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The Most Dangerous Equation [pdf]

press.princeton.edu

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Re: The Most Dangerous Equation [pdf]

#41

Post by kc0bfv »

6ren wrote: post #31

The last section on sex differences is interesting. It explains boys having greater variation in ability than girls by boys having only one X chromosome (XY) while girls have two (XX). This would be a neat theory, if girls somehow used an average of the two X's... which seems compellingly logical, though the (current) theory is that only one X is used, chosen at random. http://en.wikipedia.org/wiki/Barr_body

Hrm, if you're a girl, you get 1 X from Mom and 1 from Dad. So, if Mom's X's are chromosomes a and b, and Dad's is chromosome c, then your X chromosomes will be a,c or b,c with a .5 prob for each. With your suggestion, there's a .5 prob in each case that Dad's X will be used, and so a .5 prob overall that, for a girl, Dad's X will be used.

A guy has to use Mom's X. I think the paper's argument still holds, because there's a larger amount of possibilities for women than men, but I can't take this much further without circular reasoning.

Re: The Most Dangerous Equation [pdf]

#42

Post by kc0bfv »

kc0bfv wrote: post #41
6ren wrote: post #31

The last section on sex differences is interesting. It explains boys having greater variation in ability than girls by boys having only one X chromosome (XY) while girls have two (XX). This would be a neat theory, if girls somehow used an average of the two X's... which seems compellingly logical, though the (current) theory is that only one X is used, chosen at random. http://en.wikipedia.org/wiki/Barr_body

Hrm, if you're a girl, you get 1 X from Mom and 1 from Dad. So, if Mom's X's are chromosomes a and b, and Dad's is chromosome c, then your X chromosomes will be a,c or b,c with a .5 prob for each. With your suggestion, there's a .5 prob in each case that Dad's X will be used, and so a .5 prob overall that, for a girl, Dad's X will be used. A guy has to use Mom's X. I think the paper's argument still holds, because th…

Oh, for the women there's a .25 prob that a is used, and a .25 prob that b is used, and a .5 prob that c is used. Dad's X has the best chance, and his X may have made him a better partner than his peers. Also, a .25 prob for the X that made Mom a better partner. So, a .75 prob overall of getting a great X and a .25 prob of getting an unknown X.

For the dude there's a .5 prob of getting a great X and a .5 prob of getting an unknown X.

Re: The Most Dangerous Equation [pdf]

#43

Post by pseut »

forrestthewoods wrote: post #10
guylhem wrote: post #3

Absolutely totally true. Ignore the laws of statistics at your own peril. Knowledge of statistics is the best investment one can make with one's time. A/B testing is the tip of the iceberg - a simple practical application, which can be exploited much better with statistics. Learn about statistical distributions - Bernouilli, Binomial, Normal, Poisson and Hypergeometric at least, then Chi distribution to grasp real te…

If someone doesn't know much about statistics what is your recommended source to learn from?

- "Statistics" by Freedman, Pisani, and Purves: http://www.amazon.com/Statistics-4th-David-Freedman/dp/03939... (but an old edition would be fine)

- Any of Wainer's books (the author of the original pdf)

(Added later): books that explain the history of statistical thought are surprisingly good, because they explain the context and the problems the statistics were originally meant to solve. I really enjoyed "the lady tasting tea" and I think I learned from it.

Re: The Most Dangerous Equation [pdf]

#44

Post by theologic »

confluence wrote: post #24

Ah hello law of small numbers, survivorship bias and fundamental attribution error - we meet again. If you understand these 3 biases - you'll wonder what kind of world you have actually been living in all this time. I'm going to repost a my comment about this very concept as related to startups from a while ago because I believe HNers will appreciate it - it's from an article called "Startup School And Survivor Bias"…

One of the main principles that Collins destroys is that "great companies are started with a vision." He basically says a lot of great companies started with weak ideas, but were willing to change (or pivot in your writing.)

Collins primarily looked at established, large businesses. You won't catch him saying that his ideas primarily applies to start-up success. His point is that start-ups are all about luck, and he points out how many a lucky start-up blew their lead because they couldn't figure out how to establish a company.

So, rather being in opposition to your thoughts, there is a lot of common ground.

Other than that, some great thoughts. I would add that I have seen brilliant people that could not network or were not resilient. I think both of these need to be added to your startup advice, and are important success factors.

Re: The Most Dangerous Equation [pdf]

#45

Post by treeder »

jamiequint wrote: post #29
confluence wrote: post #24

Ah hello law of small numbers, survivorship bias and fundamental attribution error - we meet again. If you understand these 3 biases - you'll wonder what kind of world you have actually been living in all this time. I'm going to repost a my comment about this very concept as related to startups from a while ago because I believe HNers will appreciate it - it's from an article called "Startup School And Survivor Bias"…

Also interesting and on topic with this are any of Nicholas Taleb's books. I highly recommend his new one: Antifragile ( http://www.amazon.com/gp/aw/d/1400067820 )

I've been reading Fooled by Randomness by Taleb, great book, same topic.

