Others think that because they do argue, they are right. — Banno

Sure, and I certainly think that those who go in the ring and fight have a lot more right to claim victory compared to those who sit on the sidelines.

is a non sequitur, since it does not follow from the support of the mob that one has divine right. — Banno

It does not follow in what way? It does not follow logically, that's true. But I made an inductive statement there. I said that having the support of the people is evidence that the person in question has divine right. It's not sufficient for that to be the case, but it is evidence. I mean, could someone have divine right to rule and have no one's support? Then in what sense would he even have right to rule? :s

Then you shifted your ground from evidence to necessity. — Banno

I haven't. I merely pointed out, that if you are going to say it's a non-sequitur - that one doesn't follow from the other - you're probably assuming a logical necessity between the two. Of course there is no logical necessity there. But that doesn't mean it's not evidence. First of all, historically it is evidence. And secondly, we wouldn't expect someone who has divine right to rule not to have the support of the people (in most instances at least).

Perhaps this goes to explaining your infatuation; you want to be like him.

That probably should incite pathos, but instead i find myself disgusted. — Banno

Actually I merely pointed to Trump to illustrate that you have this attitude to everyone who disagrees with you on politics. It's not a very productive attitude, since you can't even have a conversation with people who disagree with you that way.

Thanks for adding so much to the post count, though.

Population size doesn't really matter, except when the sample size is greater than 5% of the population (so in this case). See here. — Michael

Does this assume a particular mathematical model? What if those assumptions are wrong? There's a very important effect that comes with size, especially in a country like the US. Maybe the probability is indeed 2.53% or whatever if you're dealing with physical atoms, obeying physical laws, not with people. The fact that you - and your statistics - would claim that the probability of error is the same in both cases is a fault with the methodological/statistical method applied. Unquestionably so.

Does this assume a particular mathematical model? What if those assumptions are wrong? There's a very important effect that comes with size, especially in a country like the US. Maybe the probability is indeed 2.53% or whatever if you're dealing with physical atoms, obeying physical laws, not with people. The fact that you - and your statistics - would claim that the probability of error is the same in both cases is a fault with the methodology. Unquestionably so. — Agustino

It's explicitly about polling people.

It is possible that pollsters sample 1,013 voters who happen to vote for Bush when in fact the population is evenly split between Bush and Kerry, but this is extremely unlikely (p = 2−1013 ≈ 1.1 × 10−305) given that the sample is random.

This is an assumption. Read about what being random means mathematically.

However, the margin of error only accounts for random sampling error, so it is blind to systematic errors that may be introduced by non-response or by interactions between the survey and subjects' memory, motivation, communication and knowledge

Look at these. Why do they assume probabilities are normally distributed? :s

I'm aware of that. That's why I did say of a representative sample. Obviously if you just poll 1,500 from a group of 10,000 rich white Christian Republican men then your results aren't going to be representative of the US as a whole (although they will be representative of those rich white Christian Republican men).

I brought this up specifically to address @Buxtebuddha's claim that "1,500 people is a minuscule tally". 1,500 is a good sample size, if done correctly. So if there are problems with the poll then it isn't due to how many people responded.

I brought this up specifically to address Buxtebuddha's claim that "1,500 people is a minuscule tally". — Michael

But Buxtebuddha is absolutely right. It is.

He isn't. It gives a 2.53% margin of error with a CI of 95%. That's pretty good.

In fact, due to the nature of diminishing returns, increasing the sample size any further doesn't make much of a difference. See more here:

Looking at these different results, you can see that larger sample sizes decrease the margin of error, but after a certain point, you have a diminished return. Each time you survey one more person, the cost of your survey increases, and going from a sample size of, say, 1,500 to a sample size of 2,000 decreases your margin of error by only 0.34% (one third of one percent!) — from 0.0253 to 0.0219. The extra cost and trouble to get that small decrease in the margin of error may not be worthwhile. Bigger isn’t always that much better!

He isn't. It gives a 2.53% margin of error with a CI of 95%. That's pretty good. — Michael

Yes provided the assumptions are good. They're not.

Which assumptions are wrong? That it wasn't a representative sample? On what grounds do you justify such an assertion?

Which assumptions are wrong? — Michael

To name a few.

That the probability distribution is normal.
That the sample is random.
That the sample is representative.
That there are no systematic errors.
That people answer honestly.
That people would actually behave as they say they'd behave if they actually had to vote.

On what grounds do you justify such an assertion? — Michael

On the grounds that the US is very diverse geographically speaking, and it's impossible to quantify this diversity in 1500 people. 50 states. That's 30 people per state assuming they were polled equally, which again wouldn't be representative since some states have more people. Those 30 have to be further divided into categories, blacks, whites, religious, non-religious, etc. When we get down to it, some categories will have very few people. We're going to say how blacks in Arizona vote based on two "randomly" polled black people. Give me a break... That's not representative.

Again, you're fooled by numbers.

On the grounds that the US is very diverse geographically speaking, and it's impossible to quantify this diversity in 1500 people. 50 states. That's 30 people per state assuming they were polled equally, which again wouldn't be representative since some states have more people. Those 30 have to be further divided into categories, blacks, whites, religious, non-religious, etc. When we get down to it, some categories will have very few people. We're going to say how blacks in Arizona vote based on two "randomly" polled black people. Give me a break... That's not representative. — Agustino

The whole point of a random sample is that it tends to represent diversity. You clearly don't understand statistics.

