JJ Vs. jfern: Poll on their statistical knowledge

[ATFFL]

Here is the situation:  You have just started a polling company and are going to hire a statistician.  The only two people to apply are JJ and jfern.   The only basis you have to make your decision is this thread.

Based on this, who do you hire?

A few rules:

JJ and jfern, please do not carry your debate into here.  If you would like to link to specific posts you want voters to pay attention to, feel free to link to them.  Otherwise, I would appreciate it if you did not post in here.

No personal insults, please.  This includes calling either one of the applicants jfraud.

Please do not vote based on political philosophy.  If all the math talk is going over your head, please, do not vote.

I have decided to link to the few significant comments from people other than JJ or jfern to help you decide.

muon2's comments.  muon2's follow-up.

Tredrick's comments.

James42's comments.

The poll will close in 24 hours.  The results will be hidden until then.

[Jake]

J.J. , I want someone who can actually think rationally.

[Alcon]

The results don't seem to be hidden.

[ATFFL]

The results don't seem to be hidden.

Comments are welcome and allowed.  We are up to 10 views and an unknown number of votes.  Could be 1, 2, 5 or 10. 

Perhaps we can get the applicants to treat the comments as an exit poll and see what they predict the final results will be.

[Jake]

The results don't seem to be hidden.

Comments are welcome and allowed.  We are up to 10 views and an unknown number of votes.  Could be 1, 2, 5 or 10. 

Perhaps we can get the applicants to treat the comments as an exit poll and see what they predict the final results will be.

Don't say exit polls, jfraud will accuse you of stealing Ohio for J.J.

[○∙◄☻¥tπ[╪AV┼cVê└]

The question is who is right here?

1. I  say that a sample of 940 heads and 60 tails is statistically significantly different from that of a fair coin at the 95% confidence level, that's p=5% of falsely rejecting the null hypothesis. Actually you can make p be much smaller. J.J. claims that a sample  940 heads and 60 tails is not statistically different from that of a fair coin

2. I say that for large random samples, or for the normal distribution, the 95% confidence interval has a MOE of approxixmately +- 1.96 standard deviations. J.J. says I'm wrong, and it's exactly 2.

You decide who's right.

[J. J.]

This is a polling question, as stated

The question is who is right here?

1. I  say that a sample of 940 heads and 60 tails is statistically significantly different from that of a fair coin at the 95% confidence level, that's p=5% of falsely rejecting the null hypothesis. Actually you can make p be much smaller. J.J. claims that a sample  940 heads and 60 tails is not statistically different from that of a fair coin

A mistatement of the question at hand, but one that illustrates the statistical problem.  We are looking at a poll, which is a subset of a population, a sample drawn from that population.

The first problem is:  The coin toss does represents the population as a whole, not a sample.   A poll, unless it includes the entire population, will be a sample the population as a whole.   The basic analogy fails.  A sample, which will likely not be perfectly accurate, and only a small part of the population, is what is needed.  Any poll construction must take that into account.

The second problem is the assumption that the poll makes an asumption that the result should be 50% for each candidate, like a coin toss.  The poll, to yield accurate results, must assume to be a representation of the population as a whole.  While that might be a 50/50 split, assuming only two candidates, it might not.  The key to determining if the poll is accurate is how well it represents that whole population.  This will work the same if there are more than two candidates.

Now, I'll tell you, flat out that there is a problem with polling.  There is a likelihood that and poll will not accurately represent the population.  It will make no difference what the results say, as there will always be the same likelihood that the result will not be accurate.  At the [confidence level I will suggest (95%), there will always be a 5% chance that the poll is wrong; this will be called an "outrider poll."  If the result after sampling 1000 people is 940 to 60, or 600 to 400, or 500 to 500, there is still a 5% likelihood that the poll is wrong, i.e. the poll will does not represent the population accurately.


Assuming that the poll really does use accurately represent the population as a whole (it isn't an "outrider") we will be able to calculate a range where the the "score" or the precentage that the candidate gets, will really lie.  This is called the "confidence interval" or "margin of error (MOE)."  The MOE will depend on what the candidate scores, the sample size, and the confidence level we use (planned at 95%).   It cannot be calculated until we get the results.

This is exceptionally important.  The MOE has no effect on if this poll is one of those of 5% that is completely wrong.  It assumes that it is, but it might not be the case.

[○∙◄☻¥tπ[╪AV┼cVê└]

There you have it.

1. J.J denies that a sample of 1000 coin tosses that has 940 heads and 60 tails is statistically significantly different from that of a fair coin with 95% confidence (that's  a p=5% change that you falsely reject the null hypothesis, not that the poll is "wrong")

2. J.J denies that the normal distribution has a MOE of approximately 1.96 standard deviations for the 95% confidence interval.

