Margin of Error Error

August 3, 2015
Posted by Jay Livingston

The margin of error is getting more attention than usual in the news. That’s not saying much since it’s usually a tiny footnote, like those rapidly muttered disclaimers in TV ads (“Offer not good mumble mumble more than four hours mumble mumble and Canada.”) Recent headlines proclaim, “Trump leads Bush. . .” A paragraph or two in, the story will report that in the recent poll Trump got 18% and Bush 15%.  That difference is well within the margin of error, but you have to listen closely to hear that. Most people don’t want to know abut uncertainty and ambiguity.

What’s bringing uncertainty out of the closest now is the upcoming Republican presidential debate.  The Fox-CNN-GOP axis has decided to split the field of presidential candidates in two based on their showing in the polls. The top ten will be in the main event. All other candidates – currently Jindal, Santorum, Fiorina, et al. – will be relegated to the children’s table, i.e., a second debate a month later and at the very unprime hour of 5 p.m.

But does Rick Perry’s 4% in the a recent poll (419 likely GOP voters) really in a different class than Bobby Jindal’s 25? The margin of error that CNN announced in that survey was a confidence interval of  +/- 5.  Here’s the box score.

(Click on the image for a larger view.)

Jindal might argue that with a margin of error of 5 points, his 2% might actually be as high as 7%, which would put him in the top tier. 

He might argue that, but he shouldn’t.  Downplaying the margin of error makes a poll result seem more precise than it really is, but using that one-interval-fits-all number of five points understates the precision.  That’s because the margin of error depends on the percent that a candidate gets.  The confidence interval is larger for proportions near 50%, smaller for proportions at the extreme. 

Just in case you haven’t taken the basic statistics course, here is the formula.

The  p̂  (pronounced “pee hat”) is the proportion of the sample who preferred each candidate. For the candidate who polled 50%, the numerator of the fraction under the square root sign will be 0.5 (1-0.5) = .25.  That's much larger than the numerator for the 2% candidate:  0.02 (1-0.02) = .0196.*

Multiplying by the 1.96, the 50% candidate’s margin of error with a sample of 419 is +/- 4.8. That’s the figure that CNN reported. But plug in Jindal’s 2%, and  the result is much less: +/- 1.3.  So there’s a less than one in twenty chance that Jindal’s true proportion of support is more than 3.3%. 

Polls usually report their margin of error based on the 50% maximum. The media reporting the results then use the one-margin-fits-all assumption – even NPR. Here is their story from May 29 with the headline “The Math Problem Behind Ranking The Top 10 GOP Candidates.”

There’s a big problem with winnowing down the field this way: the lowest-rated people included in the debate might not deserve to be there. The latest GOP presidential poll, from Quinnipiac, shows just how messy polling can be in a field this big. We’ve put together a chart showing how the candidates stack up against each other among Republican and Republican-leaning voters — and how much their margins of error overlap.

The NPR writer, Danielle Kurtzleben, does mention that “margins might be a little smaller at the low end of the spectrum,” but she creates a graph that ignores that reality.

The misinterpretation of presidential polls is nothing new.  But this time, that ignorance will determine whether a candidate plays to a larger or smaller TV audience.**

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* There are slightly different formulas for calculating the margin of error for very low percentages.  The Agresti-Coull formula  gives a confidence interval even if there are zero Yes responses. (HT: Andrew Gelman)

** Department of Irony: Some of these GOP politicians might complain about polls determining candidates’ ability to reach the widest audience. But none of them objects to having that ability determined by money from wealthy individuals and corporations.

“Trainwreck” and Taboo

July 30, 2015
Posted by Jay Livingston

I saw “Trainwreck” last night. The 7:00 p.m. showing at the 68th Street AMC was full. Maybe people had come just to get out of the apartment and yet avoid the beastly heat, but they enjoyed the movie.  Sometimes the laughter lasted long enough to cover up the next joke.

