Aytugrul v The Queen [2012] HCA 15: the use of statistics in DNA evidence

Aytugrul v The Queen [2012] HCA 15 was handed down last week. This appeal to the High Court concerns DNA evidence and the ways that expert evidence of this kind can be expressed. All members of the Court held that, in this case, the use of both an exclusion ratio and frequency percentage by prosecution forensic experts was admissible and was not unfair.

In this post I’ve tried – with only some success – to stay away from using phrases like matching samples. Experts in the forensic field will never talk (or at least, should never talk) in terms of samples that match or those two samples are the same. The most that can be said when applying a rigorous scientific method is that, when one sample is compared with another, it cannot be excluded as a possibility that both have the same source.

Such a statement by itself has little probative value. The utility of such an analysis for a decider of fact (if any) only comes about when it can be said with certainty that a large number of other potential samples can be excluded as being from the same source as the particular sample.

For example, in the early days of forensic science one of the only tests that could be done with a blood sample left at a crime scene was to test it for type. The most common type in Australia is type O, which almost half of us have. If it was known that a sample of blood found at a crime scene was O, as was the accused, then that evidence alone lacks much probative force. Tha fact that the accused might be the source of the sample lacks much weight on its own, given that half of the population might be, too.

There are a couple of occasions below where, for simplicity’s sake, I do jump into the vernacular and describe two samples as being the same, etc. But that kind of language does a disservice to the science, and tends to confuse the precise issue that Aytugrul v The Queen is about; whether particular information was fairly or unfairly explained to the jury.

The Trial

The accused was charged with the murder of his former partner. She was stabbed to death. A hair follicle was found on her thumbnail during a post mortem examination. A DNA sample of this hair was compared with the DNA of the accused and experts professed that the accused could not be excluded as its source. There were no witnesses to the crime. The case against the accused relied on a number of pieces of circumstantial evidence.

Two experts were called by the prosecution to give evidence of the likelihood (or unlikelihood, depending on the way one looks at it) of the hair sample belonging to the accused. The sample had been compared with a database of 4,389 others from a variety of sample groups. During evidence-in-chief this was expressed as:

A frequency ratio = this is the hypothetical number of people randomly selected that it would be necessary to compare with before finding another sample which could not be excluded. In this case, it was said that this number was 1600 people.

An exclusion percentage = This is the proportion of the general population (I think they mean everybody on the planet) who can be excluded. This was said to be 99.9%. So based on the number of comparisons actually done, it could be mathematically extrapolated so as to expect that only half of a per cent of all living people would share that DNA profile.

Both of these statements express the same concept in different ways. They state mathematical probabilities, rather than certainties relating to this specific set of facts. For example, it was conceded in cross-examination that in a football stadium crowd of 16,000 there might be no other candidates who could not be excluded at all (no matches) or there might be as many as 100. Stating how frequently an event will occur on average only really becomes dependable as the event reoccurs and sample sizes increase.

The Appeal to the Court of Criminal Appeal

The accused was convicted at trial in New South Wales. The NSW Court of Criminal Appeal upheld the conviction, McClellan CJ dissenting. He found that the presentation of the statistics encouraged a ‘subliminal rounding up’ to a probability of guilt of 100%. Unlike the High Court (which did not refer to it at all), McClellan CJ made a direct connection to the the prosecutor’s fallacy (discussed here a while ago), in his finding that the exclusion percentage was inadmissible [at 99]:

To my mind and for the reasons identified in GK and Galli, his Honour should have excluded the exclusion percentages from the evidence, all of which invited a subconscious “rounding-up” to 100. It was not sufficient for his Honour to warn the jury against the potential misuse of the percentages. The exclusion percentage figures were too compelling. To my mind his Honour’s directions would not have eliminated the risk of unfair prejudice to the appellant (GK at 341; see also Mason P at 331). That prejudice substantially outweighed the probative value of the evidence.

Simpson and Fullarton JJ disagreed and the appeal was dismissed. Simpson J also quoted Mason P from GK in her strongly worded judgment [at 196, Fullarton J agreeing on this ground]:

GK is not binding authority that evidence of the kind there under consideration is never admissible; it is a conclusion that, on the facts of that case, either s 135 or s 137 could be invoked in order to exclude the relative chance of paternity evidence. Nor is Galli authority for the proposition. Neither is authority for the proposition that “exclusion percentage” evidence is never admissible, nor that such evidence, though admissible, must inevitably be excluded under either s 135 or s 137.

In GK, Mason P said:

It is not the judicial function to give the accused a fighting chance of gaining an acquittal, as if the trial were a horse race and the judge were a handicapper deciding how much weight to place in the Crown’s saddlebags. The admissibility of evidence is not in an inverse ratio to its probative effect.