[ATFFL]

JJ and jfern, please do not carry your debate into here.  If you would like to link to specific posts you want voters to pay attention to, feel free to link to them.  Otherwise, I would appreciate it if you did not post in here.

You guys miss this part?


And, since others are not forbidden from commenting here:

You must be logged in to read this quote.

2. I say that for large random samples, or for the normal distribution, the 95% confidence interval has a MOE of approxixmately +- 1.96 standard deviations. J.J. says I'm wrong, and it's exactly 2.

This claim is demonstrably false.

If the sample is large, and the level of statistical signifiance we are using is 95%, then it's about 1.96 standard deviations. When we are outside of that range, we conclude that there's a statistically significant difference. You can choose 3 standard deviations or 99.7%, and so on.

Actually it exceptionally close to two standard deviations; a full description can be seen here:

http://www.robertniles.com/stats/stdev.shtml

[Nation]

Read through the entire thread yesterday -- made my decision.

[○∙◄☻¥tπ[╪AV┼cVê└]

JJ and jfern, please do not carry your debate into here.  If you would like to link to specific posts you want voters to pay attention to, feel free to link to them.  Otherwise, I would appreciate it if you did not post in here.

You guys miss this part?


And, since others are not forbidden from commenting here:

You must be logged in to read this quote.

2. I say that for large random samples, or for the normal distribution, the 95% confidence interval has a MOE of approxixmately +- 1.96 standard deviations. J.J. says I'm wrong, and it's exactly 2.

This claim is demonstrably false.

If the sample is large, and the level of statistical signifiance we are using is 95%, then it's about 1.96 standard deviations. When we are outside of that range, we conclude that there's a statistically significant difference. You can choose 3 standard deviations or 99.7%, and so on.

Actually it exceptionally close to two standard deviations; a full description can be seen here:

http://www.robertniles.com/stats/stdev.shtml

J.J's link doesn't prove anything. If you understand the normal distribution, you could find the values for yourself using integrals of the normal density function 1/sqrt(2*Pi) * e^(-x^2/2).  By integrating this, we find that 2 standard deviations includes 95.4499736%.

Here's a chart that clearly shows that it's not exactly 2 standard deviations. Find x such that the area from 0 to x standard deviations is approximately 95%/2=47.5%. You should get around 1.96.
http://www.statsoft.com/textbook/sttable.html

I'd like people to not vote for J.J just because they don't like me, and haven't carefully examined the facts. If you can't check for yourself whether the MOE for the 95% confidence interval of the normal distribution is closer to 1.96 standard deviations than 2, don't vote. 

Get your facts straight before you claim that I'm wrong. J.J says it's exactly 2 standard deviations. Some webpage that doesn't make it clear that they're saying that it's approximately 2 standard deviations doesn't prove sh**t. J.J. said I was wrong for saying it was 1.96 deviations.

[ATFFL]

JJ and jfern, please do not carry your debate into here.  If you would like to link to specific posts you want voters to pay attention to, feel free to link to them.  Otherwise, I would appreciate it if you did not post in here.

You guys miss this part?


And, since others are not forbidden from commenting here:

You must be logged in to read this quote.

2. I say that for large random samples, or for the normal distribution, the 95% confidence interval has a MOE of approxixmately +- 1.96 standard deviations. J.J. says I'm wrong, and it's exactly 2.

This claim is demonstrably false.

If the sample is large, and the level of statistical signifiance we are using is 95%, then it's about 1.96 standard deviations. When we are outside of that range, we conclude that there's a statistically significant difference. You can choose 3 standard deviations or 99.7%, and so on.

Actually it exceptionally close to two standard deviations; a full description can be seen here:

http://www.robertniles.com/stats/stdev.shtml

J.J's link doesn't prove anything. If you understand the normal distribution, you could find the values for yourself using integrals of the normal density function 1/sqrt(2*Pi) * e^(-x^2/2).  By integrating this, we find that 2 standard deviations includes 95.4499736%.

Here's a chart that clearly shows that it's not exactly 2 standard deviations. Find x such that the area from 0 to x standard deviations is approximately 95%/2=47.5%. You should get around 1.96.
http://www.statsoft.com/textbook/sttable.html

I'd like people to not vote for J.J just because they don't like me, and haven't carefully examined the facts. If you can't check for yourself whether the MOE for the 95% confidence interval of the normal distribution is closer to 1.96 standard deviations than 2, don't vote. 

Get your facts straight before you claim that I'm wrong. J.J says it's exactly 2 standard deviations. Some webpage that doesn't make it clear that they're saying that it's approximately 2 standard deviations doesn't prove sh**t. J.J. said I was wrong for saying it was 1.96 deviations.

You said he said it was exactly 2, he actually said it was exceedingly close to 2.  See the difference?

