How many voters does it take to change a light bulb?
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Do You Have Statistics Questions?
OK, so here's giving back to the board.
I'd like to make this space a place where comrades can ask questions if they're taking like an intro to intermediate stats class. I work in informatics, and in particular deal a lot with problems related to statistics.
So, if you've got a question like "What the fuck is a degree of freedom?", "How many people should I interview", etc..., I'm offering to help. I guess this isn't so much a course as it is my way of offering to give you the leg-up in deciding how, yes, quantity should translate into quality
Yeah I may not get back to you right away but I'll try :þ
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How many voters does it take to change a light bulb?
none. voting is for sheep.
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why the heel did people fear communism in the 50-60 please reply
cuz communism was one country (U$ and A) from ruling da world.
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What the fuck is degree of freedom?
the truth is outside, in what we do.
OK, think of it this way.
The goal of statistics is to use data (information) to make inferences.
Often, you only need so much information to make an inference.
As a broad generality, the "degree of freedom" describes the "amount" of information left over after you`ve made that inference. If you have a lot of "left over" information, these data can take any aribtrary value. Hence they are "free" to vary.
Let me give you a concrete, although non-statistical, example to illustrate this point. Suppose we have three free variables, A, B and C. Imagine that we also know
A+B+C=0. Now, even if we have no idea what B or C are, we know that ONCE we find out what B and C are, we will know A; namely, A must equal -B-C. But, except for that, B and C are "free to vary" in this example. Hence, to make any inferences about this equation, there are "two" degrees of freedom.
Why is this important? Well, it basically comes down to the addage: "don`t use each data point more than once to make your inference."
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Fascinating. . . so it's like significant figures, but in variables--and the inference bit is like how you need a unique equation for each variable when solving systems of equations.
I'm not in a statistics class, but I really want to learn. Do you have any recommendations for self-teaching or whatever?
the truth is outside, in what we do.
How can I show for causation via statistics?
How many dice rolls would I need to throw before I could claim that the dice was unfair?
Hmm... If you have programming experience, my advice would be to write computer programs that mimic different statistical concepts and play around with them to get an intuive feel.
A good book I liked was "Lady Luck" by Warren Weaver. It was also my first statistics book
http://books.google.com/books?id=S9Wk5NqiXqkC
It is written in a non-technical fashion and is very accessible. Amazingly, it`s not out of print decades later, which is almost unheard of for a scientific text. It also goes into the philosophy behind a lot of the ideas in statistics.
I assume you`re talking about a 6-sided die, right?
Then each side should come up 1/6th of the time, or 0.1666666...
Because an unfair die can be unfair in many, many ways (e.g., you could get a loaded die that returns a "1" with probability 1/5 or probability 3/4), each of these requires a separate analysis.
So, let me rephrase your question:
"how many times should I roll a fair die to show it`s fair"?
Short answer:
For most practical purposes, 1000 throws will do the trick. 500,000 rolls should satisfy virtually all skeptics.
Long answer: To be perfectly honest, it depends.
Pretend you want to get at this question: how many times should I throw a fair die, before I can establish that it is unlikely that I won`t get a given number between one and six about 1/6th of the time?
To be concrete. If the die is unloaded, you get a "1" with probability 1/6. But when you throw it, say, 100 times, you expect to get about 17 "1"s. However, you could still get 100 "1"s, or 0 "1"s. You could just be royally, royally unlucky. It`s just that the probability of you getting all 100 "1" is extremely, extremely small (about 1.5 x 10^-78).
If you have a loaded die, then out of a hundred throws you could still get 17 "1"s, 17 "6"s, etc...
Here`s where it depends. Let`s pretend you have a fair die. If you throw it 100 times, the probability that you get less than about 10 "1"s, or more than about 25 "1"s, is less than 5%. In otherwords, 95% of the time, 100 throws will result in between 10 and 25 "1"s, 10 and 25 "2"s, etc... In other words, after 100 throws of a fair die, you`ve met the basic scientific standard that the die is NOT loaded so that it shows any side more than 25 times or less than 10 times. Thus, you`ve shown that your die is accurate to within about 7 percentage points. This might be "good enough" for some purposes, not good enough for others. It just depends.
For instance, let`s pretend you`re a die manufacturer and you want to be certain that your die is accurate to within 0.01 percentage points. Then you need to roll the die about 5000 times to get it within 0.01 percentage points. To establish, by scientific convention, that a fair die returns a "1" or any other number, between 0.165 % of the time and 0.167% of the time (basically at this point it`s fair), then you need about 500,000 throws.
Let`s suppose here`s your dilemma. I want to show that X causes Y, even though Z,U,V have also been hypothesized to cause Y.
Use regression analysis (linear or otherwise) to show that ONLY variable X predicts Y, and that Z,U,V don`t predict Y.
Of course, this doesn`t mean some unknown, unforseen variable, W isn`t causing Y. That`s part of why I have philosophical misgivings about whether causation can ever be truly shown.
But, if for the question at hand, you`ve established that variables X,Z,U,V are pretty exhaustive in terms of potentially causing Y, and you rule out Z,U, and V but not X, then it`s fair to say X causes Y.
