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From: Michael Robinson on 16 Jul 2010 20:22

"Artemus" <bogus(a)invalid.org> wrote in message
news:i1qse4$bq1$1(a)news.eternal-september.org...
>
> "Michael Robinson" <kellrobinson(a)n_o_s_p_a_m.n_o_s_p_a_m.yahoo.com> wrote
> in message
> news:l6adnZjIINVRA93RnZ2dnUVZ_u2dnZ2d(a)giganews.com...
>>
>> More options Jul 16, 1:24 pm
>> Newsgroups: sci.math
>> From: gearhead <nos...(a)billburg.com>
>> Date: Fri, 16 Jul 2010 10:24:41 -0700 (PDT)
>> Local: Fri, Jul 16 2010 1:24 pm
>> Subject: stats/probability question
>> Reply | Reply to author | Forward | Print | Individual message | Show
>> original | Remove | Report this message | Find messages by this author
>>
>> I'm an engineering undergrad in an intro stats course. We had a
>> question in the book that's really dumb.
>>
>> problem as stated:
>>
>> Your candidate has 55% of the votes in the entire school. But
>> only
>> 100 students will show up to vote. What is the probability that the
>> underdog (the one with 45% support) will win? To find out, set up a
>> simulation.
>> a) Describe how you will simulate a component and its outcomes.
>> b) Describe how you will simulate a trial.
>> c) Describe the response variable.
>>
>> The answer in the back of the book says using a two digit random
>> number to determine each vote (00-54 for your candidate, 55-99 for the
>> underdog) you would run a string of trials with 100 votes to each
>> trial.
>>
>> Now, this is one misconceived exercise. Let me explain why.
>>
>> Say the school has 1000 students. If all of them show up, the
>> underdog has 0% chance of winning. If exactly one voter shows up,
>> underdog has 45% chance of winning. In an election where 100 voters
>> show up, underdog's chance of winning the election HAS to lie
>> somewhere between 0% and 45%. No ifs, ands or buts.
>
> You're assuming that for *every* case of 100 randomly selected voters
> it is *impossible* for more than 45 of them to be underdog supporters.
> It is possible, albeit the probability is low, that 100% of them are
> underdog supporters.
>
>> The probability of a win for underdog can never exceed 45%. When the
>> exercise asks "how often will the underdog win" I interpret that as
>> meaning what are his chances, i.e., the probability that he will win.
>> But if you run a simulation, you can get anything, including results
>> above 45%. I don't think simulating has any validity here, at least
>> the procedure suggested in the answer key. That is a lot of
>> simulating to do by hand,
>
> By hand???? This is trivial using a spreadsheet.
>
>> 100 per trial, but it is nowhere close to
>> even starting to answer the actual question. You would first of all
>> have to know the population of the school and then do some very
>> demanding simulations that would only be practical on a computer.
>>
>> Practical considerations aside, the question is
>> meaningless unless know something about the magnitude of the
>> school population.
>> Consider: if the total population is 108, the underdog cannot win,
>> because he only has 49 (48.6 rounded up) supporters total. Chance of
>> winning 0%. Period. "Underdog" has NO CHANCE of winning the
>> election. But if you run a simulation the way the book suggests, he's
>> going to win some. In fact he wins about half.
>
> My simulations show the underdog wins 44.96% of the time over 10,000
> runs. The max votes he got on any one run was 66.
> Art
>
How many kids were in the school that you ran the simulation for?
Underdog's maximum theoretical chances of winning (as the school population
increases without bound) is about 13.5%. And it's less than that for any
real school. You made a mistake somewhere.


From: Bill Sloman on 16 Jul 2010 23:22
On Jul 17, 9:39 am, "Michael Robinson" <kellrobin...(a)yahoo.com> wrote:
> "Bill Sloman" <bill.slo...(a)ieee.org> wrote in message
>
> news:1d191484-6c12-4546-a609-fe32f7aadb54(a)n8g2000prh.googlegroups.com...
> On Jul 17, 8:12 am, "amdx" <a...(a)knology.net> wrote:
>
> > > 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.
>
> > Oh, so Obama's election was just a statistical anomaly.
> > I feel so much better now.
>
> Actually, the US electors who got out to vote for Obama represent a
> very large "school", and the likelysampling error on the result was
> about 0.12% of his winning margin - 9,522,083 - out of 131,257,328
> votes cast. The square root of 131,257,328 is about 11,457.
>
> http://en.wikipedia.org/wiki/United_States_presidential_election,_2008
>
> He won quite decisively - the biggest margin of any non-incumbent
> candidate so far.
>
> --
> Bill Sloman, Nijmegen
>
> Oh boy, you're asking for it Bill.  Jim's going to come out with his gun.

