Sample of 1000 coin tosses

[○∙◄☻¥tπ[╪AV┼cVê└]

1. Suppose our null hypothesis is that we have a fair coin (50% heads, 50% tails

2. Suppose that our level of statistical signifiance is 95%, so that we have a p=5% value of falsely rejecting the null hypothesis

3. Suppose we flip a coin 1000 times, and get 940 heads, and 60 tails.

Do we reject the null hypothesis and conclude that our coin is statistically significantly different from that of a fair coin?














Note: This was the central argument that I had with J.J. Later I decided to talk about it in terms of an unrealistic opinion poll of of 1000 random people, with replacement of Kerry 94%, Bush 6%.  People took that to mean I didn't understand how opinion polls have undecded voters, voters who refuse to answer, third party supporters, various systematic errors where some types of people are more likely to answer, and these are samples of a finite population (they missed the with replacement part) that affects the statistics. Origiinally J.J. had argued that since the 94% heads is less than the  95% confidence, it's not statistically signifiant. Amazingly people decided he's better at statistics than me.

[Erc]

Using your usual proportion test, the alpha's somewhere on the order of 9.93x10^-171.

Using a more accurate binomial method, the alpha's actually somewhere on the order of 1.96x10^-204.

So yeah, I think we can reject the hypothesis that this is a fair coin, and can conclude with 95% confidence that, for an infinite number of trials, it would up up heads somewhere between 90.9 and 97.1% of the time.

[Jake]

No one really cares. Something I don't think you or J. J. have caught onto.

[J. J.]

Basically, the question is invalid because of your implications in the note;  nobody on the other thread asked about a statistically situation similar to a coin toss.

You've basically commited the fallacy of false analogy.  James 42, and Tedrick, have pointed the problem out in their comments.

A poll does not assume that the candidates have a 50/50 split.  A poll assumes that the sample is representative of the population as a whole. 

What the result is, statistically, is not important for this test.  A result of 94%, 80%, 51%, 45%, or 12% will still have the chance of being incorrect, e.g. at the 95% confidence level, any of these results has a 5% chance of being much more incorrect than expected.

The second proble, which is related, is that a coin toss is not a sample, but a total population.

It's these things that you don't seem able to comprehend

[○∙◄☻¥tπ[╪AV┼cVê└]

Basically, the question is invalid because of your implications in the note;  nobody on the other thread asked about a statistically situation similar to a coin toss.

You've basically commited the fallacy of false analogy.  James 42, and Tedrick, have pointed the problem out in their comments.

A poll does not assume that the candidates have a 50/50 split.  A poll assumes that the sample is representative of the population as a whole. 

What the result is, statistically, is not important for this test.  A result of 94%, 80%, 51%, 45%, or 12% will still have the chance of being incorrect, e.g. at the 95% confidence level, any of these results has a 5% chance of being much more incorrect than expected.

The second proble, which is related, is that a coin toss is not a sample, but a total population.

It's these things that you don't seem able to comprehend

I never said that the Kerry/Bush poll was realistic. If you have only Bush and Kerry responses, and you want to see if there's a lead, you compare it to a 50%-50% tie. I think everyone but Erc missed the point.

[J. J.]

I never said that the Kerry/Bush poll was realistic. If you have only Bush and Kerry responses, and you want to see if there's a lead, you compare it to a 50%-50% tie. I think everyone but Erc missed the point.

I'll let Etc speak for himself.

You've missed the point again.  The poll itself is not constructed on the premise that the candidates have a 50%-50% tie.  It's constructed on the premise that the sample is representative of the whole population.

Now here is a question.  For these results, at a 95% confidence level, and a sample size of 1000, what is the likelihood that the leading candidate's result is outside the MOE?

A.  Kerry 94, Bush 6

B.  Kerry 51, Bush 49

C.  Bush 60, Kerry 40

D.  Bush 80, Kerry 20

Assume that undecided/third party voters answers will not be counted in the sample.  This is a poll of people who have made up their minds.

[ATFFL]

I'll let Etc speak for himself.

Is this one of your cute nicknames or a genuine typo?  Either way, I laughed my tuckus off.

And this was NOT the premise of the original debate.  It is what jfern tried to change the subject to after it became clear he knew little to nothing about the real world application of stastics in polling.

[J. J.]

I'll let Etc speak for himself.

Is this one of your cute nicknames or a genuine typo?  Either way, I laughed my tuckus off.