The “Trainwreck” story is standard rom-com: Amy Schumer plays a young woman who rejects the idea of commitment and love. Circumstances put her together with a man she seems to have nothing in common with. You can guess the rest. But this is Amy Schumer’s movie, so there’s an important twist – the conventional sex roles are reversed. It’s the man who is sweet and naive and who wants a real relationship; the woman has a lot of sex with a lot of different guys, drinks a lot, smokes weed, and resists love until at the end, she decides to become the woman he wants her to be.

Here is the R-rated version of the trailer.



What interested me was not the movie itself, but the reaction in some conservative quarters. For Armond White at the National Review (here), the movie triggered something like what Jonathan Haidt calls “disgust” – a reaction to the violation of strong taboos that surround things like food, sex, blood and other bodily matters, and death. These taboos are often arbitrary, not rational. Pork is an “abomination” because . . . well, because it is, and because pigs are “unclean.”

“Trainwreck” has no pork, but it does have what some find unclean.

Schumer’s tampon jokes and gay jokes, female versions of locker-room humor, literally drag pop culture to the toilet. A girl-talk scene set in adjoining restroom stalls — one revealing dropped panties, the other panty-less (obviously Amy) — is just Apatow using women to show off his indecency.

Indecency indeed. But something is indecent only to members of groups that deem it indecent. Some groups are not at all disgusted by pork.  And for some audiences, tampon jokes and toilet-stall conversations about Johnny Depp movies are not indecent; they’re just funny. What audiences might those be? Women.

As a comedian and now as a filmmaker, Schumer talks about women-things – body functions and body parts. These jokes seem to elicit two different kinds of laughter.  Back when researchers studying small group interaction were trying to code and categorize behavior, laughter posed a problem. It could be coded as “Shows Tension,” but it might also be “Shows Tension Release.” (See this earlier post on laughter.)  With Amy Schumer jokes, the male laughter is mostly nervous, full of tension about a taboo subject. But the female laughter seems much less inhibited – tension release, maybe even a relief, as if to say, “Someone is finally talking publicly and frankly about things we could only whisper about,” since most of the time they have had to pretend to share the male taboo..

Take the tampon joke that the National Reviewer finds indecent. It would seem obvious that used  tampons look different depending on where you are in your period – less bloody on the final day, more so a few days earlier. But at the mere mention of this fact in “Trainwreck,” hilarity ensues, especially among women in the audience.                        

The thing about taboos – ideas about what is indecent or disgusting – is that entire social structures get built around them. To violate the taboo is to threaten the entire edifice. Powerful taboos on women-things often go with male domination. So for the National Review, the “Trainwreck”reversal of rom-com gender roles makes the movie dangerous and subversive. Here are some excerpts from the review just to give the flavor of this Purity-and-Danger-like conflating of taboo, female sexuality, and social/political threat to the established order.  (I have added the boldface.)

Schumer turns female sexual prerogative into shamelessness the degradation of sex — and women uses sex to promote feminist permissiveness. She enjoys a sexual license Amy brazenly practices the same sexual habits as men Lacking . . . old-fashioned sense of shame, It’s merely brazen, like Lena Dunham’s HBO series, Girls (also about a promiscuous female writer Schumer’s film can be seen to distort human relations into smut. This is not just disrespectful, it confirms Schumer’s project of cultural takeover, she aims to acquire cultural power Schumer disguises a noxious cultural agenda as personal fiat. She’s a comedy demagogue who okays modern misbehavior yet blatantly revels in PC notions about feminism, abortion, and other hot-button topics

Wow.

I should add that not all conservative publications felt so threatened. Joe Morganstern at the Wall Street Journal gave the movie a warm review. Breitbart saw the movie’s essential conservatism (“The anti-slut message is a healthy one,”) and praised Schumer as a comic actor.  Still, the National Review piece seems emblematic of something broader in the cultural conservative camp – a taboo-like reaction to female sexuality.

Mass Shootings – Definitions and Data

July 28, 2015
Posted by Jay Livingston

A few days ago, I wrote to date, since Sandy Hook, the US has had seventy-five “mass shootings.” I now put that phrase in quotation marks because taken literally, it’s misleading.

Here is the opening from a story in the New Orleans Times-Picayune (here) posted Sunday night.