Re: The Most Dangerous Equation [pdf]

#46

Post by russelldavis »

6ren wrote: post #40
ef4 wrote: post #37

Earlier quoted context omitted.

I don't understand how that fits with the existence of X-linked-recessive diseases. ( https://en.wikipedia.org/wiki/Genetic_disorder#X-linked_rece... ) These seem to be well-known cases in which you really do get a phenotype that's a function of both X chromosomes.

You're right, it doesn't fit. Now I recall that rates of red-green colour blindness are exactly predicted by whether one or both must be defective (7% for boys, .49% for girls). Both being active but the defective version having no effect would explain the evidence, but doesn't fit the Barr body theory... it would need to know which one to choose (and it wouldn't be "random").

X-chromosome inactivation is actually consistent with X-linked "recessive" conditions, but it's a little tricky, and the wikipedia page doesn't really explain it. Basically, X-linked phenotypes aren't dominant/recessive in the same way as the others. Usually, dominance takes place between chromosome pairs within each cell. However, with X-chromosome inactivation, dominance takes place between cells. For example, women who are labeled "carriers" for colorblindness actually are colorblind in half of the cells in their eyes, but the other half are sufficient to perceive color almost as well as non-carriers.

Re: The Most Dangerous Equation [pdf]

#47

Post by foxylad »

wes-k wrote: post #22
grannyg00se wrote: post #16

Excellent. Reminds me of the lecture describing that "the greatest shortcoming of the human race is our inability to understand the exponential function" http://youtu.be/F-QA2rkpBSY

Thanks for sharing this! Albert Bartlett does a wonderful job explaining the consequences of sustained growth rates. I find overpopulation to be one of the greatest concerns that we are not adequately dealing with. Albert's bacteria in a bottle analogy made me think of Elon Musk's attempt to bring human life to other planets.. will we not just be expanding our time of growth? Maybe we should start choosing a way to r…

I didn't understand why everyone was wittering on about sustainability until I read "Collapse" by Jarod Diamond. It illustrates how dangerous it is to ignore sustainability, and how rare it is in human societies.

It seems to me that we have a choice:

1. Figure out how to cut our population growth to 0%, and then educate everyone on the planet as why they should do this instead of breeding to the max. Our kids will be happier than us.

2. Breed to the max until everyone on earth (and maybe Mars) is only just hanging on by their fingernails, probably living extremely unpleasant lives of violent competition and constant starvation. Our kids will be less happy than us.

Sadly I think option 1 is unlikely due to the tragedy of the commons.

Re: The Most Dangerous Equation [pdf]

#48

Post by sesqu »

FrojoS wrote: post #36

quote: "Obviously, they assumed that variability decreased proportionally to the number of coins and not to its square root." Why is this so important? The fact, that the variability increases with smaller sample size was ignored completely by the protagonists in the provided examples. Realizing weather this inverse effect is linear or not doesn't seem to be the main problem in peoples intuition. disclaimer: I have p…

In the first example, which you quoted, they ended up allowing for greatly more variability than intended, leaving the regulator vulnerable for exploitation. The author speculated as to what sort of exploitation might have occurred, but did not state that it did.

The rest of the examples had nothing to do with the specific relationship between standard deviation and sample size, but with the more basic fact that a relationship exists. This observation is arguably the more important one, and is poorly argued in the chapter. It's also why some people always demand error bars, though I personally prefer plotting individual data points where possible.

The last example, while interesting, had very little to do with the equation (despite a claim to the contrary), which makes me believe the topic was an afterthought.

Re: The Most Dangerous Equation [pdf]

#49

Post by gizmo686 »

confluence wrote: post #24

Ah hello law of small numbers, survivorship bias and fundamental attribution error - we meet again. If you understand these 3 biases - you'll wonder what kind of world you have actually been living in all this time. I'm going to repost a my comment about this very concept as related to startups from a while ago because I believe HNers will appreciate it - it's from an article called "Startup School And Survivor Bias"…

>But honestly - startup founders literally have no idea why things take off and they have no idea why they win. That's why they have to keep pivoting - it increases their luck surface area and their ability to gain traction - after which they simply must hold on tight while surfing the wave.

Sounds like you have some solid advice, pivot often.

Re: The Most Dangerous Equation [pdf]

#50

Post by oelewapperke »

SiVal wrote: post #12
guylhem wrote: post #3

Absolutely totally true. Ignore the laws of statistics at your own peril. Knowledge of statistics is the best investment one can make with one's time. A/B testing is the tip of the iceberg - a simple practical application, which can be exploited much better with statistics. Learn about statistical distributions - Bernouilli, Binomial, Normal, Poisson and Hypergeometric at least, then Chi distribution to grasp real te…

> "Knowledge of statistics is the best investment one can make with one's time." Do you have any numbers to back that up? ;-)

I worked a while next to a statistics department of a university. Given the wealth of the people in that building - or even the smell, on bad days, I'd say you can probably do better with your time - anywhere else.
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