And this was NOT the premise of the original debate.  It is what jfern tried to change the subject to after it became clear he knew little to nothing about the real world application of stastics in polling.

Typo, sorry Erc.

[○∙◄☻¥tπ[╪AV┼cVê└]

I never said that the Kerry/Bush poll was realistic. If you have only Bush and Kerry responses, and you want to see if there's a lead, you compare it to a 50%-50% tie. I think everyone but Erc missed the point.

I'll let Etc speak for himself.

You've missed the point again.  The poll itself is not constructed on the premise that the candidates have a 50%-50% tie.  It's constructed on the premise that the sample is representative of the whole population.

Now here is a question.  For these results, at a 95% confidence level, and a sample size of 1000, what is the likelihood that the leading candidate's result is outside the MOE?

A.  Kerry 94, Bush 6

B.  Kerry 51, Bush 49

C.  Bush 60, Kerry 40

D.  Bush 80, Kerry 20

Assume that undecided/third party voters answers will not be counted in the sample.  This is a poll of people who have made up their minds.

5% by definition if you're asking what I think you're asking, which is for each sample, find the odds that ti's not in the the 95% confidence interval.

[○∙◄☻¥tπ[╪AV┼cVê└]

And this was NOT the premise of the original debate.  It is what jfern tried to change the subject to after it became clear he knew little to nothing about the real world application of stastics in polling.

Completely wrong, we had been arguing about this for a while. It was only later that I started talking about unrealistic opinion polls, which was a bad idea, because everyone thought that meant I knew nothing about opinion polls.

We have 1000 coin tosses (similiar to a public opinion poll). Let's suppose we have 94% heads, 6% tails, which you say isn't significant. That's 940 heads, 60 tails.

We want to test to see whether the coin is fair, so we have as the null hypothesis that half of the coin tosses are head.

We do a 2 sided p-test, so we find the probability of >=940 heads or <= 60 heads, assuming 50% heads. Thse are equal, we get double the prob of >=940 heads,

= 2 * ((1000 choose 940)/2^1000 + (1000 choose 941)/2^1000 + ..... (1000 choose 1000)/2^1000)

= 2 * 2^1000 ((1000 choose 940)+.... (1000 choose 1000))
= 2^-999 * 21085589806256698338895915954866340659073446946309785488248164975385806906208\817116070351056358296
=  1.866527237e-301   *  0.2108558981e98 = 0.3935682768e-203

So do you still think that 940 heads and 60 tails is not statistically significantly different from that of a fair coin?

[J. J.]

I never said that the Kerry/Bush poll was realistic. If you have only Bush and Kerry responses, and you want to see if there's a lead, you compare it to a 50%-50% tie. I think everyone but Erc missed the point.

I'll let Etc speak for himself.

You've missed the point again.  The poll itself is not constructed on the premise that the candidates have a 50%-50% tie.  It's constructed on the premise that the sample is representative of the whole population.

Now here is a question.  For these results, at a 95% confidence level, and a sample size of 1000, what is the likelihood that the leading candidate's result is outside the MOE?

A.  Kerry 94, Bush 6

B.  Kerry 51, Bush 49

C.  Bush 60, Kerry 40

D.  Bush 80, Kerry 20

Assume that undecided/third party voters answers will not be counted in the sample.  This is a poll of people who have made up their minds.

5% by definition if you're asking what I think you're asking, which is for each sample, find the odds that ti's not in the the 95% confidence interval.

You got that right.  Whatever the result, it's 5%.

Now, if we poll 1000 voters, in an electorate of 1000 (assuming no one wants a third candidate and there are no undecides), what is the chance that this poll will be outside of the confidence level?

[○∙◄☻¥tπ[╪AV┼cVê└]

You got that right.  Whatever the result, it's 5%.

Now, if we poll 1000 voters, in an electorate of 1000 (assuming no one wants a third candidate and there are no undecides), what is the chance that this poll will be outside of the confidence level?

In this case in depends on two things.
1. Are these random with replacement as I was stating?
2. Do you take the size of the population into account when calculating the MOE?

No for 1, yes for 2 is probably the most reasonable assumption. In that case the MOE=0. For no for 1, and no for 2, the MOE is calculated purely from the sample results, and MOE > 0.

In either case with no for 1, the answer would be 0% (provided that we define the confidence interval to be an closed interval, so it includes that one point for MOE=0).

[ATFFL]

Terribly sorry, allow me to amend my statement.

