Summary: Few of us have a confident understanding of probabilities and statistics. I’d say most of us relate to a scene from Dumb and Dumber:
Loyd Christmas: What do you think the chances are of a guy like you and a girl like me… ending up together?
Mary Swanson: Well, Lloyd, that’s difficult to say. I mean, we don’t really…
Lloyd Christmas: Hit me with it! Just give it to me straight! I came a long way just to see you, Mary. The least you can do is level with me. What are my chances?
Mary Swanson: Not good.
Lloyd Christmas: You mean, not good like one out of a hundred?
Mary Swanson: I’d say more like one out of a million.
Lloyd Christmas: So you’re telling me there’s a chance… YEAH!
And the reason we relate is because at some point it becomes meaningless to us. We play the lottery and we see commercials for wonder drugs. It all seems great, even if we don’t understand why.
Would I say this book is for everyone, no. It doesn’t rule anyone out, but it can be dry. The reader must want to improve their grasp of probabilities and uncertainty, to improve their innumeracy. This book provides a mental tool to help – natural frequencies.
Detail Review: Before I get to the contents of Gerd Gigerenzer’s book, I’d like to comment on the tangible book. It has many small numbers creating a grey pallet. The name of the book is reflected so two versions of it are represented on the cover. There’s also a symbol which appears to be a sigma, but I’m not sure. Together it makes for a busy visual. Within the book the font is of average size and there are helpful visuals sprinkled throughout. The result is 246 pages you can get through without feeling overcome by it.
The introduction sections of the book layout the ideas with the middle going into real world examples to explain them. The last few sections provide some funny and light hearted content.
Early on he sets the stage. I like the definitions, the philosophy, and the varying views of risk people have. Here are some examples:
The definition of innumeracy in general is the inability to do basic math, but this book is focused on the inability to understand statistical relevance. Gigerenzer breaks it into four types: illusion of certainty, ignorance of risk, miscommunication of risk, and clouded thinking. The excerpt from Dumb and Dumber was an example of clouded thinking since Lloyd understood the sheer magnitude of the chances Mary was giving him but didn’t know how to draw proper inferences from it.
The author also defines different views of risk. He describes three types – degrees of belief, propensities, and frequencies. Degrees of belief are similar to what a doctor would assign the chances of survival are to a patient who is undergoing a new surgical procedure. Propensities are more about the properties of an object like a die. The traditional die has six sides and given a uniform weighting and edge will result in a distribution of 1 in 6. The design dictates the likeliness. Six Sigma design and quality programs stress this sort of risk.
The last is Frequencies and it’s the focus of the book. Frequencies take actual events, defines a reference class, and observes what happens. Roll the die a thousand times and see how many sixes resulted. Frequencies are both powerful and flawed. They are powerful because they take design to the next level, the system. With frequencies you can draw conclusions with complex situations. The downside is the event has to happen… well frequently.
With frequencies the book then goes on to explain relative risks and conditional probabilities. The writings use health care as the back drop. Here’s an excerpt for Relative Risk:
What is the benefit of a cholesterol-lowering drug on the risk of coronary heart disease? In 1995, the results of the West of Scotland Coronary Prevention Study were presented in a press release “People with high cholesterol can rapidly reduce… their risk of death by 22 per cent by taking a widely prescribed drug called Pravastatin sodium. This is the conclusion of a landmark study presented today at the annual meeting of the American Heart Association.” The benefit of this cholesterol-reducing drug, just like that most medical treatment, was reported by the press in the form of a relative risk reduction. What does “22 percent” mean? Studies indicate that a majority of people think that out of 1,000 people with high cholesterol, 220 of these people can be prevented from becoming heart attack victims. This, however, is not true… Out of 1,000 people who took Pravastatin over a period of 5 years, 32 died, whereas of 1,000 people who did not take Pravastatin but rather a placebo, 41 died. The following three presentations of the raw result – a total mortality reduction from 41 to 32 in every 1,000 people – are all correct, but they suggest different amounts of benefit and can evoke different emotional reactions in ordinary citizens.
