Statistics and the Evaluation of Evidence for Forensic Scientists. Franco Taroni

Statistics and the Evaluation of Evidence for Forensic Scientists - Franco Taroni


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say. This statistic provides a measure of the difference, known as a standardised difference, between the two sets of measurements that takes account of the natural variation there is in the refractive index measurements of glass fragments from within the same window. If the absolute value of images is less than (or equal to) some pre‐specified value, known as a threshold value, then the two sets of fragments are deemed to be similar and the second stage is implemented. If the absolute value of images is greater than the threshold value, then the two sets of fragments are deemed to be dissimilar. The two sets of fragments are then deemed to have come from different sources and the second stage is not implemented. (Note the use here of the word statistic, which in this context can be thought of simply as a function of the observations.) A classic example of such an approach is the use of the Student images‐test or the modified Welch test for the comparison of means (Welch 1937; Walsh et al. 1996; Curran et al. 2000).

      The procedure can be criticised on two points. First, in the comparison stage the threshold provides a qualitative step that may provide very different outcomes for two different pairs of observations. One pair of sets of fragments may provide a value of images, which is just below the threshold, whereas the other pair may provide a value of images just above the threshold. The first pair will proceed to the significance stage, the second stage will not. Yet, the two pairs may have measurements, which are close together. The difference in the consequences is greater than the difference in the measurements merits (such an approach is called a fall‐off‐the‐cliff effect; see Evett (1991) who attributed this term to Ken Smalldon. Criticisms have been developed in Robertson and Vignaux (1995b). They wrote:

       This sudden change in decision due to crossing a particular line is likened to falling off a cliff, one moment you are safe, the next dead. In fact, rather than a cliff we have merely a steep slope. Other things being equal, the more similar the samples the stronger the evidence that they had a common origin, and the less similar the samples the stronger the evidence that they came from different sources. (p. 118)

      A better approach, as suggested in the quotation from Robertson and Vignaux (1995b) above and that is described in Section 7.3, provides a measure of the value of the evidence that decreases as the distance between the two sets of measurements increases, subject, as explained later, to the rarity or otherwise of the measurements.

      A review of the two‐stage approach and the development of a Bayesian approach is provided by Curran et al. (2000) and Curran and Hicks (2009).

      As with DNA profiling, there are problems associated with the definition of a suitable population from which probability distributions for refractive measurements may be obtained; see, for example, Walsh and Buckleton (1986).

      These examples have been introduced to provide a framework within which the evaluation of evidence may be considered. In order to evaluate evidence, something about which there is much uncertainty, it is necessary to establish a suitable terminology and to have some method for the assessment of uncertainty. First, some terminology will be introduced followed by a method for the measurement of uncertainty. This method is probability. The role of uncertainty, as represented by probability, in the assessment of the value of scientific evidence will form the basis of the rest of this chapter. A commentary on so‐called knowledge management, of which this is one part, has been given by Evett (1993b, 2015).

      The crime scene and suspect (associated with a PoI) materials have fundamentally different roles. The assignment of a probability for a correspondence between two randomly chosen sets of materials is not the important issue. One set of materials, crime scene or suspect, can be assumed to have a known source. It is then required to assess the probability of the corresponding material, suspect or crime scene, corresponding in some sense, to the known set of materials, under two competing hypotheses. Examples 1.1 and 1.2 serve to illustrate this.

      Example 1.2 (continued) As before, consider the investigation of a crime. A window has been broken during the commission of the crime. Several fragments are taken for investigation and measurements made of their refractive indices. These fragments, as their origin is known, are sometimes known as control fragments and the corresponding measurements are


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