Category Archives: numeracy

Medical Decisions–Risk Saavy

screeningLearnMoreThis post looks at the medical/health component of decision making as addressed in Gerd Gigerenzer’s new book, Risk Saavy, How to Make Good Decisions. First, Gigerenzer has contributed greatly to improving health decision making. This blog includes three consecutive posts on the Statistics of Health Decision Making based on Gigerenzer’s work.

He points out both the weaknesses of screening tests and our understanding of the results. We have to overcome our tendency to see linear relationships when they are nonlinear. Doctors are no different. The classic problem is an imperfect screening test for a relatively rare disease. You cannot think in fractions or percentages. You must think in absolute frequencies. Breast cancer screening is one example. Generally, it can catch about 90% of breast cancers and only about 9% test positive who do not have breast cancer. So if you have a positive test, that means chances are you have breast cancer. No! You cannot let your intuition get involved especially when the disease is more rare than the test’s mistakes. If we assume that 10 out of 1000 women have breast cancer, then 90% or 9 will be detected, but about 90 of the 1000 women will test positive who do not have disease. Thus only 9 of the 99 who test positive actually have breast cancer. I know this, but give me a new disease or a slightly different scenario and let a month pass, I will still be tempted to shortcut the absolute frequencies and get it wrong.

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Gigerenzer — Risk Saavy

risksaavyindexGerd Gigerenzer has a 2014 book out entitled:  Risk Saavy, How to Make Good Decisions, that is a refinement of his past books for the popular press.  It is a little too facile, but it is worthwhile. Gigerenzer has taught me much, and he will likely continue. He is included in too many posts to provide the links here (you can search for them). My discussion of the book will be divided into two posts. This one will be a general look, while the next post will concentrate on Gigerenzer’s take on medical decision making.

As in many books like this, the notes provide insight. Gigerenzer points out his disagreements with Kahneman with respect to heuristics all being part of the unconscious system. As he notes heuristics, for instance the gaze heuristic, can be used consciously or unconsciously. This has been a major issue in my mind with Kahneman’s System 1 and System 2. Kahneman throws heuristics exclusively into the unconscious system. I also side with Gigerenzer over Kahneman, Ariely, and Thaler that the unconscious system is associated with bias. As Gigerenzer states: “A system that makes no errors is not intelligent.” He interestingly points out the use of the gaze heuristic by Sully Sullenberger to decide to not return to LaGuardia, but instead to land in the Hudson River.

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Affect Gap

affect-space-webThis post is based on the paper: “The Affect Gap in Risky Choice: Affect-Rich Outcomes Attenuate Attention to Probability Information,” authored by Thorsten Pachur,  Ralph Hertwig, and Roland Wolkewitz that appeared in Decision, 2013, Volume 1, No. 1, p 64-78.  This is a continuation of the affect/ emotion theme. It is more of a valence based idea than Lerner’s Appraisal Tendency Framework.  This is more thinking about emotion than actually experiencing it although the two can come together.

Often risky decisions involve outcomes that can create considerable emotional reactions. Should we travel by plane and tolerate a minimal risk of a fatal terrorist attack or take the car and run the risk of traffic jams and car accidents? How do people make such decisions?  Decisions under risk typically obey the principle of the maximization of expectation.
The expectation expresses the average of an option’s outcomes, each weighted by its
probability. This, of course, underlies expected utility theory and cumulative prospect theory and these models do a good job in accounting for choices among relatively affect-poor

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Regression to the Mean

regressionI have mentioned Michael Mauboussin’s book The Success Equation before, but this will be the closest I come to a review.  The title makes it sound like a self help book, but it is much more substantial.  However, his notes and bibliography somehow miss both Ken Hammond and Robin Hogarth which frankly seems unlikely. Hogarth’s books Educating Intuition (post Learning, Feedback and Intuition) and Dance with Chance (post Dancing with Chance) have much in common.

Mauboussin most unique contribution from my view is to bring Bill James and his successors from baseball to the world of skill and luck and investment. And Mauboussin is amazingly honest about the luck involved in investment which is his world. He pretty much says that you cannot be an expert in his field but only experienced. Using sports, especially baseball, makes the book’s ideas much more understandable. That brings us to the idea for this post.  Mauboussin calls it reversion to the mean and Kahneman calls it regression to the mean.  Either way, baseball makes it more understandable.

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Numeracy and Cultural Cognition

globalThis post brings up the latest paper by Dan Kahan and his colleagues, Erica Dawson, Ellen Peters, and Paul Slovic: “Motivated Numeracy and Enlightened Self-Government,”  Cultural Cognition Project, Working Paper No. 116.   This paper strengthens the already strong arguments.
The experiment that was the subject of this paper was designed to test two opposing accounts of conflict over decision relevant science. The first—the Science Comprehension Thesis (“SCT”)—attributes such conflicts to the limited capacity of the public to understand the significance of valid empirical evidence. The second—the Identity-protective Cognition Thesis (“ICT”)—sees a particular recurring form of group conflict as disabling the capacities that individuals have to make sense of decision-relevant science: when policy-relevant facts become identified as symbols of membership in and loyalty to affinity groups that figure in important ways in individuals’ lives, they will be motivated to engage empirical evidence and other information in a manner that more reliably connects their beliefs to the positions that predominate in their particular groups than to the positions that are best supported by the evidence.

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The Statistics of Health Decision Making-Therapy

stat2imagesGigerenzer says that we must teach risk literacy in medical school and statistical literacy to all in primary school. He and his colleagues go into considerable detail to say how this should be done. Teaching statistics early is not sufficient. It is also essential to represent probabilistic information in forms that the human mind can grasp. To this end, visual and hands-on material can enable a playful development of statistical thinking. For instance, tinker-cubes are lego-like units that first graders can use to represent simple events, to combine to represent joint events, and to count to determine conditional frequencies.