Three Ways to Present the Benefit
Absolute risk reduction: The absolute risk reduction is the proportion of patients who die without treatment (placebo) minus those who die with treatment. Pravastatin reduces the number of people who die from 41 to 32 in 1,000. That is, the absolute risk reduction is 9 in 1,000, which is 0.9 percent.
Relative risk reduction: The relative risk reduction is the absolute risk reduction divided by the proportion of patients who die without treatment. For the present data, the relative risk reduction is 9 divided by 41, which is 22 percent. Thus, Pravastatin reduces the risk of dying by 22 percent.
Number needed to treat: The number of people who must participate in the treatment to save one life is the number needed to treat (NNT). This number can be easily derived from the absolute risk reduction. The number of people who needed to be treated to save one life is 111, because 9 in 1,000 deaths (which is about 1 in 111) are prevented by the drug.
Another situation described in the book is mammography screening for breast cancer. Several randomized trials of women 40 and older were conducted in Sweden. What the trial found was screening resulted in reducing the risk of dying from breast cancer by 25%. That’s a huge number and one that can change health behaviors. However, this number is the relative risk reduction. What the study found was out of 1,000 women, 4 would die without screening. With screening, 3 die. That’s an absolute risk reduction of 0.1%(1 out of 1,000) and a relative risk reduction of 25% (1 out of 4). Another way to think of these results is out of every 1,000 women who did not get regular mammography screening, 4 die of breast cancer. For 1,000 women who did get regular mammography screening, 3 die of breast cancer. If you’re one of the four, this is a big deal. If you’re one of the 996 then the screening made no discernible difference (may have actually led to false positives, pain, discomfort, or anxiety). Alternatively, for women between the ages of 50 and 69 who participate in breast cancer screening will average an increase in their life expectancy by 12 days.
For those who remember the OJ Simpson case, you’ll recall the name Alan Dershowitz. He was one of Simpson’s lead attorneys. After the case was over he penned a book describing how they strategized the defense. One aspect involved domestic violence. He used figures from the FBI crime reports for 1992 and found a ratio of 1 out of 2,500 battered women are killed annually by a husband or boyfriend. OJ had previously hit Nicole Brown Simpson, the murder victim. The defense used these figures to argue that men who beat their domestic partners rarely go on to murder them.
But these numbers aren’t quite right. Dershowitz is arguing what the chances are someone murders their spouse after they have beaten them – about 1 in 2,500. A low likelihood. But the question should be spun around and stated: what is the probability of a man murdering his domestic partner given that he battered her and that she was murdered. The part about Nicole Brown Simpson being murdered is relevant. Here’s the frequency tree illustrating it (for round numbers 1 in 2,500 equates to 40 out of 100,000):
In the late 70s, the Mexican government faced the problem of how to increase the capacity of the Viaducto, a four-lane motorway. Rather than building a new highway or extending the existing one, the government implemented a clever, inexpensive solution: It had the lines on the four-lane highway repainted to make it six-lanes wide. Increasing the number of lanes from four to six meant a 50 percent increase in capacity. Unfortunately, the much narrower lanes also resulted in an increase in traffic fatalities, which, after a year forced the government to turn the highway back into a four-lane road. Reducing the number of lanes from six to four meant a 33 percent decrease in capacity. In an effort at touting its progress in improving the country’s infrastructure, the government subtracted the decrease from the increase and reported that its action had increased the capacity of the road by 17 percent. In reality, of course the capacity returned to what it had been, resulting in no net benefits. The net costs were the price of the paint and increase in traffic fatalities.
Other Book Reviews by Ben Leeson:
Simple Heuristics That Make Us Smart / The IBM Data Governance Unified Process: Driving Business Value with IBM Software and Best Practices – A Book Review / How Pleasure Works – A Book Review / Why We Make Mistakes – A Book Review / Drive: The Surprising Truth About What Motivates US – A Book Review / Rules of Thumb – A Review / I Hate People – A Review / The Job Coach for Young Professionals – A Review / A Review of The Fearless Fish Out of Water: How to Succeed When You’re the Only One Like You / A Quick Review of Johnny Bunko (a manga story)