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How does the weight subtraction of the pits in a die effect the ultimate probability of the die?
Sorry Dean you've got me here. I tried googling it but still have no clue.
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Imagine putting the die flat on a table. By tipping the die, it's possible to roll the die over to another face. Pegg calculated the minimum amount of energy required for each possible tip. The amount of energy needed to tip the die from 3 to 6 is slightly less than the energy needed to tip it from 3 to 1, for example.
In a toss, the die bounces around randomly, losing energy with each bounce. Eventually, the die doesn't have enough energy to escape from a certain orientation. By calculating centers of gravity for different numbers of drilled pits and using those data to create a Markov matrix for each bounce, Pegg came up with the following results.
Computed results for 10,000 tosses of a die with drilled dimples.
Dice used in gambling casinos are shaped much more precisely than those sold in novelty stores and with many board games. To ensure fairness, the drilled pits are filled with paint of the same weight as the plastic that was drilled out to make the spots (see Fun and Games in Nevada, 4/28/97).
Here.
^MarxSchmarx, do a Chi-Square test on that shit, my SPSS license is expired!
ETA: nevermind, I thought they actually rolled a die 10,000 timesNow I don't care.
ETAII: I was wrong, the license isn't expired, I was using the wrong version! I went ahead and did a Chi-Square even though it doesn't make much sense.
I know this is a bizarre way to think about it, but if those numbers had been produced by actually rolling 10,000 dice (instead of computed based on tipping energy or whatever), the results of the Chi-Square say that there would be a 99.8% chance that the variance they display is random. Or rather, only a 0.2% chance that the missing weight actually has any effect on the roll of a die. On the basis of your 10,000 rolls, you would be able to say with 99.8% confidence that, were you to do an infinite number of rolls, each number would appear {infinity/6} times.
There's no way I trust that whatever method that guy used to measure tipping energy was so precise that it introduced no appreciable error into 10,000 trials. However, if it was that precise, then it would no longer make sense to think about it in the same terms as the outcome of 10,000 rolls; because if we do 10,000 rolls, the question is, "are dice affected by the missing weight of holes?", but if the machine that measures tipping energy is infinitely precise, and produces the results shown in that picture, then the question becomes "how biased do dice become as a result of the weight of the missing holes?" Because the fact that they are biased would be an established fact.
What needs to be done now is to make some undergrad TAs throw 10,000 dice rolls for extra credit.
Last edited by JimmyJazz; 31st December 2008 at 08:10.
The point about physics is well taken, which is admittedly a tough engineering question.
JimmyJazz is correct. What this example by Mr. Pegg highlights is that 10,000 throws results in inadequate precision to detect bias for this particular die.
Indeed, if those of you with access to a Chi-square test (there are a few online) want to play around with it, multiply the figures in Janius's post by 50 and run a chi-sq. test to see that by 500,000, the die is no longer fair.
Another way of thinking about this is that a (really) fair die will result in skews at least as pronounced as this if thrown 10,000 times, as JimmyJazz points out, 99.8 % of the time. Thus, if the house discards its dies after less than 10,000 throws, it is very unlikely it will make a difference if there is one loaded die in the bunch.
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R
Do you use R the statistical programming language? Or something more mainstream?
Hmm, an autonomist marxist statistical research unit with R geeks might be a funny idea.
OMG awesome. Now I can prove this to my friends, they are wrong! Thanks.Imagine putting the die flat on a table. By tipping the die, it's possible to roll the die over to another face. Pegg calculated the minimum amount of energy required for each possible tip. The amount of energy needed to tip the die from 3 to 6 is slightly less than the energy needed to tip it from 3 to 1, for example.
In a toss, the die bounces around randomly, losing energy with each bounce. Eventually, the die doesn't have enough energy to escape from a certain orientation. By calculating centers of gravity for different numbers of drilled pits and using those data to create a Markov matrix for each bounce, Pegg came up with the following results.
Computed results for 10,000 tosses of a die with drilled dimples.
Dice used in gambling casinos are shaped much more precisely than those sold in novelty stores and with many board games. To ensure fairness, the drilled pits are filled with paint of the same weight as the plastic that was drilled out to make the spots (see Fun and Games in Nevada, 4/28/97).
Here.
Yup.
Maybe they should organize the Bukharinist caucus at the next useR.
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What is the probablity evolution being wrong ...
(I dont really get this thread ..)
"Marxist psychology is not a school amidst schools, but the only genuine psychology as a science. A psychology other than this cannot exist. And the other way around: everything that was and is genuinely scientific belongs to Marxist psychology" -Lev Vygotsky
"The Bolsheviks have shown that they are capable of everything that a genuine revolutionary party can contribute within the limits of historical possibilities. They are not supposed to perform miracles. For a model and faultless proletarian revolution in an isolated land, exhausted by world war, strangled by imperialism, betrayed by the international proletariat, would be a miracle."
-Rosa Luxemburg
Zero.What is the probablity evolution being wrong ...
It's for people who have questions about statistics and probability and related shiiiiiit.
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