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The Statistics of Health Decision Making- Causes and Consequences of Illiteracy

statimagesGerd Gigerenzer has produced much work that is relevant and easy to understand for the laymen.  Gigerenzer has defended the effectiveness and our abilities to use heuristics.  He has also tirelessly promoted statistics education and transparent presentation of statistical information.  This post tries to summarize some unique and interesting material with respect to the causes and consequences of our statistical illiteracy.

Gerd Gigerenzer along with Wolfgang Gaissmaier, Elke Kurz-Milcke, Lisa M. Schwartz, and Steven Woloshin suggest that the long opposition to health statistics can be traced back to the struggle between three 19th-century visions of the physician: artist, determinist, or statistician.  They argue that these professional ideals go hand in hand with patients’ corresponding ideals, which even today determine the mixture of feelings about health statistics: The artist embodies paternalism and requests blind trust from the patient, the determinist strives for perfect knowledge of causes and invites the illusion of certainty in patients, and the statistician relies on facts rather than medical charisma, paving the way for shared decision making. The first two ideals effectively deter interest in health statistics.

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The Statistics of Health Decision Making-Statistical Illiteracy

statanalysis_03This will be the first post of a three-part series. They will all be based on a 2008 monograph that appeared in Psychological Science in the Public Interest, entitled:  “Helping Doctors and Patients Make Sense of Health Statistics.” Gerd Gigerenzer was the primary author.  I have started posts on numeracy, especially health numeracy, based on journal articles, but they tended to be focused on the public’s generally poor numeracy skills.  This always stopped me in my tracks, because it left out the doctors who have skills much like the public, and it left out the researchers, screening test providers, drug makers, and device makers who tend to have excellent skills.  They sometimes use those skills to take advantage of the doctors, patients, and the public(for my purposes journalists are just part of the public).  This monograph puts  the pieces together.

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Health Numeracy

numeracyimagesIsaac Lipkus  and Ellen Peters authored: “Understanding the Role of Numeracy in Health: Proposed Theoretical Framework and Practical Insights,”  It was published in Health Education Behavior in December 2009.  I find it to be a very useful article.  There are articles summarizing all the research in the area, and articles explaining the best way to measure numeracy, and many books and articles showing the many human weaknesses with respect to numeracy.  This article does a good job of putting the pieces together.

Numeracy, that is how facile people are with mathematical concepts and their applications.  Lipkus and Peters propose six critical  functions of health numeracy. These functions are integrated into a theoretical framework on health numeracy that has implications for risk-communication and medical-decision-making processes. They examine practical underpinnings for targeted interventions aimed at improving such processes as a function of health numeracy.

I. Numeracy facilitates computation.

Men and women ages 50 to 80 were presented with information about treatment efficacy in one of four formats:  numbers needed to treat, absolute risk reduction, relative risk reduction, or a combination of the three formats. Those with poorer numeracy were less likely to identify the most effective treatment and were less able to accurately compute degree of benefit.
II. Numeracy encourages more information seeking and greater depth of processing.

Recent research has shown that the highly numerate integrate the perceived attractiveness of risky and riskless options in traditional framing choices more than the less numerate; the less numerate respond more superficially instead to the frame of the information provided. Consistent with dual process models of attitude change, greater seeking and scrutiny of numerical data can increase its persuasiveness and hence its effects on decisions/behaviors, should the data be judged credible, accurate, and deemed personally relevant.

III. Numeracy improves interpretation of the meaning of provided numbers.

In general, the less numerate provide subjective risk estimates that exceed those provided by an “objective” criterion. In choice decisions, the less numerate are more likely to select options that do not maximize expected utility. Whereas the highly numerate appear to derive affective meaning from the given numbers and make decisions from this meaning, the less numerate rely less on specified probabilities and other sources of numeric information

IV. Numeracy facilitates assessments of likelihood and value

Numeracy is related to the consistency with which individuals provide mathematically equivalent numerical responses on different risk perception scales.  Those who were more numerate were more likely to provide identical (i.e., mathematically equivalent) answers on multiple scales.

V. Numeracy can increase or decrease acceptance of numerical data

Consistent with the less numerate trusting numeric data less, Peters and colleagues found that the less numerate also appeared to use it less and be influenced more by competing, less relevant affective considerations; the highly numerate drew more precise affective meaning from numbers and numerical comparisons that appeared to guide their decisions instead. In one study, subjects were offered a prize if they drew a colored jellybean from their choice of one of two bowls. The first Bowl A contained 9 colored and 91 white beans; Bowl B contained 1 colored and 9 white beans, so the odds of success were objectively better in Bowl B. Nevertheless, participants low in numeracy often chose Bowl A (33% and 5% of low and high numerate, respectively, chose from Bowl A) because “it looked more inviting.” Participants were asked about their feelings to the 9% chance of winning in Bowl A on a scale ranging from very bad to very good; they were also asked to report how clear those feelings were. Compared to the less numerate, high-numerate participants reported feelings towards the objectively lower 9% chance that were more clear and negative compared to the less numerate. This secondary affect (likely produced through a comparison of the objective probabilities in the two bowls) appeared to drive choices of the highly numerate.

VI. Numeracy promotes behavior change

This function suggests that numeracy may affect the motivation to take action and engage in behaviors based on quantitative information. Numeracy may either increase or decrease the likelihood of action perhaps through one or more of the functional values discussed (e.g., information seeking, computation, interpretation of meaning, etc.).