Not really a worry. I'm in Sydney at the moment, but since Jim has
kill-filed my posts, he won't know that, and would be waddling around
the Netherlands (where carrying a gun is illegal if you aren't a cop
or en route to your shooting club) posing no great threeat to me, if
something of a menace to all the other residents of the country.

--
Bill Sloman, Nijmegen
From: Robert Baer on 17 Jul 2010 04:46
Michael Robinson wrote:
> More options Jul 16, 1:24 pm
> Newsgroups: sci.math
> From: gearhead <nos...(a)billburg.com>
> Date: Fri, 16 Jul 2010 10:24:41 -0700 (PDT)
> Local: Fri, Jul 16 2010 1:24 pm
> Subject: stats/probability question
> Reply | Reply to author | Forward | Print | Individual message | Show
> original | Remove | Report this message | Find messages by this author
>
> I'm an engineering undergrad in an intro stats course. We had a
> question in the book that's really dumb.
>
> problem as stated:
>
> Your candidate has 55% of the votes in the entire school. But
> only
> 100 students will show up to vote. What is the probability that the
> underdog (the one with 45% support) will win? To find out, set up a
> simulation.
> a) Describe how you will simulate a component and its outcomes.
> b) Describe how you will simulate a trial.
> c) Describe the response variable.
>
> The answer in the back of the book says using a two digit random
> number to determine each vote (00-54 for your candidate, 55-99 for the
> underdog) you would run a string of trials with 100 votes to each
> trial.
>
> Now, this is one misconceived exercise. Let me explain why.
>
> Say the school has 1000 students. If all of them show up, the
> underdog has 0% chance of winning. If exactly one voter shows up,
> underdog has 45% chance of winning. In an election where 100 voters
> show up, underdog's chance of winning the election HAS to lie
> somewhere between 0% and 45%. No ifs, ands or buts.
> The probability of a win for underdog can never exceed 45%. When the
> exercise asks "how often will the underdog win" I interpret that as
> meaning what are his chances, i.e., the probability that he will win.
> But if you run a simulation, you can get anything, including results
> above 45%. I don't think simulating has any validity here, at least
> the procedure suggested in the answer key. That is a lot of
> simulating to do by hand, 100 per trial, but it is nowhere close to
> even starting to answer the actual question. You would first of all
> have to know the population of the school and then do some very
> demanding simulations that would only be practical on a computer.
>
> Practical considerations aside, the question is
> meaningless unless know something about the magnitude of the
> school population.
> Consider: if the total population is 108, the underdog cannot win,
> because he only has 49 (48.6 rounded up) supporters total. Chance of
> winning 0%. Period. "Underdog" has NO CHANCE of winning the
> election. But if you run a simulation the way the book suggests, he's
> going to win some. In fact he wins about half.
> I'm saying the book is wrong.
> Back to our school of 1000 students, out of whom 450 would vote for
> "underdog." If only 100 students vote, what are his chances of
> winning? Simulation will send you on the wrong track here unless
> you're ready for some head scratching and a big grind on the computer. I'm
> sure this problem has a neat theoretical solution.
>
> In class today I saw this problem and just was mystified until I worked out
> the implications, and now it's clear that it's just incredibly stupid. How
> would you convince the teacher of that? If I point out that it's
> impossible to get any answer above 45%, she might say, well this isn't
> theoretical, we're just running simulations, which is the whole point of
> the game. To convince her I might have to work out the actual correct
> simulation methodology, which is likely a very big headache and something I
> don't have time for. So I may just let it slide and not even bring it up.
> But I'm still interested in the theoretical solution, if anybody can cough
> it up. It's a probability problem now, not empirical statistics.
>
> ---------------------------------------
> Posted through http://www.Electronics-Related.com
The unacceptable answer is the fact that the "sample size" is
insufficient for any MEANINGFUL results and thus ANY "calculations" are
moot.
But...these are idiots that lie with numbers and actually get away
