The scenario is that a suspect has been arrested and a number of fragments of glass have been found on his outer clothing. A reference sample of glass has been supplied from the broken glass object.
Evaluate the weight of forensic evidence represented by the fragments found on the suspect’s jumper and to determine the appropriate means of communicating this evidential value to a jury.
Treat this exercise as a series of TWO individual questions both of which must be answered in order to provide any case against the suspect (who must remain “innocent until proven guilty” beyond reasonable doubt).
STEP 1: Is the difference in mean values between the forensic sample of fragments and the reference sample from the window, sufficient to be considered ‘significantly different’?
This is a simple Normal Parametric Statistical comparison between the means of two data sets. Compare the Refractive Index (RI) values first and then compare each of the elemental compositions separately, IF the RI values are shown to be NOT statistically significantly different.
You will be faced with a series of t-test results (you must use an appropriate t-test for the data available) and you must decide whether these individual t-test results tell you, either:
The respective glass samples (the forensic sample and the reference sample) come from two different sources (the difference in mean values IS statistically significant) OR
The respective glass samples could have come from the same source (the difference in mean values is NOT statistically significant)
Decide it’s the former hypothesis, then the glass samples could NOT have come from the same source and the suspect could therefore NOT have been responsible for breaking the glass object that he is alleged to have broken.
If it is the latter hypothesis that you support, then the glass on the suspect’s jumper could have come from the broken glass object. Note that because they are indistinguishable does not mean that they are from a common source (the broken glass object); only that they could have come from a common source.
You would ONLY proceed to step 2 IF the latter hypothesis was the one you supported.
STEP 2: Evaluate the appropriate evidential weight given by finding a number of matching glass fragments on the suspect’s jumper.
For this you will use the Likelihood Ratio which is given by:
Likelihood Ratio= Similarity/Typicality
IF…the two samples of glass (the fragments from the suspect’s jumper and the reference sample taken from the broken glass object) did indeed come from the same source…
THEN… one would expect them to be indistinguishable as both samples would be identical in refractive index and in elemental composition.
SO…similarity (the probability of getting results which are not significantly different IF the two samples had a common source) would be 1.0 (it would be definite).
IF…the two samples of glass came from two separate and unrelated sources (the reference sample was taken from the broken glass object from the scene while the fragments on the suspect’s jumper came from some other broken glass object),
THEN… the typicality (the probability of getting indistinguishable results from two different glass objects) would be determined by how common (typical) the glass was. For this value, you would need to search databases to see how many other similar (indistinguishable) glass samples were on the database that matched the broken glass object.
SO… typicality can be established by determining the frequency with which the type of glass (glass of that RI and elemental composition) occurs in the population of glass recovered in all previous ‘forensic glass’ cases.
Probability= (No of desired outcomes)/(Total no.of possible outcomes)=(No of possible ‘matching’ glass samples)/(Total number of glass samples)
It is this probability (which should be quite a small fraction) which acts as the DENOMINATOR of the likelihood ratio calculation.
Your Likelihood Ratio value then gives you an indication of the appropriate weight (or strength) of evidence against the defence proposition and in support of the prosecution proposition.
You will find relevant Likelihood Ratio to Verbal Scale tables available on Moodle.