While about equal percentages of the general public will be either happy or upset with the outcome of the presidentialÂ and congressional elections, 100% of statisticians will be cheering Nate Silver.

The reason I’ve watched Silver’s blog very closely is because I’m a big believer in the Central Limit Theorem, which states that the mean of an infinite number of reasonably large random samples will be the population mean. Although there were not an infinite number of polls taken before the election – it only seemed that way – there was definitely a large number.

In states where 50 or more polls were taken and ALL or all but one or two showed a small advantage in favor of President Obama, the probability that the true population mean was in favor of Mitt Romney was very, very, very low.

Then, if you take several states where that was the case, the probability that several of them actually had a population mean in favor of Romney would be even lower. It would not be the product of the individual probabilities because it is very unlikely that those probabilities are independent. If the polls in one state were all wrong, it would be due to bias in their sampling and that same bias would exist in other state samples as well.

What impressed me about Silver was not his math, not his models. I made the same predictions in my statistics class weeks ago. In fact, I just received this email from a student,

“Dr. De Mars,

If Obama wins can you please “statistically” explain to me why you projected that last month? “

No, what impressed me about Silver was his courage. Every statistician who looked at his results nodded in agreement. Some even tweeted when Silver was disparaged,

“I guess the Republicans have secretly disproved the Central Limit Theorem.”

It’s one thing to make predictions in your class, or make snarky comments on twitter. It’s another to make them in the New York Times and on national television. Although the probability may have been 92% of an Obama victory, there was still an 8% chance he would be wrong and been publicly humiliated on every conservative network and blog, and on all of the moderate and liberal ones that didn’t understand math.

Most people wouldn’t take an 8% chance of that – which is why Nate Silver is my hero. By taking a chance, going out on a limb, he brought mathematics, statistics and science in general to a much higher profile and level of confidence. Now maybe people will believe scientists about that global warming stuff, too.

This cognac is to you, Nate. You’re my hero.

You mean the law of large numbers. CLT refers to the asymptotic normality of the mean.

Agree with every word!

I’m an undergraduate in applied mathematics and Nate Silver is my hero too! ðŸ˜›

Incorrect,

Then these guys are wrong also.

“Definition of ‘Central Limit Theorem – CLT’

A statistical theory that states that given a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from the same population will be approximately equal to the mean of the population. Furthermore, all of the samples will follow an approximate normal distribution pattern, with all variances being approximately equal to the variance of the population divided by each sample’s size.

Read more: http://www.investopedia.com/terms/c/central_limit_theorem.asp#ixzz2BZ8uPGt1

Also see this from the Department of Mathematics, Cal State Univ SB

http://www.math.csusb.edu/faculty/stanton/probstat/clt.html

@Incorrect LoLN is for individual sample results, and you can’t predict a chance with that. With the polls, you don’t have access to those a lot of the time. You just have the means of separate polls. You can use that to make a prediction of the mean of the population, though. That’s how he concluded that Mitt had 8% chance of winning.

CLT is correct. The above comment is correct in its description of LoLN. See:

http://en.wikipedia.org/wiki/Central_limit_theorem#Relation_to_the_law_of_large_numbers

Technically, would he have been “wrong” if Romney won? He didn’t say it was a sure thing. He did give him an 8% chance. That being said no one outside the nerds like us would really understand that and you’re right that he would have been ridiculed by the masses.

Dave, that’s exactly what I thought.

Epicene, 10 points for making me laugh out loud today.

@Dave No, he wouldn’t have been wrong at all. That is why the weather man always says there is a 10% chance of rain. If it rains, he was still right!

Yes, Andrew, you know that, I know that and Dave knows that but he would have been pilloried in the press nonetheless.