with it.
The TRUE technical answer is "insufficient sample size for any
meaningful answer. Case closed, period.".
From: ehsjr on 17 Jul 2010 13:09
Robert Baer wrote:
> Michael Robinson wrote:
>
>> More options Jul 16, 1:24 pm
>> Newsgroups: sci.math
>> From: gearhead <nos...(a)billburg.com>
>> Date: Fri, 16 Jul 2010 10:24:41 -0700 (PDT)
>> Local: Fri, Jul 16 2010 1:24 pm
>> Subject: stats/probability question
>> Reply | Reply to author | Forward | Print | Individual message | Show
>> original | Remove | Report this message | Find messages by this author
>>
>> I'm an engineering undergrad in an intro stats course. We had a
>> question in the book that's really dumb.
>>
>> problem as stated:
>>
>> Your candidate has 55% of the votes in the entire school. But
>> only
>> 100 students will show up to vote. What is the probability that the
>> underdog (the one with 45% support) will win? To find out, set up a
>> simulation.
>> a) Describe how you will simulate a component and its outcomes.
>> b) Describe how you will simulate a trial.
>> c) Describe the response variable.
>>
>> The answer in the back of the book says using a two digit random
>> number to determine each vote (00-54 for your candidate, 55-99 for the
>> underdog) you would run a string of trials with 100 votes to each
>> trial.
>>
>> Now, this is one misconceived exercise. Let me explain why.
>>
>> Say the school has 1000 students. If all of them show up, the
>> underdog has 0% chance of winning. If exactly one voter shows up,
>> underdog has 45% chance of winning. In an election where 100 voters
>> show up, underdog's chance of winning the election HAS to lie
>> somewhere between 0% and 45%. No ifs, ands or buts.
>> The probability of a win for underdog can never exceed 45%. When the
>> exercise asks "how often will the underdog win" I interpret that as
>> meaning what are his chances, i.e., the probability that he will win.
>> But if you run a simulation, you can get anything, including results
>> above 45%. I don't think simulating has any validity here, at least
>> the procedure suggested in the answer key. That is a lot of
>> simulating to do by hand, 100 per trial, but it is nowhere close to
>> even starting to answer the actual question. You would first of all
>> have to know the population of the school and then do some very
>> demanding simulations that would only be practical on a computer.
>>
>> Practical considerations aside, the question is
>> meaningless unless know something about the magnitude of the
>> school population.
>> Consider: if the total population is 108, the underdog cannot win,
>> because he only has 49 (48.6 rounded up) supporters total. Chance of
>> winning 0%. Period. "Underdog" has NO CHANCE of winning the
>> election. But if you run a simulation the way the book suggests, he's
>> going to win some. In fact he wins about half.
>> I'm saying the book is wrong.
>> Back to our school of 1000 students, out of whom 450 would vote for
>> "underdog." If only 100 students vote, what are his chances of
>> winning? Simulation will send you on the wrong track here unless
>> you're ready for some head scratching and a big grind on the
>> computer. I'm
>> sure this problem has a neat theoretical solution.
>>
>> In class today I saw this problem and just was mystified until I
>> worked out
>> the implications, and now it's clear that it's just incredibly
>> stupid. How
>> would you convince the teacher of that? If I point out that it's
>> impossible to get any answer above 45%, she might say, well this isn't
>> theoretical, we're just running simulations, which is the whole point of
>> the game. To convince her I might have to work out the actual correct
>> simulation methodology, which is likely a very big headache and
>> something I
>> don't have time for. So I may just let it slide and not even bring it
>> up. But I'm still interested in the theoretical solution, if anybody
>> can cough
>> it up. It's a probability problem now, not empirical
>> statistics.
>> ---------------------------------------
>> Posted through http://www.Electronics-Related.com
>
> The unacceptable answer is the fact that the "sample size" is
> insufficient for any MEANINGFUL results and thus ANY "calculations" are
> moot.
> But...these are idiots that lie with numbers and actually get away
> with it.
> The TRUE technical answer is "insufficient sample size for any
> meaningful answer. Case closed, period.".