[○∙◄☻¥tπ[╪AV┼cVê└]

You said he said it was exactly 2, he actually said it was exceedingly close to 2.  See the difference?

He clearly worded it as if I was wrong to say that the 95% confidence interval has a MOE about 1.96 standard deviations. Seeing as I was right, and it's actually slightly under 1.96, I didn't look so carefully at exactly what he said. You are right that he didn't say exactly there.

I don't consider 1.96 to be exceedingly close to 2. If you calculate directly from the normal density function, 2 stanrdard deviations includes  95.4499736%.

Here's where he tells me I'm wrong to say that MOE is 1.96 standard deviations. We were talking about 95% confidence, so that part is irrelevant.

So I meant standard deviation. It would have been the MOE for a 68.27% confidence interval. I didn't say anything about the level of confidence there. You have yet to respond to the following:
I pointed out you were wrong about saying I was wrong about MOE=1.96 standard deviations - no reply
I asked you why they say that a poll of 1000 says

You must be logged in to read this quote.

- no reply

Are you ever going to admit you're wrong?

MOE does not = 1.96 SD.  MOE, also known as confidence interval, is function of sample size confidence Level (which is standard deviation), sample size, and poll results.  Here is the description, again, not you have the mentality to comprehend it:

To be honest, I'm not sure exactly what J.J. is trying to claim about MOE, since he's made contradictory statements (like MOE is very close to 2 standard deviations, MOE depends a lot things other than standard deviation). Perhaps if he had answered my comments here more clearly, I'd know what his position was.

J.J, I win.

Anyone who understands statistics will agree with the following 2 statements.

1. The radius of the 95% confidence interval (the MOE) for a sample of 1000 or the normal distribution is approximately 1.96 standard deviations

2. Assuming any reasonble probability p for falsely rejecting the null hypothesis, if we get 940 heads and 60 tails in a sample 1000, we must reject the null hypothesis of a fair coin, and conclude we are have statistically significantly difference from a fair coin.

In order to be consistant, you have to disagree with those statements.

[Citizen James]

I suppose I can't write in some random individual from off the street, can I?

Judging soley from apparent understanding of statistical polling processes, and leaving out things like emotional maturity (which seems somewhat lacking in both candidates), I'd have to admit JJ seems to have a clearer understanding of statistical theory.

[○∙◄☻¥tπ[╪AV┼cVê└]

I suppose I can't write in some random individual from off the street, can I?

Judging soley from apparent understanding of statistical polling processes, and leaving out things like emotional maturity (which seems somewhat lacking in both candidates), I'd have to admit JJ seems to have a clearer understanding of statistical theory.

So you'd like someone who takes a sample of 1000 coin tosses, with 940 heads and 60 tails, and doesn't conclude that the coin is statstically significantly different from that of a fair coin? He doesn't understand statistical significance or hypothesis testing. He's had months to figure out the correct answer, and he hasn't. The probability being at least that far from a fair coin is 3.935682768*10^-204.

Also, he's stated that the MOE for the 95% confidence interval is not about 1.96 standard deviations for the normal function.

How would he be more qualified than me? Does no one on this board understand the term statistically significant?

[○∙◄☻¥tπ[╪AV┼cVê└]

To the people choosing J.J. How do you deal with the fact that J.J. doesn't understand statistical significance, and seems not understand how MOE is related to standard deviation? Why would he make a better candidate than me? Do you have real reasons for thinking he's better at statistics, or is this just a popularity contest, and you hate me

A vote for J.J. is a vote for that a sample of 940 heads and 60 tails is not statistically significantly different that of a fair coin.

[○∙◄☻¥tπ[╪AV┼cVê└]

Do you have real reasons for thinking he's better at statistics, or is this just a popularity contest, and you hate me?

I could not tell the two of you apart based on the statistical arguments since I have not taken a Statistics & Probability class in over 30 years. I did not vote. But as far as the glib and nasty attacks and counter-attacks... who knows? I would guess for most people at the forum it really is NOT based on facts but on who has been more creative in their attacks. I doubt if it even breaks down along party lines. Where is The Vorlon when you need him?!?

He's probably staying away from this mess on purpose, LOL.

[J. J.]

Nobody on this thread have said that they "hate" you.  I have never said that I "hate" you on any thread.

Here is something, which I wouldn't refer to as negative, that I said on the subject:

Go read a statistics book, or talk to a statistics professor, whatever, since you obviously can't accept the simple logic I put out because you hate me or something.  I'm sure I have more experience with statistics than you.

I do not hate you, but I also don't like people being attacked unfairly.  That is one of the reasons you never saw the "John Kerry: A War Criminal from a Family of Drug Dealers" thread.  

As far as I know, no poster on this thread "hates" you.

[○∙◄☻¥tπ[╪AV┼cVê└]

Nobody on this thread have said that they "hate" you.  I have never said that I "hate" you on any thread.

