statistics folly
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From: Joel Koltner on 16 Jul 2010 15:53 "Michael Robinson" <kellrobinson(a)n_o_s_p_a_m.n_o_s_p_a_m.yahoo.com> wrote in message news:spKdnR2-x6_1Mt3RnZ2dnUVZ_vKdnZ2d(a)giganews.com... > If the school population is many, many magnitudes larger than the number of > voters, the chance that underdog will win just reduces to 45% (the same as > the underdog's chance of winning if only one student votes). Only if you do a very large number of samples as well. Consider the following: You have a very large school, 45% want the underdog. If only one person shows up to vote, what's the likelihood the underdog wins? Clearly 45%, right? But now let's have THREE people show up to vote... what are the underdog's chances? (U=underdog, N=non-underdog) Votes Likelihood Winner Underdog Weighting UUU 0.091 U 0.091 UUN 0.111 U 0.111 UNU 0.111 U 0.111 UNN 0.136 N NUU 0.111 U 0.111 NUN 0.136 N NNU 0.136 N NNN 0.166 N Underdog's chance: 0.425 (hopefully the formatting doesn't get too messed up there...) As you can see, the answer isn't 45% but rather 42.5%. By taking a limited number of samples, you get a certain about of "noise" in the final outcome due to the inability to cast a fraction of a vote; that makes the outcome different from the case where every voter is counted (in which case the noise averages out to zero). Somewhat-related EE application: Sigma-delta modulators? ---Joel
From: Joel Koltner on 16 Jul 2010 16:02 "Joerg" <invalid(a)invalid.invalid> wrote in message news:8abmkrFbojU1(a)mid.individual.net... > One question I always pondered is, why are they teaching this in > engineering school anyhow? Some EE ends up using it? :-) Stats show up an awful lot in... -- Communication texts, worrying about the effect of nose on signal intelligibility --> Those trying to cook up new modulation formats should worry about this -- Error-correcting codes --> Those worrying about choosing error-correctoin schemes should worry about it -- Phil Hobbs' book :-) -- Tim Wescott's book :-) I think the real answer is that curriciulums often have historical roots that are hard to change even when the material becomes of margin use for most students. Many a practicing BSEE can do just fine recalling no more statistics than, e.g., how to calculate a mean... ---Joel
From: Tim Wescott on 16 Jul 2010 16:27 On 07/16/2010 12:13 PM, Michael Robinson wrote: >> They're really just wording the question kinda poorly (and they're also >> assuming the student population is very, very large -- as you point out, > if >> there are only 100 kids at the school, you can come up with very > definitive >> answers). What they really mean is something like: >> >> -- You're performing sampling where 45% of the time you get answer A > (someone >> votes for the underdog), and 55% of the time you get answer B (a vote for > the >> other guy). If you perform 100 random samples, what's the likelihood that > >> you'll get more than 50 'A' answers? >> >> This is a standard statistics question, along the lines of, "If you roll a > >> fair dice 100 times, what's the likelihood you'll get '3' 20 or more > times?" >> >> Part of engineering is figuring out what your "customer" really wants when > >> their own description is kinda flaky. :-) >> >> ---Joel >> >> > If the school population is many, many magnitudes larger than the number of > voters, the chance that underdog will win just reduces to 45% (the same as > the underdog's chance of winning if only one student votes). > And in the case where the school population is relatively small, the > simulation methodology suggested is so bad it's not even wrong. Sampling > will always return about 45%, and we have seen that the chances of the > underdog winning can range as low as zero. The exercise is meaningless. > I think I should go for a walk. Uh, no. The probability distribution of the resulting vote is a binomial distribution (http://en.wikipedia.org/wiki/Binomial_distribution), with a peak at 55 votes for the winner and 45 votes for the loser. It'll have a variance of 100 * 0.45 * 0.55 = 24.75. With that many votes it'll be pretty close to a normal distribution, so the probability that a vote will go the wrong way is about 16%. So when you get back from your walk, you probably want to brush up on your statistics. Doing this by simulation makes no sense unless the aim of the exercise is to teach the student how to do Monte Carlo simulation, or to help them get a feel for that 16% probability of a wrong vote. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html
From: Joerg on 16 Jul 2010 16:39 Joel Koltner wrote: > "Joerg" <invalid(a)invalid.invalid> wrote in message > news:8abmkrFbojU1(a)mid.individual.net... >> One question I always pondered is, why are they teaching this in >> engineering school anyhow? > > Some EE ends up using it? :-) > > Stats show up an awful lot in... > > -- Communication texts, worrying about the effect of nose on signal > intelligibility --> Those trying to cook up new modulation formats > should worry about this > -- Error-correcting codes --> Those worrying about choosing > error-correctoin schemes should worry about it > -- Phil Hobbs' book :-) > -- Tim Wescott's book :-) > Also Monte Carlo in SPICE, named after _the_ casino city. Actually, formally it's a whole country unto itself. > I think the real answer is that curriciulums often have historical roots > that are hard to change even when the material becomes of margin use for > most students. Many a practicing BSEE can do just fine recalling no > more statistics than, e.g., how to calculate a mean... > Ok, yes, I agree that we all need it. My point really was, isn't this sort of stuff the job of a high school to teach? There has got to be a reason why we all must go to high school before heading towards engineering :-) -- Regards, Joerg http://www.analogconsultants.com/ "gmail" domain blocked because of excessive spam. Use another domain or send PM.
From: Joel Koltner on 16 Jul 2010 16:49
"Joerg" <invalid(a)invalid.invalid> wrote in message news:8abucoFpvoU1(a)mid.individual.net... > Ok, yes, I agree that we all need it. My point really was, isn't this > sort of stuff the job of a high school to teach? Ah, sorry, I had missed that point. :-) I did have a stats class in high school, but there were was another one in college as well... that was rather more advanced. Although I'd have to say I learned more about stats when they started being applied in engineering classes rather than just being somewhat abstract mathematical tools. ---Joel |