapters 4 and 5), then the SEM-EDX method would be sufficient and useful for this purpose. The difference in the concentrations of these elements present in the sample is likely to be small. Therefore a statistical approach is imperative to detect any significant differences in the amounts of these elements.

The first stage of the SEM-EDX is the use of a scanning electron microscope (SEM; Figure 1.1(c)), which gives detailed three-dimensional images of a specimen (Figure 1.1(d)). The SEM works by using a beam of electrons as the source of illumination. A filament (e.g. made of tungsten) provides the source of electrons. As the filament is heated the electrons escape (thermionic emission) and a high voltage is applied to accelerate the negatively charged electrons away from the positively charged filament. The electrons interact with the specimen (e.g. glass sample) in various ways.

The X-rays produced by the SEM can provide information on elemental composition (Figure 1.1(e)), which is of interest here. The X-rays collected from the SEM are processed by an independent instrument (detector). Nowadays, an energy dispersive X-ray (EDX) detector is commonly used. This analyses the energy of the X-rays. The detector for the EDX system relies on a semiconductive crystal.

Quantitative analysis by the SEM-EDX method requires a surface of the sample be flat and smooth. An embedding procedure in resin could be used for sample preparation. This process ...

Table of contents

• Cover
• Title Page
• Copyright
• Dedication
• Preface
• 1: Physicochemical data obtained in forensic science laboratories
• 2: Evaluation of evidence in the form of physicochemical data
• 3: Continuous data
• 4: Likelihood ratio models for comparison problems
• 5: Likelihood ratio models for classification problems
• 6: Performance of likelihood ratio methods
• Appendix A: Probability
• Appendix B: Matrices: An introduction to matrix algebra
• Appendix C: Pool adjacent violators algorithm
• Appendix D: Introduction to R software
• Appendix E: Bayesian network models
• Appendix F: Introduction to calcuLatoR software
• Index