This Sunday morning, I was reading the NYT when I came upon this picture illustrating Stephanie Koontz’s tribune “when numbers mislead“, a rather dull summary of an unreferenced and impossible-to-google paper called “The Trouble With Averages” [what about Quételet?!] dealing with the impact of marriage(s) on happiness (and vice-versa). [Funny enough, Andrew was telling me about this economist from Warwick working on happiness just yesterday night!] I however wanted mostly to point out how a-statistical this picture was, from a meaningless Venn diagram (reminding me of Templeton!) to the notion of opposing average and variation, to outliers standing in the wrong place (intersection of whatever!). [I do not think it is relevant to stress the innumeracy revealed by the column and its title!]
Archive for innumeracy
I received very recently this book, Guesstimation 2.0, written by Lawrence Weinstein from Princeton University Press for review in CHANCE and decided to check the first (2008 )volume, Guesstimation, co-written by Lawrence Weinstein and John A. Adam. (Discovering in the process that they both had a daughter named Rachel, like my daughter!)
The title may be deemed to be very misleading for (unsuspecting) statisticians as, on the one hand, the book does not deal at all with estimation in our sense but with approximation to the right order of magnitude of an unknown quantity. It is thus closer to Innumeracy than to Statistics for Dummies, in that it tries to induce people to take the extra step of evaluating, even roughly, numerical amounts (rather than shying away from it or, worse, of trusting the experts!). For instance, how much area could we cover with the pizza boxes Americans use every year? About the area of New York City. (On the other hand, because Guesstimation forces the reader to quantify one’s guesses about a certain quantity, it has a flavour of prior elicitation and thus this guesstimation could well pass for prior estimation!)
In about 80 questions, Lawrence Weinstein [with John A. Adam in Guesstimation] explains how to roughly “estimate”, i.e. guess, quantities that seem beyond a layman’s reach. Not all questions are interesting, in fact I would argue they are mostly uninteresting per se (e.g., what is the surface of toilet paper used in the U.S.A. over one year? how much could a 1km meteorite impacting the Earth change the length of the day? How many cosmic rays would have passed through a 30 million-year-old bacterium?), as well as very much centred on U.S. idiosyncrasies (i.e., money, food, cars, and cataclysms), and some clearly require more background in physics or mechanics than you could expect from the layman (e.g., the energy of the Sun or of a photon, P=mgh/t, L=mvr (angular momentum), neutrino enery depletion, microwave wavelength, etc. At least the book does not shy away from formulas!) So Guesstimation and Guesstimation 2.0 do not make for a good bedtime read or even for a pleasant linear read. Except between two metro stations. Or when flying to Des Moines next to a drunk woman… However, they provide a large source of diverse examples useful when you teach your kids about sizes and magnitudes (it took me years to convince Rachel that 1 cubic meter was the same as 1000 liters!, she now keeps a post-it over her desk with this equation!), your students about quick and dirty computing, or anyone about their ability to look critically at figures provided in the newsy, the local journal, or the global politician. Or when you suddenly wonder about the energy produced by a Sun made of… gerbils! (This is Problem 8.5 in Guesstimation and the answer is as mind-boggling as the question!) Read more »
Yuk! Among the many articles celebrating this tremendous step in particle physics, there are many sentences like the one above, found in Le Monde. (This is actually the title of the article, with the additional sentence “Il y a désormais plus de 99,9999 % de chances que l’observation soit correcte.”) Both sentences being utterly meaningless, it would be nice if journalists and presumably physicists could understand the meaning of a p-value..! Other blogs have already pointed out the fallacy of the inversion of p(|x|>5σ) into this meaningless 99.9999% so I will not fill many pages about the issue, however it sounds like there is an innumeracy issue there. Still, both my kids did basic confidence intervals in high school, where they were pointed the danger of the p-value inversion fallacy. (Of course, this presentation is fairly new in French high schools. In my days, days of yore, statistics was definitely not a high school subject!)
(Heard on the public radio, from a presidential candidate whose ideas are close to mine’s, but who is definitely missing in quantitative as well as verbal skills!)
It has been shown that the probability of a major nuclear accident in France is of one out of six every ten years. It is like a gun where you put six bullets in the barrel and press the trigger every ten years.