This is what jfern tries to change any statically discussion to after it has become blatantly obvious that he is wrong.

My heartfelt apologies.

[○∙◄☻¥tπ[╪AV┼cVê└]

Terribly sorry, allow me to amend my statement.

This is what jfern tries to change any statically discussion to after it has become blatantly obvious that he is wrong.

My heartfelt apologies.

1. We had been arguing about this particular problem for months.
2. What was I wrong on? I haven't seen one person give a good answer here.

[J. J.]

You got that right.  Whatever the result, it's 5%.

Now, if we poll 1000 voters, in an electorate of 1000 (assuming no one wants a third candidate and there are no undecides), what is the chance that this poll will be outside of the confidence level?

In this case in depends on two things.
1. Are these random with replacement as I was stating?
2. Do you take the size of the population into account when calculating the MOE?

No for 1, yes for 2 is probably the most reasonable assumption. In that case the MOE=0. For no for 1, and no for 2, the MOE is calculated purely from the sample results, and MOE > 0.

In either case with no for 1, the answer would be 0% (provided that we define the confidence interval to be an open interval, so it includes that one point for MOE=0).

I have not asked you to calculate MOE (yet, at least).

There is no replacement.  You have polled the entire population.

What is the chance that the poll is one of those 1 in 20 "bad" polls, an outrider?

[○∙◄☻¥tπ[╪AV┼cVê└]

You got that right.  Whatever the result, it's 5%.

Now, if we poll 1000 voters, in an electorate of 1000 (assuming no one wants a third candidate and there are no undecides), what is the chance that this poll will be outside of the confidence level?

In this case in depends on two things.
1. Are these random with replacement as I was stating?
2. Do you take the size of the population into account when calculating the MOE?

No for 1, yes for 2 is probably the most reasonable assumption. In that case the MOE=0. For no for 1, and no for 2, the MOE is calculated purely from the sample results, and MOE > 0.

In either case with no for 1, the answer would be 0% (provided that we define the confidence interval to be an open interval, so it includes that one point for MOE=0).

I have not asked you to calculate MOE (yet, at least).

There is no replacement.  You have polled the entire population.

What is the chance that the poll is one of those 1 in 20 "bad" polls, an outrider?

Do you think I'm retarded? 0% of course.

[J. J.]

Terribly sorry, allow me to amend my statement.

This is what jfern tries to change any statically discussion to after it has become blatantly obvious that he is wrong.

My heartfelt apologies.

1. We had been arguing about this particular problem for months.
2. What was I wrong on? I haven't seen one person give a good answer here.

No, you are comparing apples to oranges, again.  You have  yet to comprehend that.

[○∙◄☻¥tπ[╪AV┼cVê└]

Terribly sorry, allow me to amend my statement.

This is what jfern tries to change any statically discussion to after it has become blatantly obvious that he is wrong.

My heartfelt apologies.

1. We had been arguing about this particular problem for months.
2. What was I wrong on? I haven't seen one person give a good answer here.

No, you are comparing apples to oranges, again.  You have  yet to comprehend that.

Huh? If this is about the Kerry 94% Bush 6% poll, I stated that it was a completely random with replacement sample of a large population, with everyone choosing Bush or Kerry. Yes, I was assuming un-realistic poll, with no undecided voters, people without telephones, people who refuse to answer, people who lie, third party voters, systematic errors, and so on. Yes, 120 million is finite, but it's hardly relevant.

[J. J.]

You got that right.  Whatever the result, it's 5%.

Now, if we poll 1000 voters, in an electorate of 1000 (assuming no one wants a third candidate and there are no undecides), what is the chance that this poll will be outside of the confidence level?

In this case in depends on two things.
1. Are these random with replacement as I was stating?
2. Do you take the size of the population into account when calculating the MOE?

No for 1, yes for 2 is probably the most reasonable assumption. In that case the MOE=0. For no for 1, and no for 2, the MOE is calculated purely from the sample results, and MOE > 0.

In either case with no for 1, the answer would be 0% (provided that we define the confidence interval to be an open interval, so it includes that one point for MOE=0).

I have not asked you to calculate MOE (yet, at least).

There is no replacement.  You have polled the entire population.

What is the chance that the poll is one of those 1 in 20 "bad" polls, an outrider?

Do you think I'm retarded? 0% of course.

No comment on the retarded part.  

Okay, if instead of polling, you "survey" a population by recording the results of 1000 coin tosses.  That is your total population.  What is your chance that this survey is a bad sample of these exact 1000 coin tosses?