The whole point of a random sample is that it represents diversity. You clearly don't understand statistics. — Michael

Sure. And I'm telling you that you cannot capture the actual diversity in just 1500 people and I've even explained you why.

We're going to say how blacks in Arizona vote based on two "randomly" polled black people. Give me a break... That's not representative. — Agustino

No, because a sample size of 2 is terrible. A sample size of 1,500 people chosen at random from all black people in Arizona would be representative of how blacks in Arizona vote.

Sure. And I'm telling you that you cannot capture the actual diversity in just 1500 people and I've even explained you why. — Agustino

I linked you to an article on the subject. That's the explanation.

No, because a sample size of 2 is terrible. A sample size of 1,500 people chosen at random from all black people in Arizona would be representative of how blacks in Arizona vote. — Michael

Oh yeah!! if we were talking just 1500 random black people from Arizona, sure! They'd be representative - of black people from Arizona.

Oh yeah!! if we were talking just 1500 random black people from Arizona, sure! They'd be representative - of black people from Arizona. — Agustino

Yes, and if we take 1,500 random Americans then that would be representative of Americans.

I linked you to an article on the subject. That's the explanation. — Michael

:s nope, that's no explanation at all. That's just parroting the theory to me, not showing that you've actually thought about it. You'll start thinking about it when you start thinking about all the things that can go wrong, and realise how uncertain it really is.

Yes, and if we take 1,500 random Americans then that would be representative of Americans. — Michael

Wrong. There's a lot of diversity in Americans. There's black non-religious Americans, black religious Americans, black homosexuals, black lesbians, etc. you're telling me you'll capture each of those groups accurately within 1,500 people total? :s

I don't need to think about it. The expert statisticians are the ones who actually have the training and knowledge to determine these things. I'm showing you their results.

Wrong. There's a lot of diversity in Americans. There's black non-religious Americans, black religious Americans, black homosexuals, black lesbians, etc. you're telling me you'll capture each of those groups accurately within 1,500 people total? — Agustino

Yes. If 10% of the population are black and 5% lesbian and 50% religious then a random sample size of 1,500 is likely to also have 10% black, 5% lesbian, and 50% religious, etc. Hence why a random sample size of 1,500 is representative.

Of course, as the article I linked to said, "it is possible that pollsters sample 1,013 voters who happen to vote for Bush when in fact the population is evenly split between Bush and Kerry", but "this is extremely unlikely (p = 2⁻¹⁰¹³ ≈ 1.1 × 10⁻³⁰⁵) given that the sample is random".

The expert statisticians are the one's who actually have the training and knowledge to determine these things. I'm showing you their results. — Michael

Yes, that's why unfortunately I think you'd make a not so good decision maker because you trust the "experts" quite blindly. I'm an engineer by profession. I've been trained not to trust any expert whatsoever unless I verify for myself and think through their assumptions.

Yes. If 10% of the population are black and 5% lesbian and 50% religious then a random sample size of 1,500 is likely to also have 10% black, 5% lesbian, and 50% religious, etc. Hence why a random sample size of 1,500 is representative. — Michael

And that presumes that the 10% black out of the 1500 - meaning 150 people - are representative of the black population in the whole country. That's false. Blacks in Minnesota will probably be different than blacks in DC. And you're not adequately going to quantify that.

And that presumes that the 10% black out of the 1500 - meaning 150 people - are representative of the black population in the whole country. That's false. Blacks in Minnesota will probably be different than blacks in DC. And you're not adequately going to quantify that. — Agustino

And if 5% of blacks are in Minnesota and 5% are in DC then due to the random sampling it is likely that 5% of the blacks in the sample are from Minnesota and 5% are from DC.

The statistics is pretty clear. You arguing against the experts without having their expertise is like me arguing with you over how best to build a bridge.

Of course, as the article I linked to said, "it is possible that pollsters sample 1,013 voters who happen to vote for Bush when in fact the population is evenly split between Bush and Kerry", but "this is extremely unlikely (p = 2−1013 ≈ 1.1 × 10−305) given that the sample is random". — Michael

No, it's not that unlikely, because that assumes the whites (to pick an example), etc. are randomly distributed through the cities, geographical regions of US, and so forth.

And if 5% of blacks are in Minnesota and 5% are in DC then due to the random sampling it is likely that 5% of the blacks in the sample are from Minnesota and 5% are from DC. — Michael

Right, so about 8 black people will be taken as representative for all blacks in Minnesota, and all blacks in DC :s

Yes, that's why unfortunately I think you'd make a not so good decision maker because you trust the "experts" quite blindly. — Agustino

What is it with Republicans and experts?

Next you're going to be a climate change denier.

What is it with Republicans and experts?

Next you're going to be a climate change denier. — Michael

Everyone should be skeptical of experts, not just Republicans. To me, it's more amazing how easily people bow their heads to experts once the experts perform some mathematical magic tricks that they don't understand ;) Much like witch doctors did 2000 years ago.

Everyone should be skeptical of experts, not just Republicans. To me, it's more amazing how easily people bow their heads to experts once the experts perform some mathematical magic tricks that they don't understand ;) Much like witch doctors did 2000 years ago. — Agustino

There's a difference between being skeptical and refusing to believe that they're right (claiming them wrong) because their conclusions are contrary to your non-expert expectations. Go study statistics and then get back to me.

>:O >:O >:O