A couple of years ago, Deborah Mayo called my attention to the Canadian version of the Reference Manual on Scientific Evidence.1 In the course of discussion of mistaken definitions and uses of p-values, confidence intervals, and significance testing, Sander Greenland pointed to some dubious pronouncements in the Science Manual for Canadian Judges [Manual].
Unlike the United States federal court Reference Manual, which is published through a joint effort of the National Academies of Science, Engineering, and Medicine, the Canadian version, is the product of the Canadian National Judicial Institute (NJI, or the Institut National de la Magistrature, if you live in Quebec), which claims to be an independent, not-for-profit group, that is committed to educating Canadian judges. In addition to the Manual, the Institute publishes Model Jury Instructions and a guide, Problem Solving in Canada’s Courtrooms: A Guide to Therapeutic Justice (2d ed.), as well as conducting educational courses.
The NJI’s website describes the Instute’s Manual as follows:
“Without the proper tools, the justice system can be vulnerable to unreliable expert scientific evidence.
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The goal of the Science Manual is to provide judges with tools to better understand expert evidence and to assess the validity of purportedly scientific evidence presented to them. …”
The Chief Justice of Canada, Hon. Beverley M. McLachlin, contributed an introduction to the Manual, which was notable for its frank admission that:
“[w]ithout the proper tools, the justice system is vulnerable to unreliable expert scientific evidence.
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Within the increasingly science-rich culture of the courtroom, the judiciary needs to discern ‘good’ science from ‘bad’ science, in order to assess expert evidence effectively and establish a proper threshold for admissibility. Judicial education in science, the scientific method, and technology is essential to ensure that judges are capable of dealing with scientific evidence, and to counterbalance the discomfort of jurists confronted with this specific subject matter.”
Manual at 14. These are laudable goals, indeed, but did the National Judicial Institute live up to its stated goals, or did it leave Canadian judges vulnerable to the Institute’s own “bad science”?
In his comments on Deborah Mayo’s blog, Greenland noted some rather cavalier statements in Chapter two that suggest that the conventional alpha of 5% corresponds to a “scientific attitude that unless we are 95% sure the null hypothesis is false, we provisionally accept it.” And he, pointed elsewhere where the chapter seems to suggest that the coefficient of confidence that corresponds to an alpha of 5% “constitutes a rather high standard of proof,” thus confusing and conflating probability of random error with posterior probabilities. Greenland is absolutely correct that the Manual does a rather miserable job of educating Canadian judges if our standard for its work product is accuracy and truth.
Some of the most egregious errors are within what is perhaps the most important chapter of the Manual, Chapter 2, “Science and the Scientific Method.” The chapter has two authors, a scientist, Scott Findlay, and a lawyer, Nathalie Chalifour. Findlay is an Associate Professor, in the Department of Biology, of the University of Ottawa. Nathalie Chalifour is an Associate Professor on the Faculty of Law, also in the University of Ottawa. Together, they produced some dubious pronouncements, such as:
Weight of the Evidence (WOE)
“First, the concept of weight of evidence in science is similar in many respects to its legal counterpart. In both settings, the outcome of a weight-of-evidence assessment by the trier of fact is a binary decision.”
Manual at 40. Findlay and Chalifour cite no support for their characterization of WOE in science. Most attempts to invoke WOE are woefully vague and amorphous, with no meaningful guidance or content.2 Sixty-five pages later, if any one is noticing, the authors let us in a dirty, little secret:
“at present, there exists no established prescriptive methodology for weight of evidence assessment in science.”
Manual at 105. The authors omit, however, that there are prescriptive methods for inferring causation in science; you just will not see them in discussions of weight of the evidence. The authors then compound the semantic and conceptual problems by stating that “in a civil proceeding, if the evidence adduced by the plaintiff is weightier than that brought forth by the defendant, a judge is obliged to find in favour of the plaintiff.” Manual at 41. This is a remarkable suggestion, which implies that if the plaintiff adduces the crummiest crumb of evidence, a mere peppercorn on the scales of justice, but the defendant has none to offer, that the plaintiff must win. The plaintiff wins notwithstanding that no reasonable person could believe that the plaintiff’s claims are more likely than not true. Even if there were the law of Canada, it is certainly not how scientists think about establishing the truth of empirical propositions.
Confusion of Hypothesis Testing with “Beyond a Reasonable Doubt”
The authors’ next assault comes in conflating significance probability with the probability connected with the burden of proof, a posterior probability. Legal proceedings have a defined burden of proof, with criminal cases requiring the state to prove guilt “beyond a reasonable doubt.” Findlay and Chalifour’s discussion then runs off the rails by likening hypothesis testing, with an alpha of 5% or its complement, 95%, as a coefficient of confidence, to a “very high” burden of proof:
“In statistical hypothesis-testing – one of the tools commonly employed by scientists – the predisposition is that there is a particular hypothesis (the null hypothesis) that is assumed to be true unless sufficient evidence is adduced to overturn it. But in statistical hypothesis-testing, the standard of proof has traditionally been set very high such that, in general, scientists will only (provisionally) reject the null hypothesis if they are at least 95% sure it is false. Third, in both scientific and legal proceedings, the setting of the predisposition and the associated standard of proof are purely normative decisions, based ultimately on the perceived consequences of an error in inference.”