[J. J.]

Huh? If this is about the Kerry 94% Bush 6% poll, I stated that it was a completely random with replacement sample of a large population, with everyone choosing Bush or Kerry. Yes, I was assuming un-realistic poll, with no undecided voters, people without telephones, people who refuse to answer, people who lie, third party voters, systematic errors, and so on. Yes, 120 million is finite, but it's hardly relevant.

My last post just explains relevance.

[○∙◄☻¥tπ[╪AV┼cVê└]

You got that right.  Whatever the result, it's 5%.

Now, if we poll 1000 voters, in an electorate of 1000 (assuming no one wants a third candidate and there are no undecides), what is the chance that this poll will be outside of the confidence level?

In this case in depends on two things.
1. Are these random with replacement as I was stating?
2. Do you take the size of the population into account when calculating the MOE?

No for 1, yes for 2 is probably the most reasonable assumption. In that case the MOE=0. For no for 1, and no for 2, the MOE is calculated purely from the sample results, and MOE > 0.

In either case with no for 1, the answer would be 0% (provided that we define the confidence interval to be an open interval, so it includes that one point for MOE=0).

I have not asked you to calculate MOE (yet, at least).

There is no replacement.  You have polled the entire population.

What is the chance that the poll is one of those 1 in 20 "bad" polls, an outrider?

Do you think I'm retarded? 0% of course.

No comment on the retarded part. 

Okay, if instead of polling, you "survey" a population by recording the results of 1000 coin tosses.  That is your total population.  What is your chance that this survey is a bad sample of these exact 1000 coin tosses?

0% to another retarded missing the point question. You're trying to estimate the probability p of heads from flipping the coin, not the probability of p for heads from your 1000 last observed coin tosses.

[○∙◄☻¥tπ[╪AV┼cVê└]

Huh? If this is about the Kerry 94% Bush 6% poll, I stated that it was a completely random with replacement sample of a large population, with everyone choosing Bush or Kerry. Yes, I was assuming un-realistic poll, with no undecided voters, people without telephones, people who refuse to answer, people who lie, third party voters, systematic errors, and so on. Yes, 120 million is finite, but it's hardly relevant.

My last post just explains relevance.

For statistical pourposes, a sample of 1000 without replacement from a population of 120 million is quite similar to a sample of 1000 from an infinite population.

A sample of 1000 with replacement is even closer to that of a sample of 1000 from an infinite population. In fact, it might be exactly the same, I'd have to think about that.

[○∙◄☻¥tπ[╪AV┼cVê└]

How exactly are coin tosses and voting related?

Yeah, I probably shouldn't have tried to compare the two. It's not the actual process that I was comparing, it's the statistical analysis that I was comparing.  One thing that people missed was I assumed the poll was completely random (no polling errors) of just Bush - Kerry voters with replacement. Of course that's unrealistic.

[J. J.]

You got that right.  Whatever the result, it's 5%.

Now, if we poll 1000 voters, in an electorate of 1000 (assuming no one wants a third candidate and there are no undecides), what is the chance that this poll will be outside of the confidence level?

In this case in depends on two things.
1. Are these random with replacement as I was stating?
2. Do you take the size of the population into account when calculating the MOE?

No for 1, yes for 2 is probably the most reasonable assumption. In that case the MOE=0. For no for 1, and no for 2, the MOE is calculated purely from the sample results, and MOE > 0.

In either case with no for 1, the answer would be 0% (provided that we define the confidence interval to be an open interval, so it includes that one point for MOE=0).

I have not asked you to calculate MOE (yet, at least).

There is no replacement.  You have polled the entire population.

What is the chance that the poll is one of those 1 in 20 "bad" polls, an outrider?

Do you think I'm retarded? 0% of course.

No comment on the retarded part. 

Okay, if instead of polling, you "survey" a population by recording the results of 1000 coin tosses.  That is your total population.  What is your chance that this survey is a bad sample of these exact 1000 coin tosses?

0% to another retarded missing the point question. You're trying to estimate the probability p of heads from flipping the coin, not the probability of p for heads from your 1000 last observed coin tosses.

I've bolded a section here.  Probabilities look at the expected next coin toss results.

A poll does not; it makes an assumption about the whole population.  It doesn't estimate the next result.  The probability, regardless of the result, is always the same at a given confidence level.

[??????????]

Bump. The good ole days.