4 shot in assault rifle attack at Desire's Sampson park A man armed with an assault rifle opened fire at a crowded park in Desire Sunday (July 26), shooting at least four people, including a man left critically wounded, New Orleans police said.

 
Is this a mass shooting? Not in most databases.

Literally, a mass shooting should be an incident where someone shoots a lot of people. The graph I used in that previous post included only public shootings. Or more precisely, public killings.  In the Lafayette movie theater, Rusty Houser killed two people and wounded nine. The FBI definition of “mass murder” sets the minimum at four deaths. By that definition, the Lafayette incident is not a mass murder.  If one of those two women had been seriously wounded rather than killed, the incident would not have been included in any database of multiple killings.

Most definitions also exclude gang killings. If gang members shoot and kill four members of another gang, even in a public place, it doesn’t get counted.  And then there are the domestic massacres – a family killed inside their home. These too do not make it into most definitions of “mass shootings.”

Now, broadening the definition, Guns Are Cool has created a Mass Shooting Tracker – a list of incidents gathered mostly from local news reports.  It includes all incidents where four or more people were shot, whether or not they died and regardless of setting.  As of yesterday, July 26th, the Tracker lists 207 shootings this year. July 26th also happens to be the 207th day of the year. You do the math.

In the assault rifle shooting above, nobody died. That’s not unusual. In 40% of the shootings, there are no deaths. In another 32%, only one person dies.  Multiple deaths are relatively rarer.

But guns are dangerous. Even when the victims are not in close range, and even when the gunman is not especially accurate, a gun can still do a lot of damage. The wounded in these shootings far outnumber the dead nearly three to one.

The Tracker’s criterion for a mass shooting is a minimum of four victims – killed or wounded. It looks like the typical incident in their database involves no deaths and enough wounded to meet that minimum.

Since the database uses news reports, when a victim is seriously wounded and dies days later, the Tracker probably does not include that in the deaths tally. For the same reason, in a large majority of cases (83%), the shooter is listed as “Unknown.” If the shooter is later identified, the Tracker database might still not pick up that story.

So the tally for this year: 207 mass shootings, 172 dead, 761 wounded.  Of course, those numbers will be dwarfed by their counterparts in non-mass shootings. Still, it illustrates one of the essential truths about guns: you can kill and wound a lot of people with them. Yes, if you have only a knife, you  can still slash several people, some maybe even fatally. But you have to get so close – literally within arm’s reach – and if they run away, you’re pretty much out of luck. Guns are so much more effective when it comes to killing and wounding. That’s why people buy them.

Bet on Obamacare, Cash in Big

July 26, 2015
Posted by Jay Livingston

The standard conservative line on Obamacare was that it would be a disaster.  They still insist that it’s a disaster, despite much evidence to the contrary. I wonder if they put their money where their scowling mouths were.

As Alex Tabarrok says, a bet is a tax on bullshit. Did they bet against healthcare and insurance companies? Probably not. But if they had, their frowns would not be turning to smiles. Just the opposite.

A hedge fund, Glenview Capital Management, did bet, but they bet on Obamacare, not against it. In case you missed the Wall Street Journal’s story on this, here’s the opening:

Glenview Capital Management LLC made a bold decision when President Barack Obama’s health-care overhaul was rolling out: Bet on it. The result has been one of the most successful hedge-fund wagers in recent years. New York-based Glenview has realized and paper gains of more than $3.2 billion since it started making investments in hospitals and insurers four years ago, according to a Wall Street Journal analysis of securities filings.

The idea was pretty simple. Obamacare was going to bring millions of new clients to the healthcare markets. Insurers would have more customers. Hospitals would have more patients whose bills would be paid. Less easy to foresee were the mergers (Athem and Cigna, Aetna and Humana) that added even more to the value of the investments.  The bottom line: “Glenview’s flagship fund has averaged a 26% annual return since the beginning of 2012 . . . much better than the industry’s 6% average.”

The irony is that the health of the healthcare industry under Obamacare puts conservatives at the WSJ and elsewhere in the unusual position of arguing that mergers and corporate profits are a sign of something bad.