statistics folly
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From: George Herold on 16 Jul 2010 16:49 On Jul 16, 4:27 pm, Tim Wescott <t...(a)seemywebsite.com> wrote: > 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%. Tim do you mind showing a bit more of your work? How did you get 16% from a variance of 24.75? Thanks, George H. > > 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 Serviceshttp://www.wescottdesign.com > > Do you need to implement control loops in software? > "Applied Control Theory for Embedded Systems" was written for you. > See details athttp://www.wescottdesign.com/actfes/actfes.html- Hide quoted text - > > - Show quoted text -
From: TTman on 16 Jul 2010 16:59 > > > 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%. Tim do you mind showing a bit more of your work? How did you get 16% from a variance of 24.75? Thanks, George H. There's an 87.5% chance he'll reply, with a 99% chance you won't understand ( and neither will I) :(
From: Tim Wescott on 16 Jul 2010 17:11 On 07/16/2010 01:49 PM, George Herold wrote: > On Jul 16, 4:27 pm, Tim Wescott<t...(a)seemywebsite.com> wrote: >> 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%. > > Tim do you mind showing a bit more of your work? How did you get 16% > from a variance of 24.75? Variance of 24.75 = sigma of around 5, 50 votes occurs at 5 votes away from the center (of 55 votes), or one sigma. There's a 34% probability that you'll hit a vote between 50 and 55, plus a 50% probability that you'll hit a vote somewhere between 50 and 100. That's an 84% chance of a correct vote, with 16% remaining for claims of stolen elections and arguments over voting procedures in Miami. -- 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: Tim Wescott on 16 Jul 2010 17:13 On 07/16/2010 01:39 PM, Joerg wrote: > 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 :-) College stats is well beyond high school stats. College stats (at least the one that I took) is a 4th year class from the mathematics department that leaves many of the math majors in the dust. -- 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: Tim Wescott on 16 Jul 2010 17:16
On 07/16/2010 01:02 PM, 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 :-) I have some hand-waving about random processes in my book, but I don't think there's much real statistics in there. Cite a page number and I'll look, though. If you want to get more than an intuitive grasp of the response of a control system to random input (either noise or a command that's modeled as stochastic) you need rather more material under your belt than I provide in that book. Of course, once you _do_ get the necessary information, you can apply it using the book... -- 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 |