# Health Numeracy

Isaac 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.

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.).

# Time Choices

Decisions with consequences that are experienced over time are everywhere.  They include spending, investments, diet, fertility, education, etc.  The DU model, discounted utility, assumes that people evaluate the pleasures and pains resulting from a decision  by exponentially discounting the value of outcomes according to how delayed in time they are.  This model comes from the field of economics.

# Atrial Fibrillation

Dr Thomas Tape wrote an article “Coherence and correspondence in medicine” that appeared in the March 2009 edition of Judgment and Decision Making.  As you might expect, Dr Tape is applying some of the ideas of Kenneth Hammond to medicine.  Tape notes that the distinction between coherence (making logical sense) and correspondence (being empirically correct) seldom appears in the medical literature.

Tape suggests that the field of medicine began with coherence approaches and has only recently adopted correspondence approaches at all. The original rationale for bloodletting was based on the idea that disease comes from an imbalance of humors.  This coherent argument was around for hundreds of years before being dispelled.  It seems surprising that patient outcome was not the indicator of choice, but even today with medical progress and sophisticated statistics, it is not so easy to tell what works.

# Regret

This backward facing emotion is a combination of self-blame and disappointment.  Interestingly, we all know that it influences our decision making. Daniel Kahneman in Thinking Fast and Slow notes that neither prospect theory or utility theory take regret into account.  It is certainly a big part of television games shows like “Who Wants to be a Millionaire” as Kahneman’s example illustrates.

Choose between 90% chance to win \$1 million OR \$50 with certainty.

Choose between 90% chance to win \$1 million OR \$150,000 with certainty.

You know that in the second example, you will regret turning down a gift of \$150k if you do not win the million.  With regret, the experience of an outcome depends on a choice you could have taken, but did not.  Kahneman  notes that since regret adds more weight to the tool box and little to better prediction, it is not really worth the trouble to include it.

# Obliquity and In Pursuit of Elegance

I am afraid I may be discussing these books only because I read them. They are not that new, but there is also some sort of synergy between them that I am working on exposing.  The authors, John Kay and Matthew May, maybe that is the synergy, are an economist/writer and a management consultant/writer.  The books are written for the popular press and published in 2011 and 2009 respectively.  The books do have something to say, but they are idea books and not science books.

# Judgments Under Stress

Ken Hammond wrote a book, Judgments Under Stress, published in 2000.  He was clearly frustrated with how the field of psychology dealt with stress and used his book as a vehicle to change the discussion.  Hammond really wants to talk about constancy while stress is a constancy disruptor. Hammond’s mentor, Egon Brunswik, saw constancy as the essence of life.  Hammond asserts that the orientation of the organism is directed toward maintaining stable relations with the environment, and that disruption of those stable relations is the definition of stress.

# Closer to home

The Shower

How do decisions go wrong?  The other day my wife told me that the bathtub faucet was leaking.  This happens occasionally and since I have “special” plastic valves, occasionally is not every decade, but every year or so.  But the leak was almost continuous drips with a kind of hissing noise.  This was a little different.  Still I figured I would replace both hot and cold water valves and be done with it.  It was almost bedtime so I hurried a bit and after replacing the hot water valve and then tightening the existing cold water valve, nothing seemed to have changed.  (I should note that the cold water valve does not get used quite as often because the water at my house is not hot, only warm.)  At this point, my mind quickly moved to a new solution, the shower diverter.  This piece of hardware enables a bathtub to provide both baths and showers.  In theory, with worn out o-rings, I believe it could cause leaks. When I got the handles and extensions off, I found a brass thing which had nothing to put a wrench on although I tried.  Over the next 12 hours, of which I was asleep for 7, I tried to figure this out.  How can I take it off, and how can I get a new one.  After a big box store, a hardware store, and two plumbing supply houses, I had made no progress.  Eventually, I pulled the diverter stem assembly (technical name I learned) out with a set of needle nosed vise grips.  Guess what, the leak did not change a bit.  I should note that I had called the plumber by this time, but it was a Friday.  Anyway, I went back to the one thing I knew and more carefully adjusted the valves and the leak was fixed.  The problem that I usually fix in a half hour took me about 16 hours of elapsed time.

# Consciousness, Confessions of a Romantic Reductionist

Christof Koch, a professor at California Institute of Technology and Chief Scientist at the Allen Institute, has written this book, Consciousness, published in 2012. It is both a science book and a personal book.  Although judgment and decision making are not the subject, free will versus determinism is one of the subjects.  This seems to be near the essence of judgment.

Koch says that classical determinism is out, but the strong version of free will is also out.  That version of free will  is the belief that if you were placed in exactly the same circumstances again, including the identical brain state as previously, you could will yourself to act differently.  To me that is a stronger version of free will than I imagined. Koch adopts a more pragmatic concept called compatibilism.  You have free will if you follow your own desires and preferences. Koch points to experiments that show the brain decides before you will something. By the time you say to yourself in your head to sit up and get out of bed, your brain beat you by half a second.

# Dancing with Chance

The book Dance with Chance is written by three scientists each with contributions in the field of judgment and decision making.  They are Spyros Makridakis, Robin Hogarth, and Anil Gaba. I have particular respect for Robin Hogarth and his work on intuition. It is aimed at a popular audience so it makes a stab at that Malcolm Gladwell glibness. They are not stringing anecdotes like Gladwell or making them up like Jonah Lehrer, but they are trying to give you the strongest case and not provide you with too many confusing facts.

# Cultural Cognition & Motivated Reasoning

Cultural cognition has grown from the ideas of Mary Douglas and Aaron Wildavsky.  The research, ideas, etc of the Cultural Cognition Project at Yale Law School are at www.culturalcognition.net – home . Dan Kahan leads the project.  The website is a great resource and there is little reason to provide much here other than to try to get you to visit it.  I will first provide the basic concept as set out by Dan Kahan and Don Braman.  Then I will provide quick summaries of the 2012 paper by Kahan, Peters, Wittlin, Slovic, Larrimore Ouellette, Braman & Mandel, “The polarizing impact of science literacy and numeracy on perceived climate change risks” and Kahan’s 2012 paper, “Ideology, Motivated Reasoning, and Cognitive Reflection: An Experimental Study.”  They are rather remarkable.