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I bought this popular math book at B&N, for my quasi-niece G2, for lack of anything obviously better on the shelf. I read it before turning it over to her, and it was fun; I think I would have liked it at her age (12) though I'm not sure if she will. Of course, it was less eye-openingi for me now: I've taken classes on Bayesian statistics, I've given talks on voting systems, I've read about the file drawer problem or the exponential stockbroker scam. Still, I did learn some things.
A big one was what he calls "don't talk about percentages of things that could be negative." More specifically, say the US adds 18,000 jobs one month, and Wisconsin adds 9,000 jobs. Does that mean Wisconsin was responsible for 50% of US job growth? The governor of WI would like to say so. But say that California added 30,000 jobs -- does that mean it was responsible for 166% of US job growth? Uh... The trick being that the US number is a net sum of positive and negative (say Texas lost 21,000 jobs) numbers; taking percentages of that is meaningless.
Another example: it's said that the top 1% have taken 93% of US income growth. Sounds pretty bad. But the next 9% might (I don't recall the numbers) might have taken 20% of income growth. Uh oh... we can balance this by actual reductions of income in the bottom 90%. So this is better and worse: more people are doing well, but the rest are actually falling behind, not just standing still. But the "middle class" would probably be less outraged by learning that they were also doing well.
Berkson's Fallacy was something I'd vaguely heard about, but forgotten. It's explained well at the link (by him, even), but the short version is that two independent variables can look negatively correlated if you select for either of them. Like, if you notice nice people or hot people, you'll find that of the people you notice, many hot people are jerks. But this needn't mean hot people are actually prone to jerkiness, just that you ignore plain jerks.
You can extend that to any two variables of desirable things. Niceness and richness, niceness and political agreeableness... say I put up with people if they're personally agreeable or politically agreeable; this will lead to my thinking that my political allies are unfortunately prone to being jerks, when it's more that I ignore opponents who are jerks.
A couple of geometrical statistics I hadn't know: correlation being the same as elliptical eccentricity, and Pearson correlation being the cosine of the angle between two vectors. Simple that way, ugly as an algebraic formula of the components.
Also, correlation is not transitive, the way that Dad and Mom are both related to Baby but not each other. Portfolio 1 might be IBM and Apple, correlated with P2 which is Apple and Honda, but not with P3, Honda and GM.
Reminders of the ubiquity of regression to the mean, and of the variance of small populations, are always useful.
Slime molds apparently suffer a voting paradox. They like oats and dislike light, it makes sense that you can balance them between a big pile of oats in the dark and a bigger pile under a UV lamp. It makes less sense that if you add a small pile of oats in the dark, the mold starts going for the big pile in the dark.
'hazard' comes from the Arabic for dice.
He talks a bit about the damage done by the cult of genius, when those magical moments of insight and revelation take a lot of work beforehand to prepare your brain.
Proof advice: try to prove it by day, disprove it by night. (More applicable if you don't know if it's true or false.) Might get insight into why it has to be true, or find out you were wrong all along.
Condorcet wanted the Rights of Man for women, Hilbert refused to endorse the Kaiser in WWI, and defended giving Emmy Noether a position.
A big one was what he calls "don't talk about percentages of things that could be negative." More specifically, say the US adds 18,000 jobs one month, and Wisconsin adds 9,000 jobs. Does that mean Wisconsin was responsible for 50% of US job growth? The governor of WI would like to say so. But say that California added 30,000 jobs -- does that mean it was responsible for 166% of US job growth? Uh... The trick being that the US number is a net sum of positive and negative (say Texas lost 21,000 jobs) numbers; taking percentages of that is meaningless.
Another example: it's said that the top 1% have taken 93% of US income growth. Sounds pretty bad. But the next 9% might (I don't recall the numbers) might have taken 20% of income growth. Uh oh... we can balance this by actual reductions of income in the bottom 90%. So this is better and worse: more people are doing well, but the rest are actually falling behind, not just standing still. But the "middle class" would probably be less outraged by learning that they were also doing well.
Berkson's Fallacy was something I'd vaguely heard about, but forgotten. It's explained well at the link (by him, even), but the short version is that two independent variables can look negatively correlated if you select for either of them. Like, if you notice nice people or hot people, you'll find that of the people you notice, many hot people are jerks. But this needn't mean hot people are actually prone to jerkiness, just that you ignore plain jerks.
You can extend that to any two variables of desirable things. Niceness and richness, niceness and political agreeableness... say I put up with people if they're personally agreeable or politically agreeable; this will lead to my thinking that my political allies are unfortunately prone to being jerks, when it's more that I ignore opponents who are jerks.
A couple of geometrical statistics I hadn't know: correlation being the same as elliptical eccentricity, and Pearson correlation being the cosine of the angle between two vectors. Simple that way, ugly as an algebraic formula of the components.
Also, correlation is not transitive, the way that Dad and Mom are both related to Baby but not each other. Portfolio 1 might be IBM and Apple, correlated with P2 which is Apple and Honda, but not with P3, Honda and GM.
Reminders of the ubiquity of regression to the mean, and of the variance of small populations, are always useful.
Slime molds apparently suffer a voting paradox. They like oats and dislike light, it makes sense that you can balance them between a big pile of oats in the dark and a bigger pile under a UV lamp. It makes less sense that if you add a small pile of oats in the dark, the mold starts going for the big pile in the dark.
'hazard' comes from the Arabic for dice.
He talks a bit about the damage done by the cult of genius, when those magical moments of insight and revelation take a lot of work beforehand to prepare your brain.
Proof advice: try to prove it by day, disprove it by night. (More applicable if you don't know if it's true or false.) Might get insight into why it has to be true, or find out you were wrong all along.
Condorcet wanted the Rights of Man for women, Hilbert refused to endorse the Kaiser in WWI, and defended giving Emmy Noether a position.