Accordingly, if relevant DNA statistical evidence is tendered through a witness of due expertise then its probative weight cannot itself be a ground for withholding it from the jury. Indeed its very significant probative weight is a factor in favour of admission notwithstanding the capacity of extremely high odds to carry a prejudicial overlay.

The evidence, put as it was, was prejudicial: all Crown evidence is intended to be prejudicial. That is why it is tendered. I have been able to discern nothing that suggests that the evidence before the jury, framed as it was, was unduly or unfairly prejudicial, or confusing or misleading such as to raise for consideration either s 135 or s 137.

Nor am I of the view that there was any deficiency in the way in which the jury was directed in relation to the DNA evidence.

The Appeal to the High Court

The appellant was granted special leave in September 2011.

The High Court described the case that came before it in these terms (French CJ, Hayne, Crennan and Bell JJ [at 2]:

This appeal concerns the admissibility of some evidence led at trial about a DNA analysis. A hair found on the deceased’s thumbnail had been subjected to mitochondrial DNA testing. The results of that testing showed two things: first, that the appellant could have been the donor of the hair and, second, how common the DNA profile found in the hair was in the community. This second aspect of the results was expressed in evidence both as a frequency ratio and as an exclusion percentage. The expert who had conducted the test gave evidence to the effect that one in 1,600 people in the general population (which is to say the whole world) would be expected to share the DNA profile that was found in the hair (a frequency ratio) and that 99.9 per cent of people would not be expected to have a DNA profile matching that of the hair (an exclusion percentage).

Objection was taken at trial under both ss 135 and 137. Initial arguments there centred around an insufficient basis for the conclusions, rather than the way they were to be communicated to the jury, but later moved to the way the raw data should be communicated to the jury.

Usually, the prosecutor’s fallacy is said to occur when statistics about the probabilities of comparison of forensic samples becomes confused with an assessment of whether the accused actually committed the crime, as a result of something said by the prosecutor or the judge during the charge to the jury. Here, it wasn’t the interpretation given to the evidence by the prosecutor or the judge that was in issue, but the method of expression of the experts themselves, and whether that evidence should have been admitted at all.

The High Court did not agree with McClellan CJ’s dissenting judgment that the exclusionary percentage would subconsciously nudge jurors from a consideration of probabilities into an assumption of guilt.

French CJ, Hayne, Crennan and Bell JJ [at 22]

No proof was attempted, whether at trial or on appeal, of the facts and opinions which were put forward (by reference to the published articles) as underpinning the adoption of some general rule that expressing the results of DNA analysis as an exclusion percentage will always (or usually) convey more to a hearer than the evidence allows regardless of what other evidence is given about frequency ratios or the derivation of exclusion percentages. Yet that was the basis on which it was asserted that a general rule should be established to the effect that evidence of exclusion percentages is always inadmissible. And absent the proof of such facts and opinions (with the provision of a sufficient opportunity for the opposite party to attempt to controvert, both by evidence and argument, the propositions being advanced) a court cannot adopt such a general rule based only on the court’s own researches suggesting the existence of a body of skilled opinion that would support it.

The question that was presented for consideration in this matter must be identified with greater specificity than is permitted by general reference to how the human mind can or commonly will deal with statistical information. In this case, the question was whether Ms Pineda’s evidence of an exclusion percentage accompanied by both reference to the relevant frequency ratio and an explanation of how the exclusion percentage was derived from the frequency ratio was evidence whose probative value was outweighed by the danger of unfair prejudice (s 137) or was evidence whose probative value was substantially outweighed by the danger that it might be unfairly prejudicial to the defendant or, perhaps, be misleading or confusing (s 135).

No reason is shown for answering either form of those more particular questions in favour of the appellant. The evidence given was clear. It was evidence adverse to the appellant but it was in no sense unfairly prejudicial, or misleading or confusing. The exclusion percentage given was high – 99.9 per cent – but relevant content was given to that figure by the frequency ratios that were stated in evidence. As the trial judge pointed out to the jury, the evidence that was given did not, and was not said to, establish that the mitochondrial DNA profile found in the hair definitely came from the appellant. There was no risk of rounding the figure of 99.9 per cent to the certainty of 100 per cent.

The appeal was dismissed. Heydon J (as is now common) penned his own interesting judgment, but was broadly in agrement with his colleagues.


I don’t envy jurors their role of assigning appropriate weight to forensic evidence, or judges their duty of explaining how they should go about it. If given too little information to work with then people with no knowledge of scientific principles may give too much credence to it; but equally, too much explanation and the expert forensic evidence becomes the centrepiece of any trial, overwhelming the other parts of the evidence that should also be considered.

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