About your answer above - how did you arrive at the conclusion that the
sample size is insufficient? I'm missing something.

Ed
From: Robert Baer on 18 Jul 2010 00:49
ehsjr wrote:
> Robert Baer wrote:
>> Michael Robinson wrote:
>>
>>> More options Jul 16, 1:24 pm
>>> Newsgroups: sci.math
>>> From: gearhead <nos...(a)billburg.com>
>>> Date: Fri, 16 Jul 2010 10:24:41 -0700 (PDT)
>>> Local: Fri, Jul 16 2010 1:24 pm
>>> Subject: stats/probability question
>>> Reply | Reply to author | Forward | Print | Individual message | Show
>>> original | Remove | Report this message | Find messages by this author
>>>
>>> I'm an engineering undergrad in an intro stats course. We had a
>>> question in the book that's really dumb.
>>>
>>> problem as stated:
>>>
>>> Your candidate has 55% of the votes in the entire school. But
>>> only
>>> 100 students will show up to vote. What is the probability that the
>>> underdog (the one with 45% support) will win? To find out, set up a
>>> simulation.
>>> a) Describe how you will simulate a component and its outcomes.
>>> b) Describe how you will simulate a trial.
>>> c) Describe the response variable.
>>>
>>> The answer in the back of the book says using a two digit random
>>> number to determine each vote (00-54 for your candidate, 55-99 for the
>>> underdog) you would run a string of trials with 100 votes to each
>>> trial.
>>>
>>> Now, this is one misconceived exercise. Let me explain why.
>>>
>>> Say the school has 1000 students. If all of them show up, the
>>> underdog has 0% chance of winning. If exactly one voter shows up,
>>> underdog has 45% chance of winning. In an election where 100 voters
>>> show up, underdog's chance of winning the election HAS to lie
>>> somewhere between 0% and 45%. No ifs, ands or buts.
>>> The probability of a win for underdog can never exceed 45%. When the
>>> exercise asks "how often will the underdog win" I interpret that as
>>> meaning what are his chances, i.e., the probability that he will win.
>>> But if you run a simulation, you can get anything, including results
>>> above 45%. I don't think simulating has any validity here, at least
>>> the procedure suggested in the answer key. That is a lot of
>>> simulating to do by hand, 100 per trial, but it is nowhere close to
>>> even starting to answer the actual question. You would first of all
>>> have to know the population of the school and then do some very
>>> demanding simulations that would only be practical on a computer.
>>>
>>> Practical considerations aside, the question is
>>> meaningless unless know something about the magnitude of the
>>> school population.
>>> Consider: if the total population is 108, the underdog cannot win,
>>> because he only has 49 (48.6 rounded up) supporters total. Chance of
>>> winning 0%. Period. "Underdog" has NO CHANCE of winning the
>>> election. But if you run a simulation the way the book suggests, he's
>>> going to win some. In fact he wins about half.
>>> I'm saying the book is wrong.
>>> Back to our school of 1000 students, out of whom 450 would vote for
>>> "underdog." If only 100 students vote, what are his chances of
>>> winning? Simulation will send you on the wrong track here unless
>>> you're ready for some head scratching and a big grind on the
>>> computer. I'm
>>> sure this problem has a neat theoretical solution.
>>>
>>> In class today I saw this problem and just was mystified until I
>>> worked out
>>> the implications, and now it's clear that it's just incredibly
>>> stupid. How
>>> would you convince the teacher of that? If I point out that it's
>>> impossible to get any answer above 45%, she might say, well this isn't
>>> theoretical, we're just running simulations, which is the whole point of
>>> the game. To convince her I might have to work out the actual correct
>>> simulation methodology, which is likely a very big headache and
>>> something I
>>> don't have time for. So I may just let it slide and not even bring
>>> it up. But I'm still interested in the theoretical solution, if
>>> anybody can cough
>>> it up. It's a probability problem now, not empirical
>>> statistics.
>>> --------------------------------------- Posted through
>>> http://www.Electronics-Related.com
>>
>> The unacceptable answer is the fact that the "sample size" is
>> insufficient for any MEANINGFUL results and thus ANY "calculations"
>> are moot.
>> But...these are idiots that lie with numbers and actually get away
>> with it.
>> The TRUE technical answer is "insufficient sample size for any
>> meaningful answer. Case closed, period.".
>
> About your answer above - how did you arrive at the conclusion that the
> sample size is insufficient? I'm missing something.
>
> Ed
The whole population is too small (a thousand if i remember
correctly), so any sample size is too small - even if ALL were sampled,
which is absurd.
Also, the sample must be "chosen" in a totally random manner, which
is next to impossible for a population of a mere 1000; the smaller the
total population, the worse it gets.
There was one idiot that lied using "statistics", sampling, etc with
a total population of TEN - and using a lot of bs blather with the
numbers in a long report, got away with the lies.

Oh, BTW, if, in a LARGE population the probability of such-and such
is X, that means that any ONE randomly chosen sample fits that sec, and
the next sample fits, etc.
Meaning if the probability of a coin toss landing on edge is 0.0001
DOES NOT mean that the coin will not land on edge 2 times (or 2,000
times) in a row; each try is independent of all others (in a fair game).
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