Manual at 41. This is, as Greenland and many others have pointed out, a totally bogus conception of hypothesis testing, and an utterly false description of the probabilities involved.
Later in the chapter, Findlay and Chalifour flirt with the truth, but then lapse into an unrecognizable parody of it:
“Inferential statistics adopt the frequentist view of probability whereby a proposition is either true or false, and the task at hand is to estimate the probability of getting results as discrepant or more discrepant than those observed, given the null hypothesis. Thus, in statistical hypothesis testing, the usual inferred conclusion is either that the null is true (or rather, that we have insufficient evidence to reject it) or it is false (in which case we reject it). 16 The decision to reject or not is based on the value of p if the estimated value of p is below some threshold value a, we reject the null; otherwise we accept it.”
Manual at 74. OK; so far so good, but here comes the train wreck:
“By convention (and by convention only), scientists tend to set α = 0.05; this corresponds to the collective – and, one assumes, consensual – scientific attitude that unless we are 95% sure the null hypothesis is false, we provisionally accept it. It is partly because of this that scientists have the reputation of being a notoriously conservative lot, given that a 95% threshold constitutes a rather high standard of proof.”
Manual at 75. Uggh; so we are back to significance probability’s being a posterior probability. As if to atone for their sins, in the very next paragraph, the authors then remind the judicial readers that:
“As noted above, p is the probability of obtaining results at least as discrepant as those observed if the null is true. This is not the same as the probability of the null hypothesis being true, given the results.”
Manual at 75. True, true, and completely at odds with what the authors have stated previously. And to add to the reader’s now fully justified conclusion, the authors describe the standard for rejecting the null hypothesis as “very high indeed.” Manual at 102, 109. Any reader who is following the discussion might wonder how and why there is such a problem of replication and reproducibility in contemporary science.
Conflating Bayesianism with Frequentist Modes of Inference
We have seen how Findlay and Chalifour conflate significance and posterior probabilities, some of the time. In a section of their chapter that deals explicitly with probability, the authors tell us that before any study is conducted the prior probability of the truth of the tested hypothesis is 50%, sans evidence. This an astonishing creation of certainty out nothingness, and perhaps it explains the authors’ implied claim that the crummiest morsel of evidence on one side is sufficient to compel a verdict, if the other side has no morsels at all. Here is how the authors put their claim to the Canadian judges:
“Before each study is conducted (that is, a priori), the hypothesis is as likely to be true as it is to be false. Once the results are in, we can ask: How likely is it now that the hypothesis is true? In the first study, the low a priori inferential strength of the study design means that this probability will not be much different from the a priori value of 0.5 because any result will be rather equivocal owing to limitations in the experimental design.”
Manual at 64. This implied Bayesian slant, with 50% priors, in the world of science would lead anyone to believe “as many as six impossible things before breakfast,” and many more throughout the day.
Lest you think that the Manual is all rubbish, there are occasional gems of advice to the Canadian judges. The authors admonish the judges to
“be wary of individual ‘statistically significant’ results that are mined from comparatively large numbers of trials or experiments, as the results may be ‘cherry picked’ from a larger set of experiments or studies that yielded mostly negative results. The court might ask the expert how many other trials or experiments testing the same hypothesis he or she is aware of, and to describe the outcome of those studies.”
Manual at 87. Good advice, but at odds with the authors’ characterization of statistical significance as establishing the rejection of the null hypothesis well-nigh beyond a reasonable doubt.
When Greenland first called attention to this Manual, I reached to some people who had been involved in its peer review. One reviewer told me that it was a “living document,” and would likely be revised after he had the chance to call the NJI’s attention to the errors. But two years later, the errors remain, and so we have to infer that the authors meant to say all the contradictory and false statements that are still present in the downloadable version of the Manual.
1 See “‘Statistical Significance’ According to the U.S. Dept. of Health and Human Services (ii),” Error Statistics Philosophy (July 17, 2015). At the time, I wrote briefly about the Canadian Manual. See “Canadian Judges’ Reference Manual on Scientific Evidence” (July 24, 2015).
2 See “WOE-fully Inadequate Methodology – An Ipse Dixit By Another Name” (May 1, 2012); “Weight of the Evidence in Science and in Law” (July 29, 2017); see also David E. Bernstein, “The Misbegotten Judicial Resistance to the Daubert Revolution,” 89 Notre Dame L. Rev. 27 (2013).
