= 27d567bc2d48d9f40e9ccc20ea370b15)
If your sample size is n times as large, the probability becomes (.05)^n
I'm not sure that follows.
You're right. That would be true if we did n independent tests, not one test with n-times the subjects.
e.g. probability of 60 or more heads in 100 tosses = .028
probability of 120 or more heads in 200 tosses = .0028
but .028^2 = .00081
I was just mentally approximating log(.001)/log(.05) = 2.3.
Thanks. Sometimes I learn a lot from people saying fairly-obvious (in retrospect) things.
In case anyone is curious about this, I guess that Eliezer knew it instantly because each additional data point brings with it a constant amount of information. The log of a probability is the information it contains, so an event with probability .001 has 2.3 times the information of an event of probability .05.
If that's not intuitive, consider that p=.05 means that you have a .05 chance of seeing the effect by statistical fluke (assuming there's no real effect present). If your sample size is n times as large, the probability becomes (.05)^n. (Edit: see comments below) To solve
(.05)^n = .001
take logs of both sides and divide to get
n = log(.001)/log(.05)
By "upward," I just meant to emphasize that it was opposing gravity, e.g., positive. But of course, now that I think about it for a minute, I see that I was wrong, it is under no tension at all. Oops.
I think I see what you mean. To clarify, though, tension doesn't have a direction. In a rope, you can assign a value to the tension at each point. This means that if you cut the rope at that point, you'd have to apply that much force to both ends of the cut to hold the rope together. It's not upward or downward, though. Instead, the net force on a section of rope depends on the change in the tension from the bottom of that piece to the top. The derivative of the tension is what tells you if the net force is upward or downward. This derivative is a force per unit length.
In general, tension is a rank-two tensor, and is just a name for when the pressure is negative.
In response to
What is the Mantra of Polya?
A way to think about this problem that clarified it for me: The top of the slinky is experiencing tension equal to its whole weight. The bottom is experiencing upward tension equal to its weight, so at the instant when it is dropped, it experiences no net force - until the upper parts of the slinky start traveling downward, removing the upward tension. (The speed-of-information-in-materials wasn't really convincing to my intuition, because it feels like, since the bottom of the slinky is in a gravitational field , it should already "know" it is falling... )
For a mantra: How about something like, "What do you know? What don't you know? How do you connect them?"
I'm not really sure what you mean by "upward tension", sorry. Tension in one dimension is just a scalar. The very bottom of the spring is under no tension at all, and the tension increases as the square root of the height for a stationary hanging slinky.
In response to
What is the Mantra of Polya?
Does the top of the slinky accelerate groundwards faster than gravity?
I'm not sure how to pronounce "Polya"
Tip: Use Google Translate to find pretty-good pronunciations of foreign names. Set the source language to the one the name comes from (Hungarian, in this case), type the name with the right accent marks (Pólya), and click the speaker button in the bottom right of the box.
Thanks for the tip.
The center of mass of the slinky accelerates at normal gravitational acceleration. The bottom of the slinky is stationary, so to compensate the top part goes extra-fast. I did a short calculation on the time for the slinky to collapse here http://arcsecond.wordpress.com/2012/07/30/dropping-a-slinky-calculation-12/
In response to
Rationality Quotes June 2012
And clearly my children will never get any taller, because there is no statistically-significant difference in their height from one day to the next.
Andrew Vickers, What Is A P-Value, Anyway?
In response to
Low hanging fruit: analyzing your nutrition
WolframAlpha is pretty good for calculating all this automatically - probably much faster than the spreadsheet. For example:
In response to
Why do people ____?
Why do I fantasize about being angry?
I'm breaking the rule a bit by asking about myself here.
Sometimes when I have down time and am daydreaming, especially if I'm walking somewhere or going for a run, I fantasize about someone wronging me (say with a traffic violation), then imagine myself getting angry, yelling at them, and physically beating them up. I think about knocking them down, screaming at them, challenging them to get up, and knocking them down again.
I've never acted on such a fantasy. I have no idea how to actually fight someone if I wanted to. It's very rare that I show anger, and I don't think I've ever punched someone as an adult. But I think about it pretty regularly, and the thoughts disturb me. I have no idea where they come from or why I take pleasure in these sorts of fantasies.
Is this a common thought pattern? Why do people have it?
In response to
Rationality Quotes May 2012
Asked today if the Titanic II could sink, Mr Palmer told reporters: "Of course it will sink if you put a hole in it."
http://www.smh.com.au/business/clive-palmer-plans-to-build-titanic-ii-20120430-1xtrc.html
= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
= f037147d6e6c911a85753b9abdedda8d){kind=logo}
I rarely make decisions involving such low probabilities, so I don't really know how to handle risk-aversion in these cases. If I'm making a choice based on a one-in-ten-million chance, I expect that even if I make many such choices in my life, I'll never get the payoff. This is quite different than handling one-in-a-hundred chances, which are small but large enough that I can expect the law of large numbers to average things out in the long term. So even if I usually subscribe to a policy of maximizing expected utility, it could still make sense to depart from that policy on issues like voting.
BTW, in my state, Maryland, Obama has a 18-point margin in the polls. That could easily be six standard deviations away from the realm where I even have a chance of making a difference.