Margin of Error

Dewey Defeats TrumanPolls, polls, polls! Everyone loves polls! Leading up to elections, we get lots of the little suckers. Yet, it seems that most people don’t understand them. Especially the people who report them.

I am here to help, because this just isn’t that complicated.

The issue is the poll’s margin of error. I was just reading an article over at the every good P M Carpenter blog, The NBC/WSJ poll reveals that sometimes a cigar really is a cigar. In it, he states that in a new poll, Obama is beating Romney by 5%, which is larger than the margin of error. (To be fair, Carpenter clearly does understand polls.)

I’m afraid that to most people, the margin of error means too much and too little. The fact that Obama is beating Romney by more than the margin of error does not mean that more people are necessarily planning to vote for him. Just the same, if Obama were beating Romney by less than the margin of error, it would still mean that it was very likely that more people were planning to vote for him.

Most margins of error are reported as 95% confidence intervals. This means that there is a 95% chance that the real number is within the margin of error. It also means that there is a 2.5% chance that the real number is one margin of error lower than this value. And there is a 2.5% chance that it is that much higher.

The NBC/WSJ poll finds that 50% of likely voters support President Obama. There is a 3.3% margin of error. This means there is a 95% chance that Obama’s actual support is between 46.7% and 53.3%. But there is a 2.5% chance that his actual support is less than 46.7% and a 2.5% chance that it is more than 53.3%.

Now let’s suppose that Obama were only ahead of Romney by 1.65% (half the margin of error). This is the one-sigma confidence limit and it indicates 66% certainty rather than 95%. If Romney similarly polled at 48.35% (half the margin of error below Obama), there would be a 66% chance that Obama’s real number was between 48.35% and 51.65%. Plus, there would be a 17% change that Obama’s real number was above 51.65%. And a 17% chance that it was below 48.35%. Thus, there is still an 83% chance that Obama is beating Romney.

The take away here is that being ahead but not by as much as the margin of error is still a very good thing. It doesn’t mean that the two candidates are tied. But just the same, this is statistics and it is possible for any given poll to be way off—even if it is a bigger difference than the margin of error.

Afterword

Polling is very difficult. The math is all fine, but there are all kinds of sampling problems that can make the math irrelevant. The best known example of this is the 1948 Dewey Defeats Truman debacle. The problem was that the polls had been based on telephone surveys when only more affluent (i.e. conservative) people had them. Now, the biggest issue is for polling organizations to figure out what exactly a “likely voter” is. This is why election day polling is so accurate—unless George W. Bush is running.

Is Mitt Romney a Psychopath?

This seems to be floating around the internet:

Does Mitt Romney Care About You?

It is funny, of course, but I think there may be a darker truth underlying it and all the jokes about Mitt “The Robot” Romney and Mitt the Clueless. Could Mitt Romney be a psychopath? It’s entirely possible. We know, for example, that while only 1% of the population are psychopaths, 4% of CEOs are.

When most people think of psychopaths, they think of movie villains: murderers like Hannibal Lecter. But most psychopaths are law abiding citizens. What distinguishes them is that they lack empathy. They have little or no ability to understand others. And what are we to make of statements from Romney like, “Everything that Ann and I have, we earned the old-fashioned way.”

Romney seems to approach life like I approached Dungeons & Dragons[1] when I was a kid. When I played it, I gamed the system, doing the minimum required to advance in the game. Romney does this in real life. Two examples are telling. First, there is his constant claim that he has done exactly what the law requires—no more and no less. He pays, “Only what the tax code requires.” And, “What is required by law—the financial disclosure—has already been made.”

Second, there is the fact that Romney, even though ridiculously wealthy, appears to only give the minimum 10% tithe to his church. This strikes me as particularly telling. If you are going to treat God the way I used to treat dungeon masters, then there is something wrong with you.

What’s important about this is that Romney seems truly confused that voters might expect him to do more than the legal minimum. It shows a lack of understanding of social interactions. Most people refrain from murder and rape because it is wrong—not because it is illegal. Psychopaths don’t do it because it is against the law. “Those are the rules, right? I’m following the rules. What’s the problem?!”

I can’t say with any degree of confidence whether Mitt Romney is a psychopath or not. There are certainly troubling signs based upon his public persona. Regardless, he is a man of limited empathy who really can’t run the country in the interests of the vast majority of its citizens.

Update (Right Away)

Others have thought this same thing. And still others have argued against it. The argument goes that most psychopaths have problems when they are in school. Well, it seems that Romney was at least a bully who enjoyed tormenting weaker children. Another argument is that most psychopaths are impulsive. In Romney’s business deals, there are some signs of impetuousness—or at least carelessness. Regardless, it isn’t right to base this call on what his business did, given there would be calmer people to modulate his impulses. And finally, most psychopaths don’t form strong family bonds. This is true, but a great many psychopaths create the illusion of family bonds.

I’m not saying that any of these attributes apply strongly to Mitt Romney. But he could still be a psychopath. Arguments like this all depend upon the ridiculous (but never stated) assumption that the rich are necessarily morally superior to the poor. No one is shocked when a poor man shoots his wife, but when a rich man does it: shock! Mitt Romney can’t be a psychopath, just look at all his money!


[1] Actually, I played RuneQuest.

Where Do You Put That Hat?

OctagonYesterday, my father came to me with a math question. He had been hired by a Coast Guard Chief Petty Officer who wanted a wooden box for her hat. She wanted it to be an octagon with a height (h) of 8 inches and a diagonal (d) of 12 inches. My father had been trying to make this work for some time, but was stymied.

I don’t do a lot of geometry, but I smelled a rat. An octagon is a very symmetrical form with equal angles and sides. The 8/12 combo just didn’t seem like it would work.

So I went online and did a search for “octagon measurements.” It took me to this excellent site called Had 2 Know, which has an “octagon calculator. You enter any parameter and it tells you all the others. I entered 12 inches for the diagonal and it spit back a height of 11.1 inches. So there was a reason my dad couldn’t make those measurements work: they are inconsistent.

I thought a hexagon might work better. Thankfully, Had 2 Know also has a hexagon calculator. And I was right: a 12 inch diagonal would dictate a 10.4 inches height—better but still a long way off from 8 inches. It seems to me that a pentagon might be the way to go, but because it has an odd number of sides, it doesn’t make sense in this discussion.

It occurs to me that what is really desired is not an octagon, but an eight-sided box. After all, the human head is not round. Go look at a bowler, for instance: it is longer front to back than side to side to side. So one could create an oblong quasi-octagon. But frankly, this is madness. Who wants an eight sided hat box? It will be a storage nightmare. I think what our Guardian really wants is a rectangle.

Eight by twelve. Perfect!

Afterword

Where did you get that hat?!