Here is something, which I wouldn't refer to as negative, that I said on the subject:

Go read a statistics book, or talk to a statistics professor, whatever, since you obviously can't accept the simple logic I put out because you hate me or something.  I'm sure I have more experience with statistics than you.

I do not hate you, but I also don't like people being attacked unfairly.  That is one of the reasons you never saw the "John Kerry: A War Criminal from a Family of Drug Dealers" thread. 

As far as I know, no poster on this thread "hates" you.

That's good to know. I suppose hate was too strong of a word.

[ATFFL]

The community has spoken.  JJ lays claim to the title of Master Stastician of Atlasia.

Now, for the love of God, will the two of you stop discussing this stuff.

[J. J.]

The community has spoken.  JJ lays claim to the title of Master Stastician of Atlasia.

Now, for the love of God, will the two of you stop discussing this stuff.

I'm not the one that wanted it discussed, which is perhaps ironic.

[○∙◄☻¥tπ[╪AV┼cVê└]

Facts don't follow the will of the majority.
I can't beleive that all 32 people were qualified to vote on this.
The results look similar to the who would you vote for poll with me and J.J.

I am disappointed in the 24 people who did not carefully consider, is 940 heads and 60 tails significantly different from that of a fair coin? You were not qualified to vote.

[ATFFL]

Facts don't follow the will of the majority.
I can't beleive that all 32 people were qualified to vote on this.
The results look similar to the who would you vote for poll with me and J.J.

I am disappointed in the 24 people who did not carefully consider, is 940 heads and 60 tails significantly different from that of a fair coin? You were not qualified to vote.

I phrased the question so people would be by default qualified.  People decided they woudl rather hire JJ. 

Until you realize there is a difference between the theory of flipping a coin 1000 times and interviewing a thousand people you will never understand why JJ won.

[J. J.]

The community has spoken.  JJ lays claim to the title of Master Stastician of Atlasia.

Now, for the love of God, will the two of you stop discussing this stuff.

First, the Vorlon's title is quite secure.  :-)  What is described here is a very simplified version of how a poll works.  There is a lot more to it than the simplified description I've presented, and the math needed for those is beyond me.

As a simplified description, this is probably a good description.

Facts don't follow the will of the majority.
I can't beleive that all 32 people were qualified to vote on this.
The results look similar to the who would you vote for poll with me and J.J.

I am disappointed in the 24 people who did not carefully consider, is 940 heads and 60 tails significantly different from that of a fair coin? You were not qualified to vote.

I phrased the question so people would be by default qualified.  People decided they woudl rather hire JJ. 

Until you realize there is a difference between the theory of flipping a coin 1000 times and interviewing a thousand people you will never understand why JJ won.

I can only suggest that if Jfern is really a grad student at a major university, that he take a printout of my description and ask someone in the statistics department to explain it to him.  Maybe he'll understand a face to face explanation better than a printout.

I have to admit, I have a very hard time believing that anyone that passed even an elementary statistics course could not see the difference between a coin toss of 1000 and a sample of 1000 voters from a population of approximately 120,000,000.

It should also be noted that in the "election" my numbers were substantially lower than they were in this poll.  That is probably an indication that while people may thing I have a better grasp of statistical analysis, they don't like my politics.  That's fine, BTW.  I seriously doubt that grasping how a poll is conducted is required for the presidency.

[○∙◄☻¥tπ[╪AV┼cVê└]

Facts don't follow the will of the majority.
I can't beleive that all 32 people were qualified to vote on this.
The results look similar to the who would you vote for poll with me and J.J.

I am disappointed in the 24 people who did not carefully consider, is 940 heads and 60 tails significantly different from that of a fair coin? You were not qualified to vote.

I phrased the question so people would be by default qualified.  People decided they woudl rather hire JJ. 

Until you realize there is a difference between the theory of flipping a coin 1000 times and interviewing a thousand people you will never understand why JJ won.

WTF? I never said there wasn't a difference. I said that if everyone supported Bush or Kerry (no I don't knows, or third parties) and you had a completely random sample, then seeing if one of them had a lead was essentially (not exactly) the same problem as seeing if a coin was different from that of a fair coin.

The origional argument was actually about the coin tossing, J.J. said that 940 heads and 60 tails wasn't statistically significant. I decided to argue with opinion polls, since it's more common to talk about statistically significant leads. In retrospect, that was a mistake, it allowed people to be needlessly distracted by by that the sample wouldn't be random, some people would be uncided, support third parties, systematic errors in polling. They tended to ignore the way I worded the problem, and thought I was talking about reality.

I really don't appreaite it when people can't read what I said and then think that means I don't understand that a Gallup poll is different from tossing a coin 1